The distribution of Ascaris lumbricoides in human hosts: a study of 1765 people in Bangladesh

TRANSACTIONS

OF THE ROYAL

The distribution Bangladesh

SOCIETY

OF TROPICAL

MEDICINE

of Ascaris lumbricoides

AND HYGIENE

(1999) 93,503-5

10

in human hosts: a study of 1765 people in

and Lutfar Andrew Hall*, Kazi Selim Anwar**, Andrew Tomkim*** Diarrhoeal Disease Research, Bangladesh, l? 0. Box 128, Dhaka 1000, Bangladesh

Rahman

International

Centre for

Abstract The Ascarzs Zutnbricoidesexpelled by 1765 people in a poor urban community in Bangladesh were recovered and counted after the subjects had been treated with pyrantel pamoate. The subjects were divided into 22 classes by age and sex (mean n = 80) to examine how prevalence, mean worm burdens and measures of aggregation of worms varied with age and between the sexes, and to see how a measure of aggregation, k, calculated in 3 ways (by maximum likelihood, from moments, or from the percentage uninfected) compared with an empirical aggregation index (the percentage of subjects who expelled an arbitrary 80% of all worms) and with the proportion who were moderately to heavily infected (defined as 3 15 worms). The prevalence of infection ranged from 64% to 95%, mean worm burdens ranged from 7 to 23 worms, and k ranged from 0.3 to 1.2. There were significant differences between adult males and females in the prevalence of infection, mean worm burdens and measures ofaggregation, differences which are probably driven more by behaviour than immunity. The parameter k was better described in terms of the proportion who were moderately to heavily infected (linear; range 0,15-0.58) than by the empirical aggregation index (non-linear; range 0.300.49). Keywords:

Ascaris Zumbricoides, expulsion, aggregation, prevalence, worm burden, Bangladesh

Introduction The intestinal nematode Ascaris Zumbricoides is estimated to infect about 24% of the world’s population (CHAN, 1997). Most infected people live in developing countries where warm and humid conditions combined with inadequate sanitation favour the transmission of infections (CROMPTON & PAWLOWSKI, 1985). Worms are not normally or evenly distributed between hosts and it is typical to find that a large proportion of all worms occur ‘In only a small proportion of all hosts (THEINHLAING et al, 1984; ELIUNS et aZ.. 1986: HOLLAND et al., 1989). Studies have shown that the distribution of worms is often empirically described by the negative binomial probability distribution. This distribution is defined by the prevalence of infection (p), the mean worm burden (M> and the parameter k, which varies inversely with the degree of aggregation (ELLIOTT, 1983). Values of k for intestinal worms typically range between 0.1 and 1.O (ANDERSON & MAY, 199 1) and k is often explained in terms of the proportion of worms in hosts: for example, it is said to be not unusual to find 80% of all worms in as few as 20% of all hosts (ANDERSON & MAY, 1991). The aggregation ofworms in a few hosts has important consequences: heavily infected hosts are of concern not only because they are most likely to experience disease, particularly if they are young or malnourished, but also because they may make a major contribution to the transmission of infections within their communities. The degree of aggregation of worms therefore has important implications for our understanding of the epidemiology of infections and how to control disease. As a part of a study of the intensity of infection and reinfection with A. lumbricoides. neonle of all sees livine in a very poor urban area in Bangladesh were treited witg an anthelmintic on 3 occasions over a period of a year and all the worms they expelled were collected (HALL et al., 1992). The present paper examines 3 things. First, it examines the distribution of worms in the community to see how the prevalence of infection and worm burdens *Present address for correspondence: Partnership for Child Development, Wellcome Trust Centre for the Epidemiology of Infectious Disease, South Parks Road, Oxford OX1 3FY. UK; . phone f44 (0)1865 281231, fax +44x0)1865 281245, . e-mail [email protected] Present addresses: l *Instimte of Public Health, Mohakhali, Dhaka 1212, Bangladesh; l **Centre for International Child Health, Institute of Child Health, 30 Guilford Street, London WClE IEH, UK.

