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Models of superinfection and acquired immunity to multiple parasite strains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

P. J. M. Milligan  and
D. Y. Downham
P. J. M. Milligan*
Affiliation:
University of Liverpool
D. Y. Downham*
Affiliation:
University of Liverpool
*
∗Postal address: Medical Research Council Laboratories, Fajara, PO Box 273, Banjul, The Gambia.
∗∗Postal address: Department of Statistics and Computational Mathematics, University of Liverpool, Liverpool L69 3BX, UK.
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Abstract

Individuals in communities in which different strains of pathogen are circulating can acquire resistance by accumulating immunity to each strain. After considering susceptibility, models of infection and immunity are defined for vector-borne diseases such as malaria and trypanosomiasis. For these models the prevalence of infection, the number of infections per individual, and the mean duration of infection, increase rapidly in young individuals, but decrease in older individuals as immunity is acquired to the various strains of pathogen; the mean interval between successive infections lengthens with age. The bivariate Poisson distribution is shown to be a close approximation to some stochastic processes. The models explain observed cross-sectional patterns of age prevalence, and longitudinal patterns in which individuals typically continue to become infected as they age, albeit with decreasing frequency. In these models the time spent infected depends on parasite diversity, as well as the inoculation and recovery rates. It is shown that control measures can cause an increase in the number of infections and the prevalence of infection in older individuals, and in the average prevalence in the community, even when strain-specific immunity is life-long.

Keywords

SUPERINFECTIONIMMUNITYMALARIATRYPANOSOMIASISMULTIPLE PARASITE STRAINS

MSC classification

Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 915 - 932
Copyright
Copyright © Applied Probability Trust 1996 

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