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The epidemiological significance of islands
Health & Place, Vol. 1, No. 4, pp. lW209, 1995 Copyright @ 1995 Elsevier Science Ltd
Pergamon
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13534?292(95)00029-1
The epidemiological significance of islands Andrew D. Cliff Department of Geography,
University of Cambridge, Downing Place, Cambridge CB2 3EN, UK
Peter Haggett Department of Geography,
University of Bristol, Bristol BS8 ISS, UK
Islands
have proved fruitful laboratories for biogeographical research from Darwin and Wallace onwards. We examine here the significance of Black’s work (Journal of Theoretical Biohgy, 11, pp. 207-211(1966)) on island epidemics. His original data on measles outbreaks on 19 islands over the 15 year period from 1949 to 1964 are reanalysed, and the confounding effects of island accessibility and population density upon estimates of the population threshold for measles endemicity are illustrated. Using later data, we extend Black’s analysis into the post-l%5 measles vaccination era both for the islands he studied and for 22 others, and then explore the potential of intra-island comparisons. Although Black confined himself to measles, this paper suggests that his ideas are extendable to a wide range of other infectious dies. Island epidemiology has implications both for practical questions of disease control and for academic questions of the persistence and origin of diseases. Keywords:
Iceland,
islands, measles, threshold
Introduction Islands have long had a fascination for biologists. When he left the Galapagos in October 1835, Charles Darwin pondered on the birds he had collected from the different islands. He was struck by the differences in mockingbird skins which he had obtained within the Galapagos group: each a distinct variant in colour and arrangement yet developing in similar ecological niches on small islands within sight of each other. The observation was to lead to later conjectures on the speed at which evolutionary differences in organisms might emerge and he wrote in his notebook that ‘. . . if there is the slightest foundation for these remarks, the Zoology of Archipelagos will be well worth examination’ (Darwin, 1963 [1835]; cited in MacArthur and Wilson, 1967, p. 3). A similar view was taken by Alfred Russel Wallace in his Island Life when he concluded that ‘Islands possess many advantages for the study of the laws and phenomena of distribution’ (Wallace, 1880, p. 733). In this paper, we explore Darwin’s theme in the context of disease-causing organisms. We follow
Black (1966) in showing how the epidemic behaviour of infectious diseases varies in relation to the different geographies of islands. Black’s original data on measles outbreaks on 19 islands over the 15 year period from 1949 to 1964 are reanalysed, and the confounding effects of island accessibility and population density upon estimates of the population threshold for measles endemicity are illustrated. Using our own data, we extend Black’s analysis into the post-1965 measles vaccination era both for the islands he studied and for 22 others, and then explore the potential of intra-island comparisons. Although Black confined himself to measles, we suggest that his ideas can be extended to a wide range of other infectious diseases. Further, we argue that island epidemiology has implications both for practical questions of disease control and for academic questions about the origin and persistence of infectious diseases. Island biogeography Although islands appear to be simple and selfdefining entities, their operational definition for 199
Epidemiological
significance of islandr: A, D. Cliff and P. Haggett
Table 1. Island area and number of species relationships Relationship
Island group
Gulf of Guinea islands West Indies Galapagos East-central Pacific West Indies Melanesia East Indies Lake Michigan islands West Indies
(z)
Biological group
0.489 0.340 0.325 0.303 0.301 0.300 0.280
Fauna (birds) Fauna (beetles) Flora (land plants) Fauna (birds) Fauna (amphibians) Fauna (ants) Fauna (birds)
0.239 0.237
Fauna (vertebrates) Fauna (birds)
Source: modified from MacArthur and Wilson (1967, table 2, P. 9).
research purposes turns out to be surprisingly elusive. Nunn, in his Oceanic Zslunds (1994, pp. l-12) discusses the problem at length. For example, since islands form a classic example of one of Mandelbrot’s fractal series (Mandelbrot, 1975), questions of their number will always remain unanswerable. Because we are concerned here with specific epidemiological questions, we confine ourselves to those islands which are (i) permanently inhabited by a human population, (ii) are sub-continental in size and (iii) for which good disease records exist. Around the world, fewer than 100 islands or island groups meet these criteria. Area-species
relationships
The relations between the size of islands and the biological diversity of their flora and fauna was first analysed in mathematical terms by Darlington (1943) in a study of carabid beetles on the islands of the West Indies. He observed that there appeared to exist an orderly relation between the size of a sample area and the number of species found in that area. Darlington expressed the relationship as follows for the herpetofauna (amphibians plus reptiles) of the West Indies: ‘division of island area by ten [in going from one island to the next] divides the fauna by two’ (Darlington, 1957; cited in MacArthur and Wilson, 1967, p. 8). Two observations on Darlington’s findings are relevant here. First, island area seldom exerts a direct influence upon the presence or absence of a species, but is simply a useful proxy for the ecological and habitat diversity found there. Second, the relationship to area is more usually expressed via the power equation, S = CA’ , where S is the number of species of a particular taxon found on a given island, and A is the island’s area. The parameter, c, depends upon both the taxon and the geographical area being investigated, while z describes the decay rate of species with decreasing island area. Actual values 200
of z for a series of sample biological studies of island fauna and flora appear in Table I, and range from 0.237 to 0.489. A z value of 0.301 characterizes the fall-off rate described by Darlington’s rule of thumb, above. Population-disease
relationships
One question which arises from biogeographical work on islands is whether a similar relationship between area and diversity exists for (i) microorganisms in general and (ii) disease-bearing microorganisms in particular. In broad terms, do small islands have a narrower range of diseases than large ones? If so, is there a consistent relationship along the lines of that discovered by Darlington and others for island flora and fauna? We can run a rough test of these ideas using data given in a recent survey by Wilson (1994) of the distribution of world diseases. Wilson’s book describes the spatial range of 251 major diseases of humans across 16 world regions. Of the diseases considered, 74 are worldwide in the sense of being reported in a recent year from every country studied: measles was a good example in the pre-vaccination period. A further 44 diseases are less widely distributed but, nevertheless, occurred in all 16 world regions. The remaining 118 diseases are spatially specific in the sense that they were reported from some regions but not from others. The various geographical distributions are summarized in Table 2. As shown in the table, the average taken over all 16 regions is 51 diseases. But the value for the three insular regions (31 diseases) is well below that for continental regions (56 diseases). The contrast is underlined by two adjacent regions in the same latitude band in Middle America: despite their geographical propinquity, the disease count for the island-studded Caribbean region (48) is well below that of the peninsular Central American region (68). The Wilson data (given on pp. 281-415) can be analysed at a sharper spatial scale by plotting the number of supplemental references to selected diseases on a country-by-country basis. This is undertaken in Figure I where the number of such disease references (vertical axis) is graphed against the population of each country (horizontal axis). To make the results comparable with those of Darlington, each of the 61 points on the graph is confined to a country which is either an island or island group. These range in size from the very small (e.g. Tokelau with 1700 people in 1988) to the very large (e.g. Australia with 16.47 million in 1988). The relationship between the two variables is statistically significant at the 95% level with an R2 of 0.57, implying that large islands have more diseases that demand reference in a standard text than do small ones.
Epidemiological
significance of islands: A. D.
Cliffand P. Haggett
Table 2. Distribution of 118 infectious diseases in 16 world regions Northern mid-latitude
regions
East Asia 67 N. Europe” 56 N. America 56 N. Africa 48 S. Europe 35
N. Mid-latitude average 52
regions
Continental/insular
regions
Tropical regions
Southern mid-latitude
Central America 68 Mid-S. Asia 66 E. South Asia 66 Sub-Saharan Africa 65 Tropical S. America 64 W. South Asia 56
Temp S. America 43 S. Africa 33
Continental average 56
Caribbean 48
Australia/New Zealand 19 Pacific 25
Insular average 31
Tropical average 62
S. Mid-latitude average 30
Grand average 51
“Including the former USSR. Source: data from Wilson (1994, pp. 182-203).
A second example of the regional concentration of different diseases can be seen from an examination of data in Benenson (1990, pp. 2329). This lists 103 arthropod-borne virus diseases: of these, 83 are confined to the tropics, 13 to Europe and 5 to Australia. Kuru, a disease of the central nervous system and found only among the Fore peoples in central New Guinea, is the outstanding example of a spatially confined disease (Alpers and Gajdusek, 1965); the various haemorrhagic fevers are others. We can conclude, therefore, that the findings of island biogeographers on macrofauna-area relationships are consistent with the microfaunapopulation relationships shown in disease data. It is to the epidemiological implications of this consistency that we now turn.
towns and the virus disease of measles, Bartlett plotted the mean period between epidemics, in weeks, against the population size of these towns. Bartlett discovered that, in large towns, measles was endemic with periodic eruptions (Bartlett’s so-called Type I waves). In cities below a certain population size threshold, measles displayed an epidemic pattern with complete disappearance of the disease (fade-out) between epidemics. A distinction was drawn between urban areas above about 10,000 people with a regular pattern of epidemics (Type II waves) and those where occasional epidemics were missed, giving a more irregular pattern (Type III waves). Given the rates of reporting at the time of Bartlett’s original study, the endemic/epidemic threshold for measles lay at a population size of around 250,000, a figure which has been confirmed on many occasions since; see Cliff et al. (1981) and Cliff and Haggett (1990) for recent reviews. As we shall see later in this paper, the existence of an endemicity threshold for a transmissible virus disease has profound implications for its persistence and control. Once the at-risk popula-
Epidemic disease thresholds
Before we can look at island epidemiology directly, we need to consider first the fundamental work carried out by the Oxford biomathematician, M. S. Bartlett (1957) in a different geographical context. Using a sample of 19 English
. 30
Diseases = 0.34 + 4.39 log population R 2 = 0.57
.