vary with age, and between the sexes. Second, using the data on worm burdens for age and sex classes the relationship between several different ways of estimating the degree of aggregation of worms is examined. And finally, to return to the epidemiological context from which the data were derived, it examines how the degree of aggregation of worms within this community varies with age and between the sexes. Subjects and Methods Households were visited in a crowded and very poor area of Mirour. a suburb of Dhaka. Baneladesh. and all their occupants were invited to takepart & the study with the aim of recruiting and treating as many people as possible in 6 months. The age and sex of all potential subjects was recorded. Participation was on the basis of the informed consent of the head of each household and the study had been approved by the Ethical Review Committee of the International Centre for Diarrhoeal Disease Research, Bangladesh (ICDDR,B). Stool examinations and worm recovey All people who agreed to participate were asked to provide a fresh faecal sample which was examined microscopically by a quantitative ether sedimentation technique (HALL, 1981). Whether the eggs of A. Zumbricoides were seen in faeces or not, every subject aged 2 1 year was then treated with pyrantel pamoate (Combantrin; Pfizer, Bangladesh) given as a single dose of 11 mg/kg bodyweight. Pyrantel pamoate paralyses A. lumbricoides so that they can no longer maintain their position in the gut and are expelled intact in the stools (AUDI et aZ., 1995). A single dose of pyrantel pamoate is reported to cure 95% of infections with A. lumbricoides (ELIUNS et al., 1986). After treatment each subject was provided with a lidded plastic chamber pot containing about 50 mL of a 5% v/v

solution

of an antiseptic

(Sepnil:

Square

Pharmaceuticals, Bangladesh) in 0.9% saline. This served to keep stools soft and to reduce unpleasant smells, because many households did not have latrines and the pots were usually stored in the small household compound. Each subject was asked to defaecate into the pot at every bowel movement over the next 24 h and mothers were asked to supervise their children’s defaecation. The pot was replaced with a clean one after 24 h, which was also left for 24 h, so that stools were collected

for at least 48 h after treatment. If subiects did not nass any stools, either in the 1st or 2nd 24 h after treatment, the buckets were left for a further 24 h. The number of

504

ANDREW

worms recovered from each subject was recorded and is termed the worm burden. Subjects were excluded from the study for any 1 of the following reasons: if stools were not collected for at least 48 h after treatment or if subjects reported not collecting all their stools; if a subject returned no worms although A. Zumbricoides eggs had been seen in the faecal sample examined before treatment; or if a subject returned only male worms but eggshad been seen in the faecal sample collected before treatment. The subjects not excluded according to these criteria were classified as having been treated satisfactorily. Analysis of data

To examine the relationship between age, sex and epidemiological parameters the following 11 age classes were used: 1-2, 3-4, 5-6, 7-8, 9-10, 11-12, 13-16, 17-26,27-36,37-46 and 247 years. These 22 age and sex classesgave an average sample size of 80 (range 44136). Subjects were also classed as pre-school children (l-4 years), school-age children (5-14 years) or as teenagers and adults (3 15 years). Because worms were not normally distributed among hosts and because worm burdens could not be transformed to a normal distribution, non-parametric tests of statistical significance were applied to the data to examine all differences in worm burdens between groups. x2 tests or Fisher’s exact test were used to compare proportions. In order to evaluate different measures of aggregation of worms in hosts 2 empirical measures were used: the proportion of subjects with moderate-to-heavy infections, defined as 2 15 worms (HALL et al., 1992); and the proportion of subjects who passed an arbitrary 80% of total worms expelled, termed the empirical aggregation index. These proportions were then compared for all age and sex classeswith the following: (i) k estimated by the method of maximum likelihood for the full and zerotruncated negative binomial distributions, hereafter called full k and zero-truncated K, using software kindly provided by Dr Brian Grenfell (University of Cambridge, UK); (ii) k estimated from the proportion of uninfected subjects, hereafter called uninfecteds’ K, according to the method described by ELLIOT (1983) in which various values of k are tried in the following equation until the 2 sides are equal i log( 1 + (F/L, = log( n/ j0) where f = the mean, n = the sample size and j0 = the number ofuninfected subjects; and (iii) k estimated from moments (the mean ?Eand variance s’) according to ELLIOTT (1983) for sample sizes of >50 as follows i = f2/(s2 -Z) hereafter called moments k; and, finally, (iv) the variance to mean ratio. In the negative binomial distribution the prevalence of infection, p, is related to the mean intensity of infection, M, in the following way p = (1 - (1 + M/k)-k) x 100 This equation was used to examine the relationship between the prevalence and mean worm burdens for all 22 groups using either the value of k determined for the total sample studied or values of k which varied as a function of the mean intensity for the 22 age and sex grouns. A linear function gave the best empirical tit. The fines-were fitted using maximum-likelihood techniques (GUYATT et al.. 1990) and the likelihood ratios were tested for statistical significance. Results

Over a period of 6 months 2884 eligible people living in 502 households were askedto take part in the study and

HALL

ETAL.

