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Immunization coverage required to prevent outbreaks of dog rabies
Vaccine, Vol. 14, No. 3, pp. 185-186, 1996 Copyright 0 1996 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0264-410X/96 $15+0.00
Elsevier 0264-410X(95)00197-2
ELSEVIER
Short Papers Immunization coverage required to prevent outbreaks of dog rabies Paul G. Coleman* and Christopher
Dye*?
WHO recommends that 70% of dogs in a population should be immunized to eliminate or prevent outbreaks of rabies. This critical percentage (p,.) has been established empirically from observations on the relationship between vaccination coverage and rabies incidence in dog populations around the world. Here, by contrast, we estimate pC by using epidemic theory, together with data available from four outbreaks in urban and rural areas of the USA, Mexico, Malaysia and Indonesia. From the rate of increase of cases at the beginning of these epidemics, we obtain estimates of the basic case reproduction number of infection, R,, in the range 1.62-2.33, implying that pC lies between 39% and 57%. The errors attached to these estimates of p, suggest that the recommended coverage of 70% would prevent a major outbreak of rabies on no fewer than 96.5% of occasions. Keywords: Rabies; dog: basic case reproduction
number:
vaccination
coverage;
About 95% of all reported animal cases worldwide are in dogs, and over 90% of human rabies fatalities are attributable to rabid dogs’. Mass vaccination is one of the principal methods of dog rabies control (with restriction of dog movement and the elimination of strays), and the critical percentage of dogs which need to be vaccinated (@ to prevent or control an outbreak is said to be 70%2,-. This criterion apparently originated as the consensus among veterinary practitioners in New York State during the 1940s4, and is therefore purely empirical. Observations worldwide on the relation between vaccination coverage and the reduction in rabies incidence have increased confidence in this figure”, but pC obtained by trial-and-error needs to be underpinned by calculations based on epidemic theory. We begin with a simple compartmental model of dog rabies in which all animals (population size Iv) are assumed to be susceptible (S), latently infected (L) or infective (I). The per capita rate at which susceptibles acquire rabies virus from infectives is j?, so newly infected animals arise at a rate PSZlweek. Infected animals remain in the latent class for a period Z=lla weeks (cr is the rate at which latent animals become infective), and infective animals have a life expectancy of f=l/y weeks (y is the death rate of rabid dogs). Deaths from other causes and births are both negligible on the timescale of a rabies epidemic, and can safely be ignored. The generation time, g, in this model is l+f=lla+lly weeks, and the basic case reproduction number of infection5, R,,is j3iVlly.R, depends explicitly on N, so we expect R, to be greater in larger (and probably *Department of Medical Parasitology, London School of Hygiene and Tropical Medicine, Keppel Street, London WClE 7HT, UK. tTo whom correspondence should be addressed. (Received 6 February 1995; revised 31 August 1995; accepted 12 September 1995)
epidemic
higher density) dog populations. If R, varies from one population to another then so too will pC, which immediately questions the view, implicit in much of the literature’-. , that the same criterion can be applied to dog populations everywhere. With these definitions and assumptions, we can write down formally a set of coupled, first order, non-linear differential equations describing rabies dynamics, as follows: dS
-=
dtu
2 dZ -= dt
-/3Lsz
= psz- aL
CTL-vz. ’
These may be solved to show that the incidence of cases is expected to grow exponentially during the early stages of an epidemic (when S=Zv) at a rate roughly equal to (R, - 1)/g. More precisely, r(t) Mkexp(rt), where y(t) is the incidence between times t and t - 1, k is a constant, and to a good approximation R,=l+r(rZf+g). We can therefore estimate r by fitting the first of these two equations to data describing the exponential growth in incidence during an outbreak, and get R, by using the second. The percentage to be immunized then comes from the well-known relation5 p,=lOO(l - l/&). Where an outbreak occurs in a partially vaccinated dog population, estimates of & and pC obtained this way will be too low; R. needs to be corrected upwards by dividing by the fraction of dogs (s) which were unvaccinated prior to the outbreak. Foggin has provided the best estimates of latent and infective periods, and therefore generation time, because his data come from natural rather than experimental
Vaccine
1996 Volume
14 Number
3
185
Short
paper:
Table 1
PG.