25
10
100
1000
Island population, 1988 (log scale) Figure
1. References to diseases in humans for island countries plotted against their 1988 populations. are based on Wilson (1994, pp. 281415).
The data
201
Epidemiological
significance of islands: A. D. Cliff and P. Haggett
COMMUNITY
COMMUNITY
A
Population large enough 17>250 to sustain virus and continuous record of infection. Type I epidemic waves
000)
B
Population too small to sustain virus, but regular Type II epidemic waves
COMMUNITY
C
Very small population. Irregular Type ill epidemic waves
Figure 2. The structure of the Bartlett model. Large communities (A) with endemic disease serve as reservoirs from which agent spread reinfects smaller communities (B and C) that experience epidemic disease with intervening fade-out rather than endemic disease. Source: Cliff and Haggett (1988, figure 4, p. 322).
tion is reduced below the endemicity threshold by whatever means (vaccination, for example), the disease should become naturally selfextinguishing because the chains of transmission whereby the virus is passed repeatedly from infective to susceptible will be broken. Second, once an area becomes disease-free, an epidemic can recur only if the virus is reintroduced from a geographical reservoir of infection elsewhere. Thus the generalized persistence of such virus diseases implies spatial transmission between geographical units as shown in Figure 2. Continuing with measles as our example, in large cities above the size threshold, like community A in Figure 2, a continuous trickle of cases is reported. These provide the reservoir of infection which sparks a major epidemic when the susceptible population, S, builds up to a critical level. Since clinical measles confers subsequent lifelong immunity to the disease, this build-up occurs only as children are born, lose their mother-conferred immunity and escape vaccination or the disease. Eventually the S population will increase sufficiently for an epidemic to occur. When this happens, the S population is diminished and the stock of infectives, I, increases as individuals are transferred by infection from the S to the I population. This generates the characteristic ‘D’-shaped relationship over time between
sizes of the S and I populations shown on the end plane of the block diagram. When the total population of a community falls below the population size threshold, as in settlement types B and C of Figure 2, measles epidemics recur only when the virus is reintroduced by the influx of infected individuals from 202
reservoir areas (community A in Figure 2). These movements
are shown
by the broad
arrows.
In
such smaller communities, the S population is insufficient to maintain a continuous record of infection. The disease dies out and the S population grows in the absence of infection. Eventually the S population will become large enough to sustain an epidemic when an index case arrives. Given that the total population of the community is insufficient to renew by births the S population as rapidly as it is diminished by infection, the epidemic will eventually die out. It is the repetition of this basic process which generates the successive epidemic waves witnessed in most communities. Of special significance is the way in which the continuous infection and characteristically regular Type I epidemic waves of endemic communities break down, as population size diminishes, into, first, discrete but regular Type II waves in community B and then, secondly, into discrete and irregularly spaced Type III waves in community C. Thus diseasefree windows will appear automatically in both time and space whenever population totals are small and geographical densities are low. Nine years after Bartlett’s original paper, his ideas were taken up in an island context by the Yale epidemiologist, Francis Black (Black, 1966). In the remainder of this paper, we look at Black’s original data, subject them to further statistical analysis, and then extend Black’s approach both to more recent data for his set of islands and to a further 22 islands not considered in Black’s work. The analysis is conducted at a macro-geographic level; by ‘macro’, we mean comparative study of many islands on a worldwide scale.
Epidemiological
significance of islands: A. D. Cliff and P. Haggett
Table 3. Black’s data for estimating measles endemicity in 19 island populations using monthly data for the period January 1949-
December
1964
Region
Island
Population (1956)
Atlantic
Iceland Greenland Bermuda Faroes St Helena Falkland
160,000 28,000 41,000 34,000 5000 2500
Pacific
Hawaii Fiji Samoa Solomons French Polynesia New Caledonia Guam Tonga New Hebrides Gilbert & Ellice Cooks Niue Nauru
550,000 345,000 118,cQO 110,000 75,000 68,000 63,000 57,000 52,000 40,000 16,000 4700 3500
Measles reporting ratiob
Measles cases reported (% months)
Annual susceptibles input’
4490 1190 1130 744 116 43
45 111 10 24 54
61 24 51 32 4 0
167,000 13,400 4440 4060 2690 2600 2200 2040 1910 1260 678 225 I67
24 8 9 6 27 9 11 28 9 56 51 21 30
100 64 28 32 8 32 80 12 30 15 6 5 5
“1956 births less infant mortality. bTotal number of reported measles cases divided by total input of susceptible children during the period of study. Source: Black (1966, table 1, p. 208).
Island macro-geography In his paper in the Journal of Theoretical Biology, Black set out to ‘confirm and refine Bartlett’s estimates by considering communities where reintroduction [of measles] is minimal and where the effect of population dispersion could be observed’ (Black, 1966, p. 207). To do this, Black analysed data on measles incidence for 19 islands or island groups (Table 3). These were located mostly in the Pacific Ocean (Cook, Fiji, French Polynesia, Gilbert & Ellice, Guam, Hawaii, New Caledonia, New Hebrides, Nauru, Niue, Samoa, Solomons and Tonga); the remainder (6) had Atlantic locations (Bermuda, Falklands, Faroes, Greenland, Iceland and St Helena). The islands ranged in population size over two orders of magnitudefrom Hawaii, with a 1956 population of 550,000, down to the Falklands with only 2500 inhabitants. The average population of the islands Black studied was 93,000. The monthly measles data used spanned a 15 year period from January 1949 to December 1964 (180 months in all). Incidence data were obtained for most islands for most months from World Health Organization reports, supplemented by figures obtained by Black from local health officers. All the islands studied had suffered at least four measles outbreaks during the 15 year period with the exception of the Falklands: this was measles free for the whole period. Black estimated reporting completeness
(measles reporting ratio in Table 3) for each of his islands by dividing the observed pattern of recording (defined as the total number of measles cases reported in the 15 years) by an expected pattern (for the highly infectious disease, measles, at a time prior to the availability of vaccination, defined as the total number of children reaching their first birthday during the 15 year study period). The mean value for case reporting over all Black’s islands was 29.6%. Five islands had reporting rates of over 40%: Cook, Gilbert & Ellice, Greenland, Iceland and St Helena. At the other end of the scale, five islands (Fiji, New Caledonia, New Hebrides, Samoa and Solomons) had low measles reporting rates of between 6 and 10%. Island groups with less than 6% reporting rates had been excluded by Black from the analysis at an earlier stage. Reanalysis of the Black data
Black (1966, p. 208) describes a ‘crude correlation’ between island populations and the endemicity of measles, but he left his data in a tabular form (Table 3). If we plot Black’s data (Figure 3), the positive association between island size and percentage endemicity becomes clear. This diagram shows the data in three different forms, with the graph axes in linear, log-linear and log-log forms. Throughout this paper, we define percentage endemicity as the percentage of the total months in the time series of an island in which measles cases were reported. 203
Epidemiological significance of islands: A. D. Cliff and P. Haggett
A Linear - linear
c.o E
8 5
1 Cookl.
2 Faroe 1.
60
3 4 5 6 7
63.1 l @Tonga 7
0
lFrench
endemicity = 16.1 + 0.0002 population R’= 0.59
Polynesia
0
Nauru New Caledonia New Hebrides Niue St Helena
200
I 600
400
B Log - linear loo-
Hawaii l . Guam
80c .o E B f z g & CL
endemicity = -121.0 R’= 0.58
+ 33.2 log population
60. Bermuda New
40-
20Nauru.
0
Niue
/Ibert
l St ~~~~~~
& E”ice ’ .Cook I.
10
1
c
l T;;;nch
100
Po,ynesia 1000
Log-log
100
log endemicity = -1.54 + 0.616 log population R*= 0.68 10
100
t
1000
Population, 1956 (in thousands)
Figure 3. Relation between measles endemicity and population size for Black’s (1966) data for 18 islands, 1949-1964. (A) Linear axes. (B) Log-linear axes. (C) Log-log axes. Data are given in Table 3 of this paper. Endemicity is measured as the percentage of months with measles cases reported.
Because both variables range over several orders of magnitude, the most effective representation is given by the log-log form with the regression equation log (percentage
endemicity)
+ b, log (1956 population), 204
= b. (1)
where 6s = -1.54 and bI = 0.616; R* = 0.68. Using equation (1) and the parameter values given, we can estimate the population at which measles cases would be reported in every month of a time series (100% occurrence)-the so-called endemicity threshold-as 558,000. Since Hawaii is at this 100% threshold, and might be argued to
Epidemiological Table 4. Accessibility
and dispersion applied to Black’s (1966) data
as
dummy variables
significance of islands: A. D. Cliff and P. Haggett
Table 5. The impact of accessibility and dispersion on Black’s (1966) population threshold estimates, in thousands”
Region
Island
Accessibility”
Dispersionb
Dummy variable
Accessibility
Dispersion
Atlantic
Iceland Greenland Bermuda Faroes St Helena
Accessible Remote Accessible Accessible Remote
Sparse Sparse Concentrated Sparse Concentrated
Active (1) Inactive (0) Difference
Accessible, 495 Remote, 977 -482
Concentrated, Sparse, 567 -2.5
Hawaii Fiji Samoa Solomons French Polynesia New Caledonia Guam Tonga New Hebrides Gilbert & Ellice Cooks Niue Nauru
Accessible Accessible Remote Accessible Accessible Remote Accessible Remote Remote Remote Remote Remote Accessible
Concentrated Sparse Sparse Concentrated Sparse Sparse Concentrated Concentrated Sparse Concentrated Concentrated Sparse Concentrated
Pacific
“For definition of accessibility, see text. %versely related to population density; see text.
constrain the form of the regression line, model (1) was re-estimated with Hawaii omitted. This revised regression had a slightly lower R* of 0.63, but yielded a very similar endemicity threshold of 570,000. Although this Hawaii-effect appears small, we have a general reservation about estimating the threshold from data which include islands at or above the threshold or with percentage reporting at or close to zero. Both the 100 and 0% values serve as caps in a closed number system, and distributions of this kind are better approached through logistic rather than linear regression. The impact of accessibility and density on thresholds
Although Black acknowledged the importance of Bartlett’s paper he noted that ‘two factors which it recognized, but did not correct for, were: masking of fade out by reintroduction of measles from outside the city and the damping effect of geographic dispersion’ (Black, 1966, p. 207). We consider these in turn. Accessibility.