1765 people (61.2%) from 490 households were dewormed satisfactorily. In all age groups older than I1 years significantly more males participated in the study than females (P < 0.002). The prevalence of infection with A. lumbricoides based on worm recovery was 85.6% while the prevalence based on stool microscopy was 77*4%, indicating that microscopy had missed 144 (8.2%) infections. Table 1 shows the prevalence and mean worm burdens in the 22 age and sex classes, and Figure la shows separately for each sex the relationship between age and the prevalence of infection. Children in this community acauire A. lumbricoides verv earlv in life: 67% of children agid l-2 years were infected. The prevalence of infection among males was significantly lower than females in the 3 oldest age-groups (all P < 0.05). Figure lb shows separately for each sex the relationship between age and the mean worm burdens. By the age of l-2 years children already had a mean of 7.4 worms (maximum, 43) but the school-age group was, as usual, most heavily infected with a mean of 20.2 worms, and nearly 10% of children passedmore than 50 worms. Figure lb also reveals significant differences between the sexes.Among males the peak mean worm burden of 2 1.8 worms was observed in the 9- 10 years age class and was significantly lower in the 3 oldest male age classes,at 9.6 worms (P< 0.001). Among females, in contrast, although the mean worm burden reached a similar peak (23.4 worms), it did so in an older age-group (13-16 years) and nearly 60% of these adolescent girls were moderatelv to heavilv infected (Table 1). Althouah mean worm burdens among older age classesof females were significantly lower than this peak (all P< O.Ol), the difference was much smaller than among males, so that females in each of the 3 oldest age-groups had significantly larger worm burdens than males in the same agegroups (16.1 vs9.6worms, P
3z.00 31.7

16.4 18.1

iG

iti

i&

c F

M F M F M F

M F

17-26

27-36

37-46

347

l-4

17.3

1765

791 974

151 143 375 400 265 431

;4” 44

:; 132 62 136 58

z96

73

101

z: 94 97

93

(n)

Subjects

1511

661 850

109 112 339 359 213 379

iz 41

4: 70 76 53 74 60 106 44 120 47

:: 87 90

72 73

(n> (%I

85.6

83.6 87.3*

72.2 78.3 90.4 89.8 80.4 87.9* *

g&2** 71.0 81.0 95.0* 77.8 93.2*

63.8 69.6 77,4 83.9 89.5 90.4 89.7 89.1 87.7 90.9 95.9 88.4 89.8 91.4 87.0 80.3

Infected

16.7

15.4 17.8***

11.4 13.7 20.2 20.2 10.8 17*0***

9.4 15.9***

g***

l;:fj**

6-9 . 11.; 17.4 20.0 18.3 21.4 20.3 21.8 18.0 18.9 22.2 16.5 23.4* 12.2 17.1

Mean

Worm

23.5

23.6 23.2

< 0.001.

0*705+++

0.649+++ 0.760+++

0.463 0.486 0.844++ 0,874 0.641+++ O-811++

< 0.01; +++P

16.5 25.6 25.4 25.1 17.6 19.9

12.0 14.5 16.5 27.1 29.4 35*3 30.6 17.7 23.0 16.8 17.9 25.6 17.8 25.2 14.1 23.3 18.4 19.1 26.8 19.7 13,8 12.9

iii1 neg. binomial

with Ascati

0.412 0.419 0.543+ 0.587 0.722 0.765 0.773 0,974 0.880 1.025 1.195 0*800+ 0.97 1 1.011 0.791 0.569++ 0.446 0.847 0.648+ 1.076 0.647 1,171

ofinfection

Variance: mean ratio

+P < 0.05; ++P

0.395

0.377 0.406

0.344 0.322 0.42 1 0.432 0.362 o-415

0.328 0.304 0.387 0.345 0.389 0.383 0,392 0,455 0.452 0.468 0.486 O-407 0.44 1 0.457 0.406 0.37 1 0.306 0.419 0.379 0.438 0.370 0.454

index

Empirical aggregation

distribution:

11.0

9-o 12.0

7.0 7.0 13.0 13.5 6.0 12.0

4.0 3.0 10.0 8.0 13.0 11.0 13.0 16~0 15.0 14.0 15.0 13.0 13.0 17.0 7.0 11.0 4.0 11.0 5.5 13.0 5.5 12,o

Median

burden

in terms ofthe prevalence

Significant differences between the sexes: *P < 0.05; **P < 0.01; ***P < 0.00 1. Significantly different from the negative (neg.) or truncated (mmc.) negative binomial

All

All

a15

5-14

ic

13-16

;:; 8.8

iG

11-12

;:; 5.6 7.6 7.5 9.6 9.6 11.5 11.6 14.2 14.4 20.6 22.0 31.9 32.1 41.6 41.0 58.1 56.9

:::

1.6

M

F

iti F M

M F M

Sex

Mean age (years)

9-10

7-8

5-6

3-4

l-2

Age (years)-

Table 1. The characteristics of22 age and sex classes in Bangladesh measures of aggregation (see text for definitions)