Coleman
and
C. Dye
Estimates of R,, pc and upper 95% confidence
Study
Country
Region
Setting
7
USA
8 9 10
Mexico Indonesia Malaysia
Memphis and Shelby County, Tennessee Hermosillo Central Java Kuala Lumpur
Urban and rural Urban Rural Urban
limits for p,, calculated
Weeks of exponential growth
Number of observations
r
SE.(r)
S
/3,,
S.E.(&)
P,
for P,
11
11
0.172
0.046
0.840
2.334
0.556
57.1
71.0
-22 12 -17
5 12 4
0.175 0.144 0.116
0.023 0.057 0.028
1.000 1.000 1.000
1.981 1.789 1.627
0.418 0.451 0.302
49.5 44.1 38.5
64.5 62.8 55.2
infections. He presents the intervals between biting and the appearance of clinical signs for 68 dogs attacked by other dogs or jackals, from which we calculate a mean of 4.18 (SE. 0.27) weeks and a median of 3.45 (S.E. 0.21) weeks. We use the mean here because it gives more conservative (larger) estimates of R, than the median (it is also longer than obtained from most experimental infections). Although there is some evidence’ that dogs are infective before signs develop, transmission is more likely when dogs behave rabidly, so we assume that latent and incubation periods are equal. With regard to the infective period, Foggin unfortunately gives only the mean (0.81 weeks) and range (0.29-1.71 weeks). We adopt his mean, but we cannot calculate the variance, so our estimates of S.E. (R,) below exclude this source of error. Four studies of dog rabies epidemics in the USA7, Mexico’, Indonesia’ and Malaysia” give the incidence of cases through time (Table I). The first of these outbreaks occurred despite an ongoing vaccination campaign, though the data in Ref. 7 suggest that no more than 16% of dogs were protected. The regression analyses leading to estimates of R, and pc were carried out in GLIM” assuming a Poisson error distribution, and restricting the data to confirmed cases of dogss” or animal7 rabies. R, varies from 1.63 to 2.33, and hence pc lies in the range 39-57%. None of the estimates in Table 1 differs significantly from any other (see S.E.s in Table 1), so the variation could be due to chance alone. There is no evidence to suggest, for example, that R, is greater in larger dog populations, though we might expect to see such an effect in a larger set of data (see above). We are interested not only in the point estimates ofp,, but also in the upper confidence limits. The upper 95% limits fall between 55% and 7 l%, that is, generally below 70%. Put another way, if the errors surrounding the point estimate of R, are roughly normal, we expect a
186
using data from four studies of dog rabies epidemics
Vaccine 1996 Volume 14 Number 3
95% upper confidence limit
coverage of 70% to prevent a major outbreak from occurring on no fewer than 96.5% of occasions. These data and our analysis therefore suggest that immunizing 70% of dogs, following the current WHO recommendation, will indeed be sufficient to prevent or control outbreaks of dog rabies.
ACKNOWLEDGEMENTS PGC is supported by a MRC research studentship.
REFERENCES 1
2 3
7
8
9
10 11
Fekadu, M. Canine rabies. In: The Natural History of Rabies (Ed. Baer, G.M.), 2nd edn. CRC Press, Boca Raton, 1991, pp. 367-378 World Health Organization. Guidelines for Dog Rabies Control. VPH/83.43 Rev. 1. WHO, Geneva, 1987 Beran, G.W. Urban rabies. In: The Natural History of Rabies (Ed. Baer, G.M.), 2nd edn. CRC Press, Boca Raton, 1991, pp. 427-443 Korns, R.F. and Zeissig, A. Dog, fox and cattle rabies in New York State. Am. J. Pub/. H&h 1948, 38, 50-65 Anderson, R.M. and May, R.M. Infectious Diseases of Humans. Oxford University Press, Oxford, 1991 Foggin, CM. Rabies and rabies-related viruses in Zimbabwe: historical, virological and ecological aspects (dissertation). University of Zimbabwe, Harare, 1988 Tierkel, E.S., Graves, L.M., Tuggle, H.G. and Wadley, S.L. Effective control of an outbreak of rabies in Memphis and Shelby County, Tennessee. Am. J. Pub/. Hlth 1950, 40, 10841088 Eng, T.R., Fishbein, H.E., Talamante, H.E. eta/. Urban epizootic of rabies in Mexico: epidemiology and impact of animal bite injuries. Bull. WHO 1993, 71, 615-624 Waltner-Toews, D., Maryono, A., Akoso, B.T., Wisynu, S. and Unruh, D.H.A. An epidemic of canine rabies in Central Java, Indonesia. Preventive Vet. Med. 1990, 8, 295-303 Wells C.W. The control of rabies in Malaya through compulsory mass vaccination of dogs. Bull. WHO 1954, 10, 731-742 Becker, N.G. fhe Analysis of Infectious Disease Data. Chapman and Hall, London, 1989
Elsevier 0264-410X(95)00197-2
ELSEVIER
Short Papers Immunization coverage required to prevent outbreaks of dog rabies Paul G. Coleman* and Christopher
Dye*?