The British cities considered by Bartlett were surrounded by other settlements, and the whole urban and regional complex was bound together strongly by travel movements. In such a geographical situation, spatial flows of population across city borders would occur and thus reintroduction of measles from outside a city might commonly result. One factor that led Black to choose islands rather than cities for his own analysis was their greater isolation and thus the smaller chance of continuous reinfection. But, even for islands, isolation can only be relative.
542
“Definitions of terms as in Tabie 4, above.
Black (1966, pp. 208-209) drew attention to two islands in his table, Bermuda and Guam, which had large transient military populations and frequent air connections to mainland points. He thought it probable that they were insufficiently isolated to be comparable directly with the other islands he studied. Hawaii had even higher travel connections and he thought it possible that fadeout of measles between epidemics might actually have occurred there but have been masked by reintroduction by visitors. One simple way of testing Black’s hypothesis is to introduce a dummy variable into the regression equation used to estimate the threshold. As Table 4 shows, a binary distinction can be drawn between ‘accessible’ and ‘remote’ islands on the basis of some connectivity index such as airline links or passenger flows. Each isiand can then be given an accessibility index based on flows per resident population. To articulate the dummy variable, the 18 islands (ignoring the Falklands) were divided into two classes of nine islands each, coding those islands with greater than median accessibility as 1 and those with less than median accesibility as 0. ‘Accessibility’ was measured as the number of tourist arrivals per head of resident population in 1990 (data from UN Statistical Yearbook, 1990-1991, pp. 943-961). The equation relating endemicity to population may be rewritten to include accessibility as log (percentage
endemicity)
+ b1 log (population)
= bO
+ b, (accessibility).
(2) The fitted model was significant with an R* of 0.71. ’ Jsing model (2) and the estimated values of the pti ameters bO- b2, we may again calculate the population endemicity threshold in the manner of equation (l), but for two circumstances: (i) when the dummy variables is 1 (= active), and (ii) when the dummy variable is 0 (= inactive). The dummy variable acts like a switch, having an effect upon the threshold estimate (by the amount 6,) only when it takes the value 1. When the dummy is zero, the term in b2 disappears from model (2). The impact of the dummy variable upon the model is shown in Table 5. As expected, accessible islands have a lower threshold. This is consistent with Black’s idea that they will receive a 205
Epidemiological significance of islands: A. D. Cliff and P. Haggett
Ol
0
1
I
1
2
3
Average dispersion
4
,
I
I
5
6
7
of new susceptibles.
D
Figure 4. Relation between the duration of measles epidemics (percentage endemicity) and the dispersion of susceptible population for seven islands. The horizontal axis measures the average dispersion of new susceptibles in the population: its derivation is discussed in the text. Source: Black (1966, figure 1, p. 209).
larger number of measles cases introduced outside.
from
Dispersion. Black (1966, p. 209) observed that much of the variation in measles prevalence might depend on ‘the duration of individual epidemics and this [is] in turn correlated inversely with population density’. Figure 4 reproduces the graph in Black’s paper on which this statement is based. It plots the observed duration in months (percentage endemicity) of significant measles epidemics (of 100 cases or more) against population dispersion. Dispersion (D) is given as the inverse of the square root of new susceptible children per year (5) divided by the island area (A) in km2, namely D = lIq(S/A).
(3)
It is one of a number of crude measures which could be used to represent the mean distance between susceptible infants added to the population each year. Note that (i) Black’s analysis shown in Figure 4 is restricted to just seven islands from his sample, each having between 2000 and 4000 new susceptible children added each year and (ii) only epidemics with 100 or more reported cases were used in computing duration. Black’s graph suggests that, with maximum theoretical crowding (that is, a spatial dispersion of zero on the horizontal axis), an epidemic would burn out in about 4 months in populations of the size examined. We have difficulty with this idea since we would expect epidemic duration to progress monotonically to zero as the spacing of susceptibles tends to zero. This would be manifested in a regression line that passes through the joint origin of the two axes. But we accept the
more general implication of Black’s argument that, ceteris p&bus, an epidemic will linger longer in a dispersed than in a crowded population. This in turn may affect the number of months in which the disease is reported and thus complicate a simple population-based estimate of the endemicity threshold. Again, Black’s ideas can be tested using a dummy variable approach. Table 4 also dichotomizes the 18 islands in terms of their population density into nine ‘concentrated’ and nine ‘sparse’ islands. A l/O coding was effected on the basis of islands which fell, respectively, above and below the median population density per km2. Addition of the density variable in a multiple regressionlike model (2), but with density replacing accessibility, very slightly improved the R2 to 0.74 as opposed to 0.68 for the simple regression using population alone. The impact of the dummy variable is shown in Table 5. When the dummy takes the value 1 (a concentrated population), the effect is to lower slightly the estimated threshold. The difference of 25,000 between the threshold estimates when the dummy is active as opposed to inactive is in the direction predicted by Black, but it is so small (and statistically non-significant) that it cannot be taken as confirmation of his hypothesis. Extension of the Black study
The work by both Bartlett and Black was published before the licensing of an effective measles vaccine in 1965 and thus before the initiation of the mass vaccination campaigns that have done so much to reduce measles incidence (Cliff et al., 1993). We can check whether Black’s findings were specific to his particular pre-vaccination time period by examining measles records after 1965. From our own archives (based on a mixture of WHO and specific local sources) we have been able to extend the measles time series for Black’s island set to cover the 26 year period from 1965 to 1990. Fitting the log-log regression of model (1) to the percentage of months in each island’s time series reporting measles against population size (in the mid-period year of 1977) yields: log (percentage
endemicity)
+ 0.311 log (population)
= 0.186
(4) with a significant R2 of 0.73. From this equation, the population threshold for 100% measles recording is estimated as 680,000. This is somewhat larger than the 558,000 threshold calculated from Black’s data (above) for the period 1945-1964, and may reflect the reduction in the susceptible populations of these islands resulting from mass measles vaccination. The impact of vaccination upon thresholds is considered in, for example, Griffiths (1973) and Schenzle and Dietz (1987);
Epidemiological
significance of islands: A. D. Cliff and P. Haggett
Table 6. Island and Island groups by WHO world regions used in threshold estimation Island
WHO region
Island
WHO region
Cape Verde Madagascar
Africa
Cyprus Faroes
Bahamas Bermudas Cuba Dominica Dominican Republic Greenland Haiti Jamaica Puerto Rico St Christopher and Nevis St Lucia Trinidad and Tobago
Americas Americas Americas Americas Americas Americas Americas Americas Americas Americas Americas Americas
Ireland Malta
Europe Europe Europe Europe Europe
Hong Kong Janan r --Macau Singapore
Asia Asia Asia Asia
American Samoa Cook Islands Fiji French Polynesia Guam Hawaii Kiribati and Tuvalu Nauru New Caledonia Niue Papua New Guinea Solomon Islands Tongo Trust Territories of the Pacific Vanuatu Wallis and Futuna Western Samoa
Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania
both have shown that mass vaccination acts to increase the critical population size for virus perpetuation. If x denotes the proportion of children not immunized artificially by vaccination, Griffiths found that Bartlett’s critical population size is multiplied by l/x*. Thus 50% immunization increase the threshold from 250,000 to 1 million, while 90% immunization increases the threshold to 2.5 million. As with the 1949-1964 time period, the next step in our analysis was to explore the addition of further explanatory variables to the basic model (4). These variables included the accessibility and population density dummy variables already described and, as earlier, no significant increase in explanation resulted. We next considered whether Black’s findings were specific to the particular set of 18 islands he chose for his study. To Black’s basic set, we added the further 22 islands listed with Black’s in Table 6. Fitting the double log model to this extended group of 40 islands for the period, 1965-1990, yielded the equation: log (percentage
endemicity)
+ 0.180 log (population),
= 0.816 (5)
with R2 = 0.69. This is again highly significant, and back calculation yields a threshold estimate of 3.8 million people. This is a change in the same direction as was found with Black’s original island set for 1965-1990. Further, while it is of a different order of magnitude to Black’s threshold, it is within the range of values for the vaccination
period suggested by Griffiths’s work, and it confirms the importance of vaccination in both reducing the susceptible population and, through this, raising the threshold.