1.088+++

1.030+ 1.141+

1.231 0.692 1.115 1.283 1.067 1.201

1.578 0.669 1.300 0.809 0.855 0.849 1.010 1,718 1.672 1.449 1.267 1.275 1.433 1.538 1.005 1.155+ 0.960 1.216 o-886+ 1.101 1.343 1.461

neg. binomial

tll.UlC.

k

hmbricoides,

0.745

0.680 0.802

0.734 0.556 0.827 0.840 0.655 0.897

0.992 1.138 1.120 0.900 0.986 0.971 0.935 0.764 0.552 0.856 0.380 0.926 0.739 1.333

1,129

0.620 0.593 0.916 0.664 0.706 0.535 0.721

est. from moments

k

0.568

0.400 0.603

0.370 0.441 0.686 0.660 0.532 0.637

0.329 0.388 0.419 0.515 0.651 0.715 0.643 0,634 0.570 0.743 1.101 0.589 0.720 0.689 0.699 0.436 0.378 0.67 1 0.575 1.049 0.506 0.926

and

39.9

37.4 41.9

33.1 30.1 49.3 49.5 24.5 40.1

37.9 46.3 38.3 48.5 52.5 52,l 46.8 50.7 45.3 40.7 58.0 31.9 38.6 24.2 37.5 13-8 43.8 20.4 38.6

Percent with 215 worms

of infection

k est. from uninfected

the intensity

s 9

h

@ 2 B

506

ANDREW HALL

ETAL.

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0.6

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20 10 30 40 Mean age of age class (years)

50

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60

Fig. 1. (a) Tire prevalence of infection with Ascaris Zumbricoides, for each of 11 age classes, by sex, in an urban community in Bangladesh. (b) The mean worm burdens with A. lumbricoides, for 11 age classes, by sex, in an urban community in Bangladesh. *P<@O5, **P
(b) 4 10

20 30 40 50 Percentage with 2 15 worms

60

Fig. 2. (a) The relationship between the empirical aggregation index (the percentage of subjects who passed 80% of all worms) and full negative binomial k for Ascarij lumbri~oides in 22 age and sex classes in an urban community in Bangladesh. (b) The relationship between the percentage ofsubjects who passed 5 15 worms in the same groups and community with the full negative binomial k.

Table 1 shows that, in contrast to the empirical aggregation index, the percentage of subjects with moderate-to-heavy infections ranges more widely, from 155% to 58%, over the same range in prevalence. Figure 2b shows that the percentage of subjects with 2 15 worms was less tightly correlated with full k (r = 0.672,

Table 2. Coefficients of correlation between statistics describing the aggregation ofAscaris 1765 people in 22 age and sex classes in Bangladesh and parameters ofbotb worm burdens aggregation

lumbricoides and measures

Empirical aggregation index”

Maximum likelihood full k

Prevalence (worm recovery) Prevalence (eggs in stools)

0+350*** 0.869***

0.898*** 0*863***

0.764*** 0.793***

Worm burden: Arithmetic mean Median Maximum Geometric mean

0.670”** 0.863”** 0.386 0.834***

0.619** 0.795*** 0.345 0.805***

0.940*** 0.950*** 0.655*** 0.938***

0.92;*** 0.796*** 0.959***

0.599**

0.746*** 0,672*** 0.401* 0.653*** 0.502* 0.333

0.670*** 0.619** 0.282 0.483* 0.459* 0.567**

Statistics

Aggregation: Emuirical aearegation index k max. likelyhood full k max. likelihood zero trunc. k est. from moments k est. from no. uninfected Variance:mean ratio

0.945*** _ ~~ 0.599** 0.823”** 0.780*** -0-020

“The empirical aggregation index is the proportion *P<0.05;**P<0.01;***P<0.001.

70

-

0*454* 0.796*** 0.908*** -0.017

% having 315 worms

of subjects who passed an arbitrary 80% of worms.

Mean worm burden

in of

IN BANGLADESH

A. LUMBRICOIDES

507

P < 0.00 1) but indicates that as the degree of aggregation decreases the proportion of moderately to heavily infected subjects increases in a linear fashion. At a K of around 1 about 60% of subjects are likely to be moderately or heavily infected (2 15 worms). This threshold is arbitrary, and the degree of morbidity is also related to the age and current health of subjects. If morbidity was experienced by children aged l-4 years with 210 worms, by children aged 5- 14 years with ~20 worms and by adults with 230 worms then 28.7% of the sample would be diseased. Figure 3a shows how full K varies with the prevalence of infection and indicates that the degree of aggregation decreases 3-fold from about O-4 to 1.2 over a narrow 30% range in prevalence, from 64% to 95%. The relationship between iz and prevalence is not likely to be linear and indicates that at prevalences lower than 60% the degree of aggregation is less than 0.4. The relationship between prevalence and the degree of aggregation of worms is perhaps easier to predict from Figure 3b, which shows that the prevalence and empirical aggregation index are linearly correlated (r = 0.85, P < O.OOl), and that the regression line points towards the origin. At the highest prevalences the empirical aggregation index approaches around 0.50. Figure 3c shows the relationship between the prevalence and the percentage of subjects who passed 215 worms. The percentage of subjects with more than 15 worms rises exponentially at prevalences above 60% and above a prevalence of 80% there is a wide degree of scatter which indicates that between 30% and 60% of people may be moderately to heavily infected. The relationship between the same 3 measures of .a 1.4 $ 1.2