WHO recommends that 70% of dogs in a population should be immunized to eliminate or prevent outbreaks of rabies. This critical percentage (p,.) has been established empirically from observations on the relationship between vaccination coverage and rabies incidence in dog populations around the world. Here, by contrast, we estimate pC by using epidemic theory, together with data available from four outbreaks in urban and rural areas of the USA, Mexico, Malaysia and Indonesia. From the rate of increase of cases at the beginning of these epidemics, we obtain estimates of the basic case reproduction number of infection, R,, in the range 1.62-2.33, implying that pC lies between 39% and 57%. The errors attached to these estimates of p, suggest that the recommended coverage of 70% would prevent a major outbreak of rabies on no fewer than 96.5% of occasions. Keywords: Rabies; dog: basic case reproduction
number:
vaccination
coverage;
About 95% of all reported animal cases worldwide are in dogs, and over 90% of human rabies fatalities are attributable to rabid dogs’. Mass vaccination is one of the principal methods of dog rabies control (with restriction of dog movement and the elimination of strays), and the critical percentage of dogs which need to be vaccinated (@ to prevent or control an outbreak is said to be 70%2,-. This criterion apparently originated as the consensus among veterinary practitioners in New York State during the 1940s4, and is therefore purely empirical. Observations worldwide on the relation between vaccination coverage and the reduction in rabies incidence have increased confidence in this figure”, but pC obtained by trial-and-error needs to be underpinned by calculations based on epidemic theory. We begin with a simple compartmental model of dog rabies in which all animals (population size Iv) are assumed to be susceptible (S), latently infected (L) or infective (I). The per capita rate at which susceptibles acquire rabies virus from infectives is j?, so newly infected animals arise at a rate PSZlweek. Infected animals remain in the latent class for a period Z=lla weeks (cr is the rate at which latent animals become infective), and infective animals have a life expectancy of f=l/y weeks (y is the death rate of rabid dogs). Deaths from other causes and births are both negligible on the timescale of a rabies epidemic, and can safely be ignored. The generation time, g, in this model is l+f=lla+lly weeks, and the basic case reproduction number of infection5, R,,is j3iVlly.R, depends explicitly on N, so we expect R, to be greater in larger (and probably *Department of Medical Parasitology, London School of Hygiene and Tropical Medicine, Keppel Street, London WClE 7HT, UK. tTo whom correspondence should be addressed. (Received 6 February 1995; revised 31 August 1995; accepted 12 September 1995)
epidemic
higher density) dog populations. If R, varies from one population to another then so too will pC, which immediately questions the view, implicit in much of the literature’-. , that the same criterion can be applied to dog populations everywhere. With these definitions and assumptions, we can write down formally a set of coupled, first order, non-linear differential equations describing rabies dynamics, as follows: dS
-=
dtu
2 dZ -= dt
-/3Lsz
= psz- aL
CTL-vz. ’
These may be solved to show that the incidence of cases is expected to grow exponentially during the early stages of an epidemic (when S=Zv) at a rate roughly equal to (R, - 1)/g. More precisely, r(t) Mkexp(rt), where y(t) is the incidence between times t and t - 1, k is a constant, and to a good approximation R,=l+r(rZf+g). We can therefore estimate r by fitting the first of these two equations to data describing the exponential growth in incidence during an outbreak, and get R, by using the second. The percentage to be immunized then comes from the well-known relation5 p,=lOO(l - l/&). Where an outbreak occurs in a partially vaccinated dog population, estimates of & and pC obtained this way will be too low; R. needs to be corrected upwards by dividing by the fraction of dogs (s) which were unvaccinated prior to the outbreak. Foggin has provided the best estimates of latent and infective periods, and therefore generation time, because his data come from natural rather than experimental
Vaccine
1996 Volume
14 Number
3
185
Short
paper:
Table 1
PG.