Discussion In this paper, we have carried forward Black’s ideas on the relationship between epidemic characteristics of an infectious disease and island populations. Some of our findings appear to confirm Black’s original ideas, others to contradict them. We can throw some light on this paradox by reference to Figure 5. This shows that the relationship studied by Black, namely the effects of island population (1) upon endemicity (9), and thus on threshold (lo), is only a small part of a larger and more complex system. Endemicity can also be affected by other internal and external factors. Among the internal factors, population density (2) and the number of susceptibles (3) impact on the spacing of susceptibles (4) which, in turn, may prolong the duration of an epidemic (11) and thus increase the number of months with disease cases. The immune status of the island population (5) and its internal mobility (6) may also affect the probability of local spread (13). Equally, endemicity may be affected by external factors such as the probability of externally generated infection and reinfection (12); in its turn, this is a joint product of accessibility (7) and the immune status of the visiting population (8). Note how the relationships between any two variables may be positive or negative and much depends on the relative balance of strength be207
Epidemiological significance of islands: A. D. Cliff and P. Haggett
.:.:...‘.:.,‘;.:.:.:.:,:,:.:.:.: ,(...
.
4
n
(percent moriths
threshold
i
7i ‘i
:...:,:,:,:,:,:.:;.~.~::.~.~.~. .~:._....~_.,~_._.:.:.:.:.:~...... ..:.,_:.,_:.:::.:.:...:.:: 6 Intepal mptjlity j~ljll:.:.:::.::l:III1l::::::.::li .,:_.:.::.:::. :_:.::.._::.. Iljj:iijlf:j.:::lli.:.:..:~::::::: :.,:_:,_.:_::.:::,:.:.:::_:::::~: lijl:i:j]:.:l:l:::::::::::::.:~:::1:1:::::::::::.:::::::::::::::::::: .,.,.,._.:::.:.:.:::::::::::::.:.:.:.:.:.:.:.:.:::.:.:.:.:.:.:.:.:.:.
1
I
12
introduced infection and re-infection
ij
j -
Sign indicates nature of relationship
Figure 5. Schematic relations between the characteristics of island populations (left), the nature of its contacts with the outside world (right) and epidemiological behaviour (centre). The signs indicate the positive (+) and negative (-) nature of the influences while (?) suggests that the relationship is indeterminate.
tween the several factors. A researcher trying to understand epidemic behaviour on a particular island over a particular historical period will need to unravel a much more complex set of relationships than those in the original Black model. In our analysis, we have followed both Bartlett and Black in using that most well-behaved of infectious diseases, measles. But the modelling issues raised are entirely general and other diseases might have been used. Black himself refers to the low thresholds for varicella and we have considered elsewhere the threshold values for some other diseases (Cliff and Haggett, 1990). Black’s intriguing ideas on island epidemiology have two important implications: one practical and one theoretical. International attempts by WHO to eradicate infectious diseases depend partly upon vaccination forcing up the endemic thresholds so that the infection chain which maintains the virus is broken by the lack of a susceptible population. To the success of smallpox eradication (Fenner et al., 1988) is now being added poliomyelitis. The last case in the Americas was recorded in 1994, and plans are on target for global eradication of the disease by the year 2000 (Hull and Ward, 1992; World Health Organization, 1994). In simulation studies, Eichner et al. (1995) have estimated that the minimum popula208
tion size for long-term persistence of polio virus infection ranges from 200,000 to 500,000 in populations with good hygienic standards, but as low as 50,00&150,000 in populations with poor standards of hygiene. These figures are of the same order of magnitude as those reported here for measles. The authors also outline other factors affecting endemicity that might be considered in the context of Figure 5, namely improvements in hygiene and the number of subpopulations within a general population. Both appear to be positively related to the threshold, and the finding for subpopulations is consistent with the structure of Figure 5. More generally, however, in Black’s model, the world itself can be thought of as a ‘global island’ of 5.5 billion people. Once a disease threshold is forced above this level, eradication is guaranteed, even though not every single person is vaccinated. The second implication is theoretical and historical. Threshold populations must be exceeded if there is to be the continual propagation of a virus such as measles which has no reservoir host population other than humans. As Black argues, and we have documented elsewhere (Cliff et al., 1993, Ch. 2), the relatively high population thresholds for measles seen in this paper imply that the disease must have evolved since the
Epidemiological
development of early human urban civilizations around 5000 B.P. It may be that the measles virus developed from a micobiologically similar virus in animals such as rinderpest or canine distemper. This would suggest that the disease emerged shortly after the domestication of cattle and dogs. Similar arguments on the time and place for disease evolution is now a major concern in the epidemiological literature (Haggett, 1994; Wilson et al., 1994). Like Darwin’s ideas on the Galapagos, Black’s model has profound evolutionary implications both for unravelling past questions of disease origin and for throwing light on future disease eradication.
Black, F. L. (1966) ‘Measles endemicity in insular populations: critical community size and its evolutionary implication’, Journal of Theoretical Biology, 11, pp. 207-211. Cliff, A. D. and Haggett, P. (1988) Atlas of Disease Distributions: Analytic Approaches
to Epidemiological
Data, Ox-
ford: Blackwell Reference. Cliff, A. D. and Haggett, P. (1989) Spatial aspects of epidemic control’, Progress in Human Geography, 13, pp. 313-347. Cliff, A. D. and Haggett, P. (1990) ‘Epidemic control and critical community size: spatial aspects of eliminating communicable diseases in human populations’, in Thomas, R. W. (ed.), London Papers in Regional Science, Vol. 21, London: Pion, pp. 93-110. Cliff, A. D., Haggett, P., Ord, J. K. and Versey, G. R. (1981) Soatial Diffusion: an Historical Geoeranhv of Epide’mics in an Island Community, Cambridge: Cambridge University Press. Cliff, A. D., Haggett, P. and Smallman-Raynor, M. (1993) Measles: an Historical Geography of a Major Human Viral Disease from Global Expansion to Local Retreat, Oxford:
Conclusion We noted at the outset that islands had proved fruitful laboratories for biogeographical research from Darwin (1835) and Wallace (1880) onwards. Our re-examination of Black’s (1966) thesis underlines the continuing epidemiological significance of islands for modern disease studies. We note that Black’s threshold theory can be pursued (i) at the macro-geographic level through interisland comparisons and, although not undertaken here, also at (ii) the meso-geographic level through time-series analysis of single islands, and (iii) the micro-geographic level through withinisland comparisons. Different spatial levels of analysis will cast a new light on the relationship between population size and disease persistence. Finally, we have shown that island epidemiology has important implications both for practical questions of disease control and for academic questions of the ways in which new diseases originate. Acknowledgements The research reported in this paper was conducted under the auspices of a grant from the Wellcome Trust’s History of Medicine Committee. We are grateful to Margaret Milligan of the Division of Epidemiological Surveillance and Carole Modis of the Office of Library and Health Literature Services at the World Health Organization, Geneva, for their help.
References Alpers, M. and Gajdusek, D. C. (1965) ‘Changing patterns of kuru: epidemiological changes in the period of increasing contact of the Fore peoples with Western civilization’, American Journal of Tropical Medicine and Hygiene,
significance of islands: A. D. Cliff and P. Haggett
14.
pp. 852-879. Bartlett, M. S. (1957) ‘Measles periodicity and community size’, Journal of the Royal Staiisiical Society A, 120, pp. 4870. Benenson, A. S. (ed.) (1990) Control of Communicable Diseases in Man, 15th edn, Washington: American Public Health Association.
Blackwell Reference. Darlington, P. J. (1943) ‘Carabidae of mountains and islands: data on the evolution of isolated faunas, and on atrophy of wings’, Ecological Monographs, 13, pp. 37-61. Darlington, P. J. (1957) Zoogeography: the Geographical Distribution of Animals, New York: John Wiley. Darwin, C. R. (1963 [1835]) ‘Darwin’s ornithological notes’ (edited with introduction, notes, and appendix by Nora Barlow), Bulletin of the the British Museum (Natural History), Historical Series, 2, pp. 203-278. Eichner, M., Hadeler, K. P. and Dietz, K. (1995) Stochastic models for the eradication of poliomyelitis: minimum popualtion size for polio virus persistence’ (to appear). Fenner, F., Henderson, D. A., Arita, I., Jezek, Z. and Ladnyi, I. D. (1988) Smallpox and its Eradication, Geneva: World Health Organization. Griffiths, D. A. (1973) ‘The effect of measles vaccination on the incidence of measles in the community’, Journal of the Royal Statistical Society A, 136, pp. 441-449. Haggett, P. (1994) ‘Geographical aspects of the emergence of infectious diseases’, Geografiska Annaler, B76, pp. 91-104. Hull, H. F. and Ward, N. A. (1992) ‘Progress towards the global eradication of poliomyelitis’, World Health Statistics Quarterly, 45, pp. 28&284. MacArthur, R. H. and Wilson, E. 0. (1967) The Theory of Island Biogeography, Princeton: Princeton University Press. Mandelbrot, B. B. (1975) ‘Stochastic models for the Earth’s relief, the shape and fractal dimensions of coastlines and the number-area rule for islands’, Proceedings of the National Academy of Sciences, 72, pp. 3825-3828. Nunn, P. D. (1994) Oceanic Islands, Oxford: Basil Blackwell. Schenzle, D. and Dietz, K. (1987) ‘Critical population sizes for endemic virus transmission’. in Fricke, W. and Hinz, E. (eds), Raumliche Persistenz und Diffusion von Krankheiten, Vol. 83, Heidelberg: Heidelberg Geographical Studies, pp. 31-42. Wallace, A. R. (1880) Island Life: or the Phenomena and Causes of Insular Faunas and Floras, London: Macmillan. Wilson, M. E. (1994) A World Guide to Infections: Diseases. Distributions. Diagnoses, New York: Oxford University Press. Wilson, M. E., Levins, R. and Spielman, A. (eds) (1994) ‘Disease in evolution: global changes and emergence of infectious diseases’, Annals of the New York Academy of Sciences, 740, pp. l-503. World Health Organization (1994) ‘Certification de I’kradication de la poliomyelite: les AmCriques, 1994’, Releve Epidemiologique Hebdomadaire, 69, pp. 29%295.