aggregation and the mean worm burden are shown in Figure 4, and all are roughly linear over the range of values observed. The relationship between the mean worm burden and the empirical aggregation index (Figure 4b) is unlikely to be linear at lower mean worm burdens, and a logarithmic function (not shown) empirically gives a fit that would converge with the origin. Only in Figure 4c does the trend point towards the origin and if the equation for the line is constrained through zero (which makes a negligible change in the correlation coefficient, of 0.002) then for every increase in the mean burden of 1 worm the percentage of hosts with 215 worms increases P
by abour 2.4% (y = 2,386~;

I = 0.939;

Figure 5 shows the relationship between the prevalence of infection and the mean worm burden among the 22 classes. The Figure shows that the maximum likelihood fit using K as a linear function of the mean worm burden (k = a + bM; a = 0.3035, b = 0.0299) gave a significantly better fit than using a single value of k of 0.705 derived from the total population (x2 = 27-9, P < 0.001). To return to the population from which the data on the degree of aggregation of A. lumbricoides were derived, Figure 6 shows how full K, the empirical aggregation index and the percentage with 2 15 worms vary with age and by sex. Figure 6a shows among males a convex pattern in which k increases 3-fold to reach a peak in boys aged 1 1- 12 years and is lower among the 3 oldest agegroups. Among females the pattern is different and suggests that k rises to a similar peak but shows much less convexity so that values of k for the 2 oldest female age classes are around twice the values for males of the

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Percentage infected Fig. 3. The relationship between the prevalence of infection community

lumbtioides

in 22 age and sex classesin an urban

in Bangladesh and (a) k of the negative binomial

distribution; (b) an empirical aggregation index (the percentage ofsubjects who passed 80% ofall worms); and (c)the percentage of subjects who passed 5 15 worms.

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Fig. 4. The relationship in 22 age and sex classesin an urban community in Bangladesh between the mean worm burden of Ascaris lumbricoides and (a) k of the negative binomial distribu-

tion; (b) an empirical aggregation index (the percentage of subjects containing 80% of all worms); and (c) the percentage of subjects who passed 2 15 worms.

ANDREW EL%LLETAL. men, if it is convex at all. Table 1 shows that a third of children aged l-4 years and nearly a half of all school-age children had 2 15 worms.

fl 0

5

0

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-Lineark

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- - - Constanr

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10 15 Mean worm burden

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Fig. 5. The relationship between the mean worm burden with Ascati lumbri-coides and the prevalence of infection in 22 age and

sex classesin an urban community in Bangladesh. Also shown are a maximum-likelihood fit using k as a linear function of the mean worm burden (seeFig. 4a) and a fit for constant k derived from the total sample (see Table 1). ~

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Fig. 6. The relationship between age and sex for 11 ageclassesof subjects living in an urban community in Bangladesh and (a) full k of the negative binomial distribution; (b) an empirical aggregation index (the percentage of subjects who passed 80% of all worms); and (c) the percentage of subjects who passed 3 15 worms. same age and are similar to the peak reached during late childhood. The empirical aggregation index (Fig. 6b) shows a similar pattern but the range in values is much narrower. Figure 6c shows clearly how adult women are more likely than men to have moderate-to-heavy infections and the degree of convexity is much smaller than for

