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Frequency distribution of lymphatic filariasis microfilariae in human populations: population processes and statistical estimation

Published online by Cambridge University Press:  06 April 2009

B. T. Grenfell ,
P. K. Das ,
P. K. Rajagopalan  and
D. A. P. Bundy
B. T. Grenfell
Affiliation:
Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ
P. K. Das
Affiliation:
Vector Control Research Centre, Medical Complex, Indira Nagar, Pondicherry-605 006, India
P. K. Rajagopalan
Affiliation:
Vector Control Research Centre, Medical Complex, Indira Nagar, Pondicherry-605 006, India
D. A. P. Bundy
Affiliation:
Parasite Epidemiology Research Group, Department of Pure and Applied Biology, Imperial College, LondonSW7 2BB
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Summary

This paper uses simple mathematical models and statistical estimation techniques to analyse the frequency distribution of microfilariae (mf) in blood samples from human populations which are endemic for lymphatic filariasis. The theoretical analysis examines the relationship between microfilarial burdens and the prevalence of adult (macrofilarial) worms in the human host population. The main finding is that a large proportion of observed mf-negatives may be ‘true’ zeros, arising from the absence of macrofilarial infections or unmated adult worms, rather than being attributable to the blood sampling process. The corresponding mf distribution should then follow a Poisson mixture, arising from the sampling of mf positives, with an additional proportion of ‘true’ mf-zeros. This hypothesis is supported by analysis of observed Wuchereria bancrofti mf distributions from Southern India, Japan and Fiji, in which zero-truncated Poisson mixtures fit mf-positive counts more effectively than distributions including the observed zeros. The fits of two Poisson mixtures, the negative binomial and the Sichel distribution, are compared. The Sichel provides a slightly better empirical description of the mf density distribution; reasons for this improvement, and a discussion of the relative merits of the two distributions, are presented. The impact on observed mf distributions of increasing blood sampling volume and extraction efficiency are illustrated via a simple model, and directions for future work are identified.

Keywords

Wuchereria bancroftilymphatic filariasismicrofilariaefrequency distributionstruncated negative binomial
Type
Research Article
Information
Parasitology , Volume 101 , Issue 3 , December 1990 , pp. 417 - 427
Copyright
Copyright © Cambridge University Press 1990