209
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13534?292(95)00029-1
The epidemiological significance of islands Andrew D. Cliff Department of Geography,
University of Cambridge, Downing Place, Cambridge CB2 3EN, UK
Peter Haggett Department of Geography,
University of Bristol, Bristol BS8 ISS, UK
Islands
have proved fruitful laboratories for biogeographical research from Darwin and Wallace onwards. We examine here the significance of Black’s work (Journal of Theoretical Biohgy, 11, pp. 207-211(1966)) on island epidemics. His original data on measles outbreaks on 19 islands over the 15 year period from 1949 to 1964 are reanalysed, and the confounding effects of island accessibility and population density upon estimates of the population threshold for measles endemicity are illustrated. Using later data, we extend Black’s analysis into the post-l%5 measles vaccination era both for the islands he studied and for 22 others, and then explore the potential of intra-island comparisons. Although Black confined himself to measles, this paper suggests that his ideas are extendable to a wide range of other infectious dies. Island epidemiology has implications both for practical questions of disease control and for academic questions of the persistence and origin of diseases. Keywords:
Iceland,
islands, measles, threshold
Introduction Islands have long had a fascination for biologists. When he left the Galapagos in October 1835, Charles Darwin pondered on the birds he had collected from the different islands. He was struck by the differences in mockingbird skins which he had obtained within the Galapagos group: each a distinct variant in colour and arrangement yet developing in similar ecological niches on small islands within sight of each other. The observation was to lead to later conjectures on the speed at which evolutionary differences in organisms might emerge and he wrote in his notebook that ‘. . . if there is the slightest foundation for these remarks, the Zoology of Archipelagos will be well worth examination’ (Darwin, 1963 [1835]; cited in MacArthur and Wilson, 1967, p. 3). A similar view was taken by Alfred Russel Wallace in his Island Life when he concluded that ‘Islands possess many advantages for the study of the laws and phenomena of distribution’ (Wallace, 1880, p. 733). In this paper, we explore Darwin’s theme in the context of disease-causing organisms. We follow
Black (1966) in showing how the epidemic behaviour of infectious diseases varies in relation to the different geographies of islands. Black’s original data on measles outbreaks on 19 islands over the 15 year period from 1949 to 1964 are reanalysed, and the confounding effects of island accessibility and population density upon estimates of the population threshold for measles endemicity are illustrated. Using our own data, we extend Black’s analysis into the post-1965 measles vaccination era both for the islands he studied and for 22 others, and then explore the potential of intra-island comparisons. Although Black confined himself to measles, we suggest that his ideas can be extended to a wide range of other infectious diseases. Further, we argue that island epidemiology has implications both for practical questions of disease control and for academic questions about the origin and persistence of infectious diseases. Island biogeography Although islands appear to be simple and selfdefining entities, their operational definition for 199
Epidemiological
significance of islandr: A, D. Cliff and P. Haggett
Table 1. Island area and number of species relationships Relationship
Island group
Gulf of Guinea islands West Indies Galapagos East-central Pacific West Indies Melanesia East Indies Lake Michigan islands West Indies
(z)
Biological group
0.489 0.340 0.325 0.303 0.301 0.300 0.280
Fauna (birds) Fauna (beetles) Flora (land plants) Fauna (birds) Fauna (amphibians) Fauna (ants) Fauna (birds)
0.239 0.237
Fauna (vertebrates) Fauna (birds)
Source: modified from MacArthur and Wilson (1967, table 2, P. 9).
research purposes turns out to be surprisingly elusive. Nunn, in his Oceanic Zslunds (1994, pp. l-12) discusses the problem at length. For example, since islands form a classic example of one of Mandelbrot’s fractal series (Mandelbrot, 1975), questions of their number will always remain unanswerable. Because we are concerned here with specific epidemiological questions, we confine ourselves to those islands which are (i) permanently inhabited by a human population, (ii) are sub-continental in size and (iii) for which good disease records exist. Around the world, fewer than 100 islands or island groups meet these criteria. Area-species
relationships
The relations between the size of islands and the biological diversity of their flora and fauna was first analysed in mathematical terms by Darlington (1943) in a study of carabid beetles on the islands of the West Indies. He observed that there appeared to exist an orderly relation between the size of a sample area and the number of species found in that area. Darlington expressed the relationship as follows for the herpetofauna (amphibians plus reptiles) of the West Indies: ‘division of island area by ten [in going from one island to the next] divides the fauna by two’ (Darlington, 1957; cited in MacArthur and Wilson, 1967, p. 8). Two observations on Darlington’s findings are relevant here. First, island area seldom exerts a direct influence upon the presence or absence of a species, but is simply a useful proxy for the ecological and habitat diversity found there. Second, the relationship to area is more usually expressed via the power equation, S = CA’ , where S is the number of species of a particular taxon found on a given island, and A is the island’s area. The parameter, c, depends upon both the taxon and the geographical area being investigated, while z describes the decay rate of species with decreasing island area. Actual values 200
of z for a series of sample biological studies of island fauna and flora appear in Table I, and range from 0.237 to 0.489. A z value of 0.301 characterizes the fall-off rate described by Darlington’s rule of thumb, above. Population-disease
relationships
One question which arises from biogeographical work on islands is whether a similar relationship between area and diversity exists for (i) microorganisms in general and (ii) disease-bearing microorganisms in particular. In broad terms, do small islands have a narrower range of diseases than large ones? If so, is there a consistent relationship along the lines of that discovered by Darlington and others for island flora and fauna? We can run a rough test of these ideas using data given in a recent survey by Wilson (1994) of the distribution of world diseases. Wilson’s book describes the spatial range of 251 major diseases of humans across 16 world regions. Of the diseases considered, 74 are worldwide in the sense of being reported in a recent year from every country studied: measles was a good example in the pre-vaccination period. A further 44 diseases are less widely distributed but, nevertheless, occurred in all 16 world regions. The remaining 118 diseases are spatially specific in the sense that they were reported from some regions but not from others. The various geographical distributions are summarized in Table 2. As shown in the table, the average taken over all 16 regions is 51 diseases. But the value for the three insular regions (31 diseases) is well below that for continental regions (56 diseases). The contrast is underlined by two adjacent regions in the same latitude band in Middle America: despite their geographical propinquity, the disease count for the island-studded Caribbean region (48) is well below that of the peninsular Central American region (68). The Wilson data (given on pp. 281-415) can be analysed at a sharper spatial scale by plotting the number of supplemental references to selected diseases on a country-by-country basis. This is undertaken in Figure I where the number of such disease references (vertical axis) is graphed against the population of each country (horizontal axis). To make the results comparable with those of Darlington, each of the 61 points on the graph is confined to a country which is either an island or island group. These range in size from the very small (e.g. Tokelau with 1700 people in 1988) to the very large (e.g. Australia with 16.47 million in 1988). The relationship between the two variables is statistically significant at the 95% level with an R2 of 0.57, implying that large islands have more diseases that demand reference in a standard text than do small ones.
Epidemiological
significance of islands: A. D.
Cliffand P. Haggett
Table 2. Distribution of 118 infectious diseases in 16 world regions Northern mid-latitude
regions
East Asia 67 N. Europe” 56 N. America 56 N. Africa 48 S. Europe 35
N. Mid-latitude average 52
regions
Continental/insular
regions
Tropical regions
Southern mid-latitude
Central America 68 Mid-S. Asia 66 E. South Asia 66 Sub-Saharan Africa 65 Tropical S. America 64 W. South Asia 56
Temp S. America 43 S. Africa 33
Continental average 56
Caribbean 48
Australia/New Zealand 19 Pacific 25
Insular average 31
Tropical average 62
S. Mid-latitude average 30
Grand average 51
“Including the former USSR. Source: data from Wilson (1994, pp. 182-203).
A second example of the regional concentration of different diseases can be seen from an examination of data in Benenson (1990, pp. 2329). This lists 103 arthropod-borne virus diseases: of these, 83 are confined to the tropics, 13 to Europe and 5 to Australia. Kuru, a disease of the central nervous system and found only among the Fore peoples in central New Guinea, is the outstanding example of a spatially confined disease (Alpers and Gajdusek, 1965); the various haemorrhagic fevers are others. We can conclude, therefore, that the findings of island biogeographers on macrofauna-area relationships are consistent with the microfaunapopulation relationships shown in disease data. It is to the epidemiological implications of this consistency that we now turn.
towns and the virus disease of measles, Bartlett plotted the mean period between epidemics, in weeks, against the population size of these towns. Bartlett discovered that, in large towns, measles was endemic with periodic eruptions (Bartlett’s so-called Type I waves). In cities below a certain population size threshold, measles displayed an epidemic pattern with complete disappearance of the disease (fade-out) between epidemics. A distinction was drawn between urban areas above about 10,000 people with a regular pattern of epidemics (Type II waves) and those where occasional epidemics were missed, giving a more irregular pattern (Type III waves). Given the rates of reporting at the time of Bartlett’s original study, the endemic/epidemic threshold for measles lay at a population size of around 250,000, a figure which has been confirmed on many occasions since; see Cliff et al. (1981) and Cliff and Haggett (1990) for recent reviews. As we shall see later in this paper, the existence of an endemicity threshold for a transmissible virus disease has profound implications for its persistence and control. Once the at-risk popula-
Epidemic disease thresholds
Before we can look at island epidemiology directly, we need to consider first the fundamental work carried out by the Oxford biomathematician, M. S. Bartlett (1957) in a different geographical context. Using a sample of 19 English
. 30
Diseases = 0.34 + 4.39 log population R 2 = 0.57
.