Discussion This is the largest study of its kind to date which has carefully quantified burdens with an intestinal worm in a population of hosts in which there was no previous parasite control programme, so worm populations were probably at equilibrium. In many communities the mean burden of A. lumbricoides tends to be lower among adults than children, and the cross-sectional relationship between age and intensity is typically convex. The smaller average worm burdens in adults has been explained by 2 main factors: as a result of changes in behaviour with age that reduce exposure to infective stages, perhaps because adults are more careful than children in their personal hygiene; as a result of acquired resistance to infection which prevents the establishment or survival ofworms; or perhaps as a combination of both exposure and immunity (ANDERSON & h4AY, 1991). Three observations from the present study suggest that exposure plays a large role in generating the pattern of infection observed here. First, the highest mean worm burdens were observed in different age-groups in males and females: among males aged 9- 10 years and among females aged 13- 16 years (Fig. lb). Second, both the prevalence and intensity of infection were significantly lower among adult males than among adult females (Fig. l), and the 3 groups of adult males had mean worm burdens not much higher than the youngest children in the study, an age-group which is likely to have had much less exposure to the eggs of A. lumbricoides. Third, adult women in the 2 oldest age classes, who might be expected to have experienced considerable previous exposure to A. lumbricoides, had mean worm burdens and values of full k as high as most groups of school-age children, indicating that these groups were most heavily infected and that worms were least aggregated. To explain these observations in immunological terms it would be necessary to conclude that in this community males are able to mount a significantly more effective than females, immune response against A. lumbricoides and at an earlier age as well. There is some evidence for differences between adolescent boys and girls in the intensity of reinfection with Schistosoma spp., and hormonally mediated differences in immunity have been proposed as an explanation (FULFOFCDet al., 1998), but this theory has been questioned for Schistosoma haematobium at least (FELDMEIER et al., 1998). If the differences between the sexes were to be explained in terms of some sort of ‘peak shift’ phenomenon (WOOLHOUSE, 1998) this would imply that in the first 10 years of life boys in the same community were exposed to more infective stages than girls, and there is no evidence of a difference in mean worm burdens (Table 1). The shift in the peak intensity of infection to a later age is also usually associated with a lower peak (WOOLHOUSE, 1998), which was not observed either in this community. The most likely explanation for the observations presented here for A. lumbricoides is that adolescent and adult males are less exposed to infection than females of the same age because of social and cultural practices that separate the sexes at puberty. In Bangladesh adolescent girls and women are traditionally confined to the home and its immediate surrounds to care for the house and their children while males have greater freedom of movement and typically leave the immediate community to work. The evidence presented here of infections in very young children (Fig. l), and the fact that reinfection in the youngest children, who stay in and around the household, occurs very rapidly (HALL et al., 1992), indicate that transmission in this crowded slum is very intense. The absence of drains and the fact that many latrines were simply private places to defaecate, either

A. LUMBRICOIDES

509

IN BANGLADESH

directly on to the ground or into shallow pits which overflow during heavy rains, mean that faecal contamination of the environment around households is very heavy. Practices such as cleaning and caring for young children, many of whom defaecate directly in the open, are likely to expose women to infection. The fact that the men who provided their faeces for 48 h after treatment were more likely to be those who were not at work (although we tried to deworm adult males over weekends so that they could participate) suggests that mean worm burdens amongst all men in this community may be even lower than recorded. Only 24% of men aged > 17 years passed 2 15 worms compared with 40% ofwomen of the same age range (Fig. 6~). Differences in mean worm burdens between the sexes have been noted in 1 other study of which we are aware: in southern India EWNS et al. (1986) found that adolescent and adult females passed more A. Zumbricoides after treatment than males. Similar differences in behaviour between the sexes may also occur in southern India. No differences between the sexes have been reported in other studies which recovered A. lumbricoides after treating people of all ages, including studies in Jamaica (BUNDY et al., 1987), Mexico (FORRESTER et al., 1988), Korea (C~~~etal., 1985) andIran (C~o~~etal., 1982). The negative binomial probability distribution has proved to be a useful way of describing the characteristic aggregation of worms in hosts, but it is an empirical fit rather than being driven by any known biological mechanism. The parameters ofthe negative binomial, k and M, are difficult to estimate because it is necessary to expel and recover worms to calculate them. Our data have enabled K to be put in perspective by examining it in comparison with empirical indices, and then to see how they all vary with prevalence, mean worm burdens and with age and sex. For 19 of the 22 classes defined in the present study the distribution of worms was described by the negative binomial. A S-fold range in full k, from about 0.4 to 1.2, was equivalent to a relatively small increase in the empirical aggregation index from O-30 to 0.49 (Fig. 2a) but was associated with a similar, 3-fold increase in the percentage of subjects in each group with > 15 worms, from 155% to 58.0% (r = 0.672; Fig. 2b). Although the data suggest that even at low values of full K of around 0.4, 80% of all worms were still found in 30% of hosts, Figure 2a indicates that the relationship is not likely to be linear at lower values of both parameters. Of the trends indicated by the observed points in Figures 3 and 4, which show how the prevalence and mean worm burdens are related to full K, to the empirical aggregation index and to the percentage with 215 worms, only Figures 3b and 4c have trend lines which, if extrapolated, go through zero. Whether K approaches zero at lower values of prevalence and mean worm burden cannot be said from these data, but Figures 3a and 4a are similar in their slope and shape to-Figures shown bv GUYATT et ~2. (1990) who looked at the same relations-hips with K using data’from 6 expulsion studies of A. lumbricoides and covering a wider range in prevalence and mean worm burdens. GUYA-IT et al. (1990) examined values of k ranging between 0.36 and 0.8 1, and this lowest value was reported from Korea at a prevalence of 16.5% and a mean worm burden of only 0.2 worms/ host (CHAI et al., 1985). It seems that most of the lowest recorded values of k for A. Zumbricoides lie close to 0.3 and it is interesting to note that the plots of both prevalence and worm burden against k shown in the analysis of G~ATT et al. (1990) have an intercept at which k = 0.33. If similar lines are fitted to the data in Figures 3a and 4a, the lines also intercept at k z 0.30. Above a prevalence of 50-60% the values of k shown in Figure 3a increase exponentially, which is similar to the relationshiu shown bv GUYAIT et aZ. (19901. The common feamres of an analysis of A. &tbri>oides in several communities and the analysis of worms in 22 age and