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. (1972). Handbook of Mathematical Functions. New York: Dover.Google Scholar
Anderson, R. M. (1982). The population dynamics and control of roundworm and hookworm infections. In Population Dynamics of Infectious Diseases: Theory and Applications (ed. Anderson, R. M.), pp. 67–106. London: Chapman & Hall.CrossRefGoogle Scholar
Anderson, R. M. & Gordon, D. M. (1982). The regulation of host population growth by parasite species. Parasitology 76, 119–57.CrossRefGoogle Scholar
Anderson, R. M. & May, R. M. (1985). Helminth infections of humans: mathematical models, population dynamics and control. Advances in Parasitology 24, 1–101.CrossRefGoogle ScholarPubMed
Das, P. K., Manoharan, A., Srividya, A., Grenfell, B. T., Bundy, D. A. P. & Vanamail, P. (1990). Frequency distribution of Wuchereria bancrofti microfilariae in human populations and its relationships with age and sex. Parasitology 101, 429–34.CrossRefGoogle ScholarPubMed
Dietz, K. (1982 a). The population dynamics of onchocerciasis. In Population Dynamics of Infectious Diseases: Theory and Applications (ed. Anderson, R. M.), pp. 209–241. London: Chapman & Hall.CrossRefGoogle Scholar
Dietz, K. (1982 b). Overall population patterns in the transmission cycle of infectious disease agents. In Population Biology of Infectious Diseases (ed. Anderson, R. M. & May, R. M.), pp. 87–102. Berlin: Springer Verlag.CrossRefGoogle Scholar
Denham, D. A., Dennis, D. T., Ponnudurai, T., Nelson, G. S. & Guy, F. (1971). Comparison of a counting chamber and thick smear methods of counting microfilariae. Transactions of the Royal Society of Tropical Medicine and Hygiene 65, 521–6.CrossRefGoogle ScholarPubMed
Forsythe, K. P., Grenfell, B. T., Spark, R., Kazura, J. W. & Alpers, M. P. (1989). Age-specific patterns of change in the dynamics of Wuchereria bancrofti infection in Papua New Guinea. American Journal of Tropical Medicine and Hygiene (In the Press).Google Scholar
Hairston, N. A. & De Meillion, B. (1968). On the inefficiency of transmission of Wuchereria bancrofti from mosquito to human host. WHO Bulletin 38, 308–12.Google ScholarPubMed
Hairston, N. A. & Jachowski, L. A. (1968). Analysis of the W. bancrofti population in people of Western Samoa. WHO Bulletin 38, 29–59.Google Scholar
Johnson, N. L. & Kotz, S. (1969). Discrete distributions. New York: John Wiley & Sons.Google Scholar
Macdonald, G. (1965). The dynamics of helminth infections, with special reference to schistosomes. Transactions of the Royal Society of Tropical Medicine and Hygiene 59, 489–506.Google Scholar
May, R. M. (1977). Togetherness among schistosomes: its effects on the dynamics of the infection. Mathematical Biosciences 35, 301–43.CrossRefGoogle Scholar
Nelder, J. A. & Mead, R. (1965). A simplex method of function minimization. Computer Journal 7, 308–12.Google Scholar
Pacala, S. W. & Dobson, A. P. (1988). The relation between the number of parasites/host and host age: population dynamic causes and maximum likelihood estimation. Parasitology 96, 197–210.CrossRefGoogle ScholarPubMed
Park, C. B. (1988). Microfilarial density distribution in the human population and its infertility index for the mosquito population. Parasitology 96, 265–71.Google Scholar
Pichon, G., Merlin, M., Fagneaux, G., Riviere, F. & Laigret, J. (1980). Etude de la distribution des numerations microfilariennes dans les foyers de filariose lymphatique. Tropenmedizin und Parasitologie 31, 165–80.Google Scholar
Rajagopalan, P. K. & Das, P. K. (1987). The Pondicherry Project on Integrated Disease Vector Control. Vector Control Research Centre, Pondicherry.Google Scholar
Sasa, M. (1976). Human Filariasis: a Global Survey of Epidemiology and Control. Tokyo: University of Tokyo Press.Google Scholar
Schenzle, D. (1979). Fitting the truncated negative binomial distribution without the second sample moment. Biometrics 35, 637–9.CrossRefGoogle Scholar
Sichel, H. S. (1971). On a family of discrete distributions particularly suited to represent long-tailed frequency data. In Proceedings of the Third Symposium on Mathematical Statistics (ed. Laubscher, N. F.), pp. 51–97. Pretoria, Council for Scientific and Industrial Research.Google Scholar
Southgate, B. A. (1974). Problems of clinical and biological measurements in the epidemiology and control of filarial infections. Transactions of the Royal Society of Tropical Medicine and Hygiene 68, 177–86.Google Scholar
Stein, G. Z., Zucchini, W. & Juritz, J. M. (1987). Parameter estimation for the Sichel distribution and its multivariate extension. Journal of the American Statistical Association 82, 938–44.CrossRefGoogle Scholar
Tallis, G. M. & Donald, A. D. (1964). Models for the distribution on pasture of infective larvae of the gastrointestinal nematode parasites of sheep. Australian Journal of Biological Sciences 17, 504–13.CrossRefGoogle Scholar
Tallis, G. M. & Leyton, M. (1966). A stochastic approach to the study of parasite populations. Journal of Theoretical Biology 13, 251–60.CrossRefGoogle Scholar
Wenk, P. (1986). The function of non-circulating microfilariae: Litmosoides carinii (Nematoda: Filarioidea). Deutsche tierärztliche Wochenschrift 93, 414–18.Google Scholar