25
10
100
1000
Island population, 1988 (log scale) Figure
1. References to diseases in humans for island countries plotted against their 1988 populations. are based on Wilson (1994, pp. 281415).
The data
201
Epidemiological
significance of islands: A. D. Cliff and P. Haggett
COMMUNITY
COMMUNITY
A
Population large enough 17>250 to sustain virus and continuous record of infection. Type I epidemic waves
000)
B
Population too small to sustain virus, but regular Type II epidemic waves
COMMUNITY
C
Very small population. Irregular Type ill epidemic waves
Figure 2. The structure of the Bartlett model. Large communities (A) with endemic disease serve as reservoirs from which agent spread reinfects smaller communities (B and C) that experience epidemic disease with intervening fade-out rather than endemic disease. Source: Cliff and Haggett (1988, figure 4, p. 322).
tion is reduced below the endemicity threshold by whatever means (vaccination, for example), the disease should become naturally selfextinguishing because the chains of transmission whereby the virus is passed repeatedly from infective to susceptible will be broken. Second, once an area becomes disease-free, an epidemic can recur only if the virus is reintroduced from a geographical reservoir of infection elsewhere. Thus the generalized persistence of such virus diseases implies spatial transmission between geographical units as shown in Figure 2. Continuing with measles as our example, in large cities above the size threshold, like community A in Figure 2, a continuous trickle of cases is reported. These provide the reservoir of infection which sparks a major epidemic when the susceptible population, S, builds up to a critical level. Since clinical measles confers subsequent lifelong immunity to the disease, this build-up occurs only as children are born, lose their mother-conferred immunity and escape vaccination or the disease. Eventually the S population will increase sufficiently for an epidemic to occur. When this happens, the S population is diminished and the stock of infectives, I, increases as individuals are transferred by infection from the S to the I population. This generates the characteristic ‘D’-shaped relationship over time between
sizes of the S and I populations shown on the end plane of the block diagram. When the total population of a community falls below the population size threshold, as in settlement types B and C of Figure 2, measles epidemics recur only when the virus is reintroduced by the influx of infected individuals from 202
reservoir areas (community A in Figure 2). These movements
are shown
by the broad
arrows.
In
such smaller communities, the S population is insufficient to maintain a continuous record of infection. The disease dies out and the S population grows in the absence of infection. Eventually the S population will become large enough to sustain an epidemic when an index case arrives. Given that the total population of the community is insufficient to renew by births the S population as rapidly as it is diminished by infection, the epidemic will eventually die out. It is the repetition of this basic process which generates the successive epidemic waves witnessed in most communities. Of special significance is the way in which the continuous infection and characteristically regular Type I epidemic waves of endemic communities break down, as population size diminishes, into, first, discrete but regular Type II waves in community B and then, secondly, into discrete and irregularly spaced Type III waves in community C. Thus diseasefree windows will appear automatically in both time and space whenever population totals are small and geographical densities are low. Nine years after Bartlett’s original paper, his ideas were taken up in an island context by the Yale epidemiologist, Francis Black (Black, 1966). In the remainder of this paper, we look at Black’s original data, subject them to further statistical analysis, and then extend Black’s approach both to more recent data for his set of islands and to a further 22 islands not considered in Black’s work. The analysis is conducted at a macro-geographic level; by ‘macro’, we mean comparative study of many islands on a worldwide scale.
Epidemiological
significance of islands: A. D. Cliff and P. Haggett
Table 3. Black’s data for estimating measles endemicity in 19 island populations using monthly data for the period January 1949-
December
1964
Region
Island
Population (1956)
Atlantic
Iceland Greenland Bermuda Faroes St Helena Falkland
160,000 28,000 41,000 34,000 5000 2500
Pacific
Hawaii Fiji Samoa Solomons French Polynesia New Caledonia Guam Tonga New Hebrides Gilbert & Ellice Cooks Niue Nauru
550,000 345,000 118,cQO 110,000 75,000 68,000 63,000 57,000 52,000 40,000 16,000 4700 3500
Measles reporting ratiob
Measles cases reported (% months)
Annual susceptibles input’
4490 1190 1130 744 116 43
45 111 10 24 54
61 24 51 32 4 0
167,000 13,400 4440 4060 2690 2600 2200 2040 1910 1260 678 225 I67
24 8 9 6 27 9 11 28 9 56 51 21 30
100 64 28 32 8 32 80 12 30 15 6 5 5
“1956 births less infant mortality. bTotal number of reported measles cases divided by total input of susceptible children during the period of study. Source: Black (1966, table 1, p. 208).
Island macro-geography In his paper in the Journal of Theoretical Biology, Black set out to ‘confirm and refine Bartlett’s estimates by considering communities where reintroduction [of measles] is minimal and where the effect of population dispersion could be observed’ (Black, 1966, p. 207). To do this, Black analysed data on measles incidence for 19 islands or island groups (Table 3). These were located mostly in the Pacific Ocean (Cook, Fiji, French Polynesia, Gilbert & Ellice, Guam, Hawaii, New Caledonia, New Hebrides, Nauru, Niue, Samoa, Solomons and Tonga); the remainder (6) had Atlantic locations (Bermuda, Falklands, Faroes, Greenland, Iceland and St Helena). The islands ranged in population size over two orders of magnitudefrom Hawaii, with a 1956 population of 550,000, down to the Falklands with only 2500 inhabitants. The average population of the islands Black studied was 93,000. The monthly measles data used spanned a 15 year period from January 1949 to December 1964 (180 months in all). Incidence data were obtained for most islands for most months from World Health Organization reports, supplemented by figures obtained by Black from local health officers. All the islands studied had suffered at least four measles outbreaks during the 15 year period with the exception of the Falklands: this was measles free for the whole period. Black estimated reporting completeness
(measles reporting ratio in Table 3) for each of his islands by dividing the observed pattern of recording (defined as the total number of measles cases reported in the 15 years) by an expected pattern (for the highly infectious disease, measles, at a time prior to the availability of vaccination, defined as the total number of children reaching their first birthday during the 15 year study period). The mean value for case reporting over all Black’s islands was 29.6%. Five islands had reporting rates of over 40%: Cook, Gilbert & Ellice, Greenland, Iceland and St Helena. At the other end of the scale, five islands (Fiji, New Caledonia, New Hebrides, Samoa and Solomons) had low measles reporting rates of between 6 and 10%. Island groups with less than 6% reporting rates had been excluded by Black from the analysis at an earlier stage. Reanalysis of the Black data
Black (1966, p. 208) describes a ‘crude correlation’ between island populations and the endemicity of measles, but he left his data in a tabular form (Table 3). If we plot Black’s data (Figure 3), the positive association between island size and percentage endemicity becomes clear. This diagram shows the data in three different forms, with the graph axes in linear, log-linear and log-log forms. Throughout this paper, we define percentage endemicity as the percentage of the total months in the time series of an island in which measles cases were reported. 203
Epidemiological significance of islands: A. D. Cliff and P. Haggett
A Linear - linear
c.o E
8 5
1 Cookl.
2 Faroe 1.
60
3 4 5 6 7
63.1 l @Tonga 7
0
lFrench
endemicity = 16.1 + 0.0002 population R’= 0.59
Polynesia
0
Nauru New Caledonia New Hebrides Niue St Helena
200
I 600
400
B Log - linear loo-
Hawaii l . Guam
80c .o E B f z g & CL
endemicity = -121.0 R’= 0.58
+ 33.2 log population
60. Bermuda New
40-
20Nauru.
0
Niue
/Ibert
l St ~~~~~~
& E”ice ’ .Cook I.
10
1
c
l T;;;nch
100
Po,ynesia 1000
Log-log
100
log endemicity = -1.54 + 0.616 log population R*= 0.68 10
100
t
1000
Population, 1956 (in thousands)
Figure 3. Relation between measles endemicity and population size for Black’s (1966) data for 18 islands, 1949-1964. (A) Linear axes. (B) Log-linear axes. (C) Log-log axes. Data are given in Table 3 of this paper. Endemicity is measured as the percentage of months with measles cases reported.