sex classes within 1 community presented here suggest that the relationships between the prevalence, worm burdens and measures of aggregation are similar both within and between communities. The statistic k as a measure of aggregation is difficult to grasp and its description sometimes gives the impression that worms are always highly aggregated. The evidence presented here suggests that at prevalences of <50% worms are, indeed, highly aggregated, but above this prevalence the degree of aggregation rapidly diminishes. It seems that the range in values of k is perhaps better captured by expressing it in terms of the percentage of subjects who are moderately to heavily infected than in terms of the percentage of subjects who contain a certain percentage of all worms. Although it is also known that moderately to heavily infected people are likely to become moderately to heavily reinfected after treatment (KEYMER & PAGEL, 1990), we have shown previously that over 3 rounds of treatment during a period of a year in this same community, about two-thirds of all subjects had 115 worms at least once (HALL et al., 1992). This means that over the medium-to-long term more people will benefit from treatment of their infections than would be expected from a cross-sectional study of the distribution ofworms. This analysis shows that the degree of aggregation of worms in hosts varies with age and sex in this community, and worms become more dispersed between hosts with increasing prevalence (exponentially) and mean worm burden (linearly), so that a larger proportion of subjects have moderate-to-heavy infections as full k increases (linearly). In public health terms the school-age group is, as expected, most at risk of disease in this community, but the intensity of infection in pre-school children and their mothers suggests that they too should become targets for parasite control activities in the growing slums of cities such as Dhaka. Acknowledgements

This study was supported by the British Overseas Development Administration (now Deoartment for International Development) and the United Staies AID Project Development Fund of the ICDDR,B. A. H. acknowledges current support from donors to the Partnership for Child Development including the UNDP and the Rockefeller Foundation. We thank Professor Roger Eeckles for his interest, the project staff for their diligence and enthusiasm for collecting worms, MariaGloria Basifiez for her help with maximum-likelihood analysis, and the subjects of this studv for their coooeration. The ICDDR. B is supported by countries, international agencies and donors which share its concern for the health problems of developing countries. References Abdi, Y. A., Gustaffson, L. L., Ericson, 0. & Helgren, U. (1995). Handbook of Drugs for Tropical Parasitic Infections. London: Taylor & Francis. Anderson, R. M. & May, R. M. (1991). Infectious Diseases of Humans. Oxford: Oxford University Press. Bundy, D. A. I’., Cooper, E. S., Thompson, D. E., Didier, J. M. & Simmons, I. (1987). Epidemiology and population dynamics of Ascaris lumbricoides and Tri~huris triihiura infection in the same community. Transactions of the Royal Society of Tropical Medicine and Hygiene, 81, 987-993. Chai, J.-Y., Kim, K.-S., Hong, S.-T. & Soe, B.-S. (1985). Prevalence, worm burden and other epidemiological parameters of Ascaris Zumbricoides infection in rural communities in Korea. KoreanJournal of Parasitology, 23, 241-246. Chan, M.-S. (1997). The global burden of intestinal nematode infection-fifty years on. Parasitology Today, 13,438-443.

Croll, N. A., Anderson, R. M., Gyorkos, T. W. & Ghadirian, E.

(1982). The population biology and control of Ascaris lumbricoides in a rural community in Iran. Transactions of the Royal Society of Tropical Medicine and Hygiene, 76, 187- 197. Crompton, D. W. T. & Pawlowski, Z. (1985). Life history and development of Ascaris Zumbricoides and the persistence of human ascariasis. In: Ascardasis and its Public Health Signifycame, Crompton, D. W. T., Nesheim, M. C. & Pawlowski, Z. S. (editors). London: Taylor&Francis, pp. 9-23. Elkins, D. B., Haswell-Elkins, M. & Anderson, R. M. (1986).

