A stochastic model for the analysis of age-specific prevalence curves in schistosomiasis

Abstract

INTRODUCTION IN AN attempt to gain further knowledge into the mechanisms involved in a disease it is often useful to construct a model which describes in mathematical form the essential features of the disease process. To date several models have been presented which deal with various aspects of schistosomiasis and their scope ranges from describing the entire cycle of the disease (given by Macdonald [l], Coffman and Warren [Z], Hairston [3], and Nasell and Hirsch [4]) to describing specific aspects of the disease in the human host (given by Hairston [S] and Tallis and Leyton [6]). The model presented in this paper focuses attention on the manifestation of schistosomiasis in the human host. In this development we consider the following essential features of the lifecycle: (i) the entry of the parasite into the host, (ii) the pairing of female and male parasites, (iii) the shedding of eggs by the host infected with schistosome pairs, and (iv) the death of the parasite within the host. The model we develop for the frequency distribution of the size of the population of worms within the host is the immigration-death process, and we illustrate how this model might be used to describe the mathematical form of the age--specific prevalence curves for schistosomiasis.