Because both variables range over several orders of magnitude, the most effective representation is given by the log-log form with the regression equation log (percentage
endemicity)
+ b, log (1956 population), 204
= b. (1)
where 6s = -1.54 and bI = 0.616; R* = 0.68. Using equation (1) and the parameter values given, we can estimate the population at which measles cases would be reported in every month of a time series (100% occurrence)-the so-called endemicity threshold-as 558,000. Since Hawaii is at this 100% threshold, and might be argued to
Epidemiological Table 4. Accessibility
and dispersion applied to Black’s (1966) data
as
dummy variables
significance of islands: A. D. Cliff and P. Haggett
Table 5. The impact of accessibility and dispersion on Black’s (1966) population threshold estimates, in thousands”
Region
Island
Accessibility”
Dispersionb
Dummy variable
Accessibility
Dispersion
Atlantic
Iceland Greenland Bermuda Faroes St Helena
Accessible Remote Accessible Accessible Remote
Sparse Sparse Concentrated Sparse Concentrated
Active (1) Inactive (0) Difference
Accessible, 495 Remote, 977 -482
Concentrated, Sparse, 567 -2.5
Hawaii Fiji Samoa Solomons French Polynesia New Caledonia Guam Tonga New Hebrides Gilbert & Ellice Cooks Niue Nauru
Accessible Accessible Remote Accessible Accessible Remote Accessible Remote Remote Remote Remote Remote Accessible
Concentrated Sparse Sparse Concentrated Sparse Sparse Concentrated Concentrated Sparse Concentrated Concentrated Sparse Concentrated
Pacific
“For definition of accessibility, see text. %versely related to population density; see text.
constrain the form of the regression line, model (1) was re-estimated with Hawaii omitted. This revised regression had a slightly lower R* of 0.63, but yielded a very similar endemicity threshold of 570,000. Although this Hawaii-effect appears small, we have a general reservation about estimating the threshold from data which include islands at or above the threshold or with percentage reporting at or close to zero. Both the 100 and 0% values serve as caps in a closed number system, and distributions of this kind are better approached through logistic rather than linear regression. The impact of accessibility and density on thresholds
Although Black acknowledged the importance of Bartlett’s paper he noted that ‘two factors which it recognized, but did not correct for, were: masking of fade out by reintroduction of measles from outside the city and the damping effect of geographic dispersion’ (Black, 1966, p. 207). We consider these in turn. Accessibility.
The British cities considered by Bartlett were surrounded by other settlements, and the whole urban and regional complex was bound together strongly by travel movements. In such a geographical situation, spatial flows of population across city borders would occur and thus reintroduction of measles from outside a city might commonly result. One factor that led Black to choose islands rather than cities for his own analysis was their greater isolation and thus the smaller chance of continuous reinfection. But, even for islands, isolation can only be relative.
542
“Definitions of terms as in Tabie 4, above.
Black (1966, pp. 208-209) drew attention to two islands in his table, Bermuda and Guam, which had large transient military populations and frequent air connections to mainland points. He thought it probable that they were insufficiently isolated to be comparable directly with the other islands he studied. Hawaii had even higher travel connections and he thought it possible that fadeout of measles between epidemics might actually have occurred there but have been masked by reintroduction by visitors. One simple way of testing Black’s hypothesis is to introduce a dummy variable into the regression equation used to estimate the threshold. As Table 4 shows, a binary distinction can be drawn between ‘accessible’ and ‘remote’ islands on the basis of some connectivity index such as airline links or passenger flows. Each isiand can then be given an accessibility index based on flows per resident population. To articulate the dummy variable, the 18 islands (ignoring the Falklands) were divided into two classes of nine islands each, coding those islands with greater than median accessibility as 1 and those with less than median accesibility as 0. ‘Accessibility’ was measured as the number of tourist arrivals per head of resident population in 1990 (data from UN Statistical Yearbook, 1990-1991, pp. 943-961). The equation relating endemicity to population may be rewritten to include accessibility as log (percentage
endemicity)
+ b1 log (population)
= bO
+ b, (accessibility).
(2) The fitted model was significant with an R* of 0.71. ’ Jsing model (2) and the estimated values of the pti ameters bO- b2, we may again calculate the population endemicity threshold in the manner of equation (l), but for two circumstances: (i) when the dummy variables is 1 (= active), and (ii) when the dummy variable is 0 (= inactive). The dummy variable acts like a switch, having an effect upon the threshold estimate (by the amount 6,) only when it takes the value 1. When the dummy is zero, the term in b2 disappears from model (2). The impact of the dummy variable upon the model is shown in Table 5. As expected, accessible islands have a lower threshold. This is consistent with Black’s idea that they will receive a 205
Epidemiological significance of islands: A. D. Cliff and P. Haggett
Ol
0
1
I
1
2
3
Average dispersion
4
,
I
I
5
6
7
of new susceptibles.
D
Figure 4. Relation between the duration of measles epidemics (percentage endemicity) and the dispersion of susceptible population for seven islands. The horizontal axis measures the average dispersion of new susceptibles in the population: its derivation is discussed in the text. Source: Black (1966, figure 1, p. 209).
larger number of measles cases introduced outside.
from
Dispersion. Black (1966, p. 209) observed that much of the variation in measles prevalence might depend on ‘the duration of individual epidemics and this [is] in turn correlated inversely with population density’. Figure 4 reproduces the graph in Black’s paper on which this statement is based. It plots the observed duration in months (percentage endemicity) of significant measles epidemics (of 100 cases or more) against population dispersion. Dispersion (D) is given as the inverse of the square root of new susceptible children per year (5) divided by the island area (A) in km2, namely D = lIq(S/A).
(3)
It is one of a number of crude measures which could be used to represent the mean distance between susceptible infants added to the population each year. Note that (i) Black’s analysis shown in Figure 4 is restricted to just seven islands from his sample, each having between 2000 and 4000 new susceptible children added each year and (ii) only epidemics with 100 or more reported cases were used in computing duration. Black’s graph suggests that, with maximum theoretical crowding (that is, a spatial dispersion of zero on the horizontal axis), an epidemic would burn out in about 4 months in populations of the size examined. We have difficulty with this idea since we would expect epidemic duration to progress monotonically to zero as the spacing of susceptibles tends to zero. This would be manifested in a regression line that passes through the joint origin of the two axes. But we accept the
more general implication of Black’s argument that, ceteris p&bus, an epidemic will linger longer in a dispersed than in a crowded population. This in turn may affect the number of months in which the disease is reported and thus complicate a simple population-based estimate of the endemicity threshold. Again, Black’s ideas can be tested using a dummy variable approach. Table 4 also dichotomizes the 18 islands in terms of their population density into nine ‘concentrated’ and nine ‘sparse’ islands. A l/O coding was effected on the basis of islands which fell, respectively, above and below the median population density per km2. Addition of the density variable in a multiple regressionlike model (2), but with density replacing accessibility, very slightly improved the R2 to 0.74 as opposed to 0.68 for the simple regression using population alone. The impact of the dummy variable is shown in Table 5. When the dummy takes the value 1 (a concentrated population), the effect is to lower slightly the estimated threshold. The difference of 25,000 between the threshold estimates when the dummy is active as opposed to inactive is in the direction predicted by Black, but it is so small (and statistically non-significant) that it cannot be taken as confirmation of his hypothesis. Extension of the Black study
The work by both Bartlett and Black was published before the licensing of an effective measles vaccine in 1965 and thus before the initiation of the mass vaccination campaigns that have done so much to reduce measles incidence (Cliff et al., 1993). We can check whether Black’s findings were specific to his particular pre-vaccination time period by examining measles records after 1965. From our own archives (based on a mixture of WHO and specific local sources) we have been able to extend the measles time series for Black’s island set to cover the 26 year period from 1965 to 1990. Fitting the log-log regression of model (1) to the percentage of months in each island’s time series reporting measles against population size (in the mid-period year of 1977) yields: log (percentage
endemicity)
+ 0.311 log (population)
= 0.186
(4) with a significant R2 of 0.73. From this equation, the population threshold for 100% measles recording is estimated as 680,000. This is somewhat larger than the 558,000 threshold calculated from Black’s data (above) for the period 1945-1964, and may reflect the reduction in the susceptible populations of these islands resulting from mass measles vaccination. The impact of vaccination upon thresholds is considered in, for example, Griffiths (1973) and Schenzle and Dietz (1987);
Epidemiological
significance of islands: A. D. Cliff and P. Haggett
Table 6. Island and Island groups by WHO world regions used in threshold estimation Island
WHO region
Island
WHO region
Cape Verde Madagascar
Africa
Cyprus Faroes
Bahamas Bermudas Cuba Dominica Dominican Republic Greenland Haiti Jamaica Puerto Rico St Christopher and Nevis St Lucia Trinidad and Tobago
Americas Americas Americas Americas Americas Americas Americas Americas Americas Americas Americas Americas
Ireland Malta
Europe Europe Europe Europe Europe
Hong Kong Janan r --Macau Singapore
Asia Asia Asia Asia
American Samoa Cook Islands Fiji French Polynesia Guam Hawaii Kiribati and Tuvalu Nauru New Caledonia Niue Papua New Guinea Solomon Islands Tongo Trust Territories of the Pacific Vanuatu Wallis and Futuna Western Samoa
Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania Oceania
both have shown that mass vaccination acts to increase the critical population size for virus perpetuation. If x denotes the proportion of children not immunized artificially by vaccination, Griffiths found that Bartlett’s critical population size is multiplied by l/x*. Thus 50% immunization increase the threshold from 250,000 to 1 million, while 90% immunization increases the threshold to 2.5 million. As with the 1949-1964 time period, the next step in our analysis was to explore the addition of further explanatory variables to the basic model (4). These variables included the accessibility and population density dummy variables already described and, as earlier, no significant increase in explanation resulted. We next considered whether Black’s findings were specific to the particular set of 18 islands he chose for his study. To Black’s basic set, we added the further 22 islands listed with Black’s in Table 6. Fitting the double log model to this extended group of 40 islands for the period, 1965-1990, yielded the equation: log (percentage
endemicity)
+ 0.180 log (population),
= 0.816 (5)
with R2 = 0.69. This is again highly significant, and back calculation yields a threshold estimate of 3.8 million people. This is a change in the same direction as was found with Black’s original island set for 1965-1990. Further, while it is of a different order of magnitude to Black’s threshold, it is within the range of values for the vaccination
period suggested by Griffiths’s work, and it confirms the importance of vaccination in both reducing the susceptible population and, through this, raising the threshold.