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The epidemiology and control of intestinal helminths in the Pulicat Lake region of Southern India. I. Study design and pre- and post- treatment observations on Ascar& lumbricoides infection. Transactions of the Royal Society of Tropical Medicine and Hygiene, g&774-792.

Elliott, J. M. (1983). Some Methods for the Statistical Analysis of Samples of Benthic Invertebrates, 2nd edition, reprinted. Freshwater Biological Association, Scientific Publication, no. 25. Feldmeier, H., Poggensee, G. & Krantz, I. (1998). Puberty and age-intensity profiles in schistosome infection: another hypothesis. Parasitology Today, 14,435. Forrester, J. E., Scott, M. E., Bundy, D. A. P & Golden, M. H. N. (1988). Clustering of Ascaris lumbricoides and Trichuris trichiura infections within households. Transactions of the Royal Society of Tropical Medicine and Hygiene, 82,282-288.

Fulford, A. J. C., Webster, M., Ouma, J. H., Kimani, G. & Dunne, D. W. (1998). Puberty and age-related changes in susceptibility to schistosomeinfection. Parasiwlogy Today, 14, 23-26. Guyatt, H. L., Bundy, D. A. I’., Medley, G. F. & Grenfell, B. T. (1990). The relationship between the frequency distribution of Ascaris lumbricoides and the prevalence and intensity of infectionin humancommunities. ParasiwZogy,101,139-143. Hall, A. (1981). Quantitative variability of nematode egg counts in faeces: a study among rural Kenyans. Transactions

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682-687. Hall, A., Anwar, K. S. & Tomkins, A. M. (1992). The intensity of reinfection with Ascari? lumbricoides and its implications for parasite control. Lancet, 339, 1253- 1257. Holland, C. V., Asaolu, S. O., Crompton, D. W. T., Stoddart, R. C., Macdonald, R. & Torimior, S. E. A. (1989). The epidemiology of Ascarik lumbricoides and other soil-transmitted helminths in primary school children from Ile-Ife, Nigeria. Parasitology, 99,275-285. Keymer, A. & Pagel, M. (1990). Predisposition to helminth infection. In: Hookwonn Disease. Current Status and New Directions, Shad, G. A. & Warren, K. S. (editors). London: Taylor & Francls, pp. 177-207. Thein-Hlaing, Than-Saw, Htay-Htay-Aye, Myint-Lwin & Thein-Maung-Myint (1984). Epidemiology and transmission dynamics of Ascaris Zumbricoides in Okpo village, rural Burma. Transactions of the Royal Sociey of Tropical Medicine and Hygiene, 78,497-504.

Woolhouse, M. E. (1998). Patterns in parasite epidemiology: the peak shift. Parasitology Today, 14,428-434. Received 4 May 1999; revised 5 July publication 14 July 1999

OF TROPICAL MEDICINE Denis Burkitt Fellowships

1999; accepted for

AND HYGIENE

The Denis Burl&t Fund was set up by his family in memory of Denis Burkitt, FRS, who died in 1993; it is administered by the Royal Society of Tropical Medicine and Hygiene. One Fellowship (maximum value E7000) or two separateFellowships (of E3500 each) are awarded annually for practical training, travel, or direct assistancewith a specific project (preferably clinico-pathological, geographical or epidemiological studies of non-communicable diseasesin Africa). Applications must be made at least six months before the commencement of the proposed study (by 15 March or 15 September in each year). A short report on the study should be submitted, within 3 months of the recipient’s return. Application forms are available from the Administrator, Royal Society of Tropical Medicine and Hygiene, Manson House, 26 Portland Place, London, WlN 4EY, UK; fax +44 (0)20 7436 1389, e-mail [email protected]

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SOCIETY OF TROPICAL MEDICINE AND HYGIENE Robert Cochrane Fund for Leprosy

The fund, in memory of the great leprologist Robert Cochrane, is administered by the Royal Society of Tropical Medicine and Hygiene. It is used to finance up to three travel fellowships each year to a maximum value of El000 each. The fund will support travel for l Leprosy workers who need to obtain practical training in field work or in research l Experienced leprologists to provide practical clinical training in a developing country There is no restriction on the country of origin or destination providing the above requirements are met. Applications

must be made at least six months ahead of the proposed trip, sponsored by a suitable representative

of the applicant’s employer or study centre and agreedby the host organization. A short report on the travel/study should be submitted,

within

one month of the recipient’s

return. Application

forms are available from the

Administrator, Royal Society of Tropical Medicine and Hygiene, Manson House, 26 Portland Place, London, WlN 4EY, UK; fax f44 (0)20 7436 1389, e-mail [email protected]