Coleman
and
C. Dye
Estimates of R,, pc and upper 95% confidence
Study
Country
Region
Setting
7
USA
8 9 10
Mexico Indonesia Malaysia
Memphis and Shelby County, Tennessee Hermosillo Central Java Kuala Lumpur
Urban and rural Urban Rural Urban
limits for p,, calculated
Weeks of exponential growth
Number of observations
r
SE.(r)
S
/3,,
S.E.(&)
P,
for P,
11
11
0.172
0.046
0.840
2.334
0.556
57.1
71.0
-22 12 -17
5 12 4
0.175 0.144 0.116
0.023 0.057 0.028
1.000 1.000 1.000
1.981 1.789 1.627
0.418 0.451 0.302
49.5 44.1 38.5
64.5 62.8 55.2
infections. He presents the intervals between biting and the appearance of clinical signs for 68 dogs attacked by other dogs or jackals, from which we calculate a mean of 4.18 (SE. 0.27) weeks and a median of 3.45 (S.E. 0.21) weeks. We use the mean here because it gives more conservative (larger) estimates of R, than the median (it is also longer than obtained from most experimental infections). Although there is some evidence’ that dogs are infective before signs develop, transmission is more likely when dogs behave rabidly, so we assume that latent and incubation periods are equal. With regard to the infective period, Foggin unfortunately gives only the mean (0.81 weeks) and range (0.29-1.71 weeks). We adopt his mean, but we cannot calculate the variance, so our estimates of S.E. (R,) below exclude this source of error. Four studies of dog rabies epidemics in the USA7, Mexico’, Indonesia’ and Malaysia” give the incidence of cases through time (Table I). The first of these outbreaks occurred despite an ongoing vaccination campaign, though the data in Ref. 7 suggest that no more than 16% of dogs were protected. The regression analyses leading to estimates of R, and pc were carried out in GLIM” assuming a Poisson error distribution, and restricting the data to confirmed cases of dogss” or animal7 rabies. R, varies from 1.63 to 2.33, and hence pc lies in the range 39-57%. None of the estimates in Table 1 differs significantly from any other (see S.E.s in Table 1), so the variation could be due to chance alone. There is no evidence to suggest, for example, that R, is greater in larger dog populations, though we might expect to see such an effect in a larger set of data (see above). We are interested not only in the point estimates ofp,, but also in the upper confidence limits. The upper 95% limits fall between 55% and 7 l%, that is, generally below 70%. Put another way, if the errors surrounding the point estimate of R, are roughly normal, we expect a
186
using data from four studies of dog rabies epidemics
Vaccine 1996 Volume 14 Number 3
95% upper confidence limit
coverage of 70% to prevent a major outbreak from occurring on no fewer than 96.5% of occasions. These data and our analysis therefore suggest that immunizing 70% of dogs, following the current WHO recommendation, will indeed be sufficient to prevent or control outbreaks of dog rabies.
ACKNOWLEDGEMENTS PGC is supported by a MRC research studentship.
REFERENCES 1
2 3
7
8
9
10 11
Fekadu, M. Canine rabies. In: The Natural History of Rabies (Ed. Baer, G.M.), 2nd edn. CRC Press, Boca Raton, 1991, pp. 367-378 World Health Organization. Guidelines for Dog Rabies Control. VPH/83.43 Rev. 1. WHO, Geneva, 1987 Beran, G.W. Urban rabies. In: The Natural History of Rabies (Ed. Baer, G.M.), 2nd edn. CRC Press, Boca Raton, 1991, pp. 427-443 Korns, R.F. and Zeissig, A. Dog, fox and cattle rabies in New York State. Am. J. Pub/. H&h 1948, 38, 50-65 Anderson, R.M. and May, R.M. Infectious Diseases of Humans. Oxford University Press, Oxford, 1991 Foggin, CM. Rabies and rabies-related viruses in Zimbabwe: historical, virological and ecological aspects (dissertation). University of Zimbabwe, Harare, 1988 Tierkel, E.S., Graves, L.M., Tuggle, H.G. and Wadley, S.L. Effective control of an outbreak of rabies in Memphis and Shelby County, Tennessee. Am. J. Pub/. Hlth 1950, 40, 10841088 Eng, T.R., Fishbein, H.E., Talamante, H.E. eta/. Urban epizootic of rabies in Mexico: epidemiology and impact of animal bite injuries. Bull. WHO 1993, 71, 615-624 Waltner-Toews, D., Maryono, A., Akoso, B.T., Wisynu, S. and Unruh, D.H.A. An epidemic of canine rabies in Central Java, Indonesia. Preventive Vet. Med. 1990, 8, 295-303 Wells C.W. The control of rabies in Malaya through compulsory mass vaccination of dogs. Bull. WHO 1954, 10, 731-742 Becker, N.G. fhe Analysis of Infectious Disease Data. Chapman and Hall, London, 1989