Discussion In this paper, we have carried forward Black’s ideas on the relationship between epidemic characteristics of an infectious disease and island populations. Some of our findings appear to confirm Black’s original ideas, others to contradict them. We can throw some light on this paradox by reference to Figure 5. This shows that the relationship studied by Black, namely the effects of island population (1) upon endemicity (9), and thus on threshold (lo), is only a small part of a larger and more complex system. Endemicity can also be affected by other internal and external factors. Among the internal factors, population density (2) and the number of susceptibles (3) impact on the spacing of susceptibles (4) which, in turn, may prolong the duration of an epidemic (11) and thus increase the number of months with disease cases. The immune status of the island population (5) and its internal mobility (6) may also affect the probability of local spread (13). Equally, endemicity may be affected by external factors such as the probability of externally generated infection and reinfection (12); in its turn, this is a joint product of accessibility (7) and the immune status of the visiting population (8). Note how the relationships between any two variables may be positive or negative and much depends on the relative balance of strength be207
Epidemiological significance of islands: A. D. Cliff and P. Haggett
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.
4
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i
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12
introduced infection and re-infection
ij
j -
Sign indicates nature of relationship
Figure 5. Schematic relations between the characteristics of island populations (left), the nature of its contacts with the outside world (right) and epidemiological behaviour (centre). The signs indicate the positive (+) and negative (-) nature of the influences while (?) suggests that the relationship is indeterminate.
tween the several factors. A researcher trying to understand epidemic behaviour on a particular island over a particular historical period will need to unravel a much more complex set of relationships than those in the original Black model. In our analysis, we have followed both Bartlett and Black in using that most well-behaved of infectious diseases, measles. But the modelling issues raised are entirely general and other diseases might have been used. Black himself refers to the low thresholds for varicella and we have considered elsewhere the threshold values for some other diseases (Cliff and Haggett, 1990). Black’s intriguing ideas on island epidemiology have two important implications: one practical and one theoretical. International attempts by WHO to eradicate infectious diseases depend partly upon vaccination forcing up the endemic thresholds so that the infection chain which maintains the virus is broken by the lack of a susceptible population. To the success of smallpox eradication (Fenner et al., 1988) is now being added poliomyelitis. The last case in the Americas was recorded in 1994, and plans are on target for global eradication of the disease by the year 2000 (Hull and Ward, 1992; World Health Organization, 1994). In simulation studies, Eichner et al. (1995) have estimated that the minimum popula208
tion size for long-term persistence of polio virus infection ranges from 200,000 to 500,000 in populations with good hygienic standards, but as low as 50,00&150,000 in populations with poor standards of hygiene. These figures are of the same order of magnitude as those reported here for measles. The authors also outline other factors affecting endemicity that might be considered in the context of Figure 5, namely improvements in hygiene and the number of subpopulations within a general population. Both appear to be positively related to the threshold, and the finding for subpopulations is consistent with the structure of Figure 5. More generally, however, in Black’s model, the world itself can be thought of as a ‘global island’ of 5.5 billion people. Once a disease threshold is forced above this level, eradication is guaranteed, even though not every single person is vaccinated. The second implication is theoretical and historical. Threshold populations must be exceeded if there is to be the continual propagation of a virus such as measles which has no reservoir host population other than humans. As Black argues, and we have documented elsewhere (Cliff et al., 1993, Ch. 2), the relatively high population thresholds for measles seen in this paper imply that the disease must have evolved since the
Epidemiological
development of early human urban civilizations around 5000 B.P. It may be that the measles virus developed from a micobiologically similar virus in animals such as rinderpest or canine distemper. This would suggest that the disease emerged shortly after the domestication of cattle and dogs. Similar arguments on the time and place for disease evolution is now a major concern in the epidemiological literature (Haggett, 1994; Wilson et al., 1994). Like Darwin’s ideas on the Galapagos, Black’s model has profound evolutionary implications both for unravelling past questions of disease origin and for throwing light on future disease eradication.
Black, F. L. (1966) ‘Measles endemicity in insular populations: critical community size and its evolutionary implication’, Journal of Theoretical Biology, 11, pp. 207-211. Cliff, A. D. and Haggett, P. (1988) Atlas of Disease Distributions: Analytic Approaches
to Epidemiological
Data, Ox-
ford: Blackwell Reference. Cliff, A. D. and Haggett, P. (1989) Spatial aspects of epidemic control’, Progress in Human Geography, 13, pp. 313-347. Cliff, A. D. and Haggett, P. (1990) ‘Epidemic control and critical community size: spatial aspects of eliminating communicable diseases in human populations’, in Thomas, R. W. (ed.), London Papers in Regional Science, Vol. 21, London: Pion, pp. 93-110. Cliff, A. D., Haggett, P., Ord, J. K. and Versey, G. R. (1981) Soatial Diffusion: an Historical Geoeranhv of Epide’mics in an Island Community, Cambridge: Cambridge University Press. Cliff, A. D., Haggett, P. and Smallman-Raynor, M. (1993) Measles: an Historical Geography of a Major Human Viral Disease from Global Expansion to Local Retreat, Oxford:
Conclusion We noted at the outset that islands had proved fruitful laboratories for biogeographical research from Darwin (1835) and Wallace (1880) onwards. Our re-examination of Black’s (1966) thesis underlines the continuing epidemiological significance of islands for modern disease studies. We note that Black’s threshold theory can be pursued (i) at the macro-geographic level through interisland comparisons and, although not undertaken here, also at (ii) the meso-geographic level through time-series analysis of single islands, and (iii) the micro-geographic level through withinisland comparisons. Different spatial levels of analysis will cast a new light on the relationship between population size and disease persistence. Finally, we have shown that island epidemiology has important implications both for practical questions of disease control and for academic questions of the ways in which new diseases originate. Acknowledgements The research reported in this paper was conducted under the auspices of a grant from the Wellcome Trust’s History of Medicine Committee. We are grateful to Margaret Milligan of the Division of Epidemiological Surveillance and Carole Modis of the Office of Library and Health Literature Services at the World Health Organization, Geneva, for their help.
References Alpers, M. and Gajdusek, D. C. (1965) ‘Changing patterns of kuru: epidemiological changes in the period of increasing contact of the Fore peoples with Western civilization’, American Journal of Tropical Medicine and Hygiene,
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pp. 852-879. Bartlett, M. S. (1957) ‘Measles periodicity and community size’, Journal of the Royal Staiisiical Society A, 120, pp. 4870. Benenson, A. S. (ed.) (1990) Control of Communicable Diseases in Man, 15th edn, Washington: American Public Health Association.
Blackwell Reference. Darlington, P. J. (1943) ‘Carabidae of mountains and islands: data on the evolution of isolated faunas, and on atrophy of wings’, Ecological Monographs, 13, pp. 37-61. Darlington, P. J. (1957) Zoogeography: the Geographical Distribution of Animals, New York: John Wiley. Darwin, C. R. (1963 [1835]) ‘Darwin’s ornithological notes’ (edited with introduction, notes, and appendix by Nora Barlow), Bulletin of the the British Museum (Natural History), Historical Series, 2, pp. 203-278. Eichner, M., Hadeler, K. P. and Dietz, K. (1995) Stochastic models for the eradication of poliomyelitis: minimum popualtion size for polio virus persistence’ (to appear). Fenner, F., Henderson, D. A., Arita, I., Jezek, Z. and Ladnyi, I. D. (1988) Smallpox and its Eradication, Geneva: World Health Organization. Griffiths, D. A. (1973) ‘The effect of measles vaccination on the incidence of measles in the community’, Journal of the Royal Statistical Society A, 136, pp. 441-449. Haggett, P. (1994) ‘Geographical aspects of the emergence of infectious diseases’, Geografiska Annaler, B76, pp. 91-104. Hull, H. F. and Ward, N. A. (1992) ‘Progress towards the global eradication of poliomyelitis’, World Health Statistics Quarterly, 45, pp. 28&284. MacArthur, R. H. and Wilson, E. 0. (1967) The Theory of Island Biogeography, Princeton: Princeton University Press. Mandelbrot, B. B. (1975) ‘Stochastic models for the Earth’s relief, the shape and fractal dimensions of coastlines and the number-area rule for islands’, Proceedings of the National Academy of Sciences, 72, pp. 3825-3828. Nunn, P. D. (1994) Oceanic Islands, Oxford: Basil Blackwell. Schenzle, D. and Dietz, K. (1987) ‘Critical population sizes for endemic virus transmission’. in Fricke, W. and Hinz, E. (eds), Raumliche Persistenz und Diffusion von Krankheiten, Vol. 83, Heidelberg: Heidelberg Geographical Studies, pp. 31-42. Wallace, A. R. (1880) Island Life: or the Phenomena and Causes of Insular Faunas and Floras, London: Macmillan. Wilson, M. E. (1994) A World Guide to Infections: Diseases. Distributions. Diagnoses, New York: Oxford University Press. Wilson, M. E., Levins, R. and Spielman, A. (eds) (1994) ‘Disease in evolution: global changes and emergence of infectious diseases’, Annals of the New York Academy of Sciences, 740, pp. l-503. World Health Organization (1994) ‘Certification de I’kradication de la poliomyelite: les AmCriques, 1994’, Releve Epidemiologique Hebdomadaire, 69, pp. 29%295.
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