When susceptible and infective human hosts are not equally attractive to mosquitoes: a generalisation of the Ross malaria model

Summary

Introduction

Models for vector-transmitted infections are always based on several homogeneity assumptions, even when some aspects of heterogeneity are incorporated in the model. Usually most of these assumptions are not stated explicitly, and among these is the implicit assumption that susceptible and infective hosts are bitten homogeneously by insect vectors. Some experiments and a field study documented in the literature (Baylis and Nambiro (1993) and references therein) seem to indicate the possibility that vectors have a feeding preference for infected hosts. On the other hand, if infective human hosts are especially protected against mosquito bites, for example through the use of bed nets, susceptible hosts could on average be bitten more frequently.

The model

In order to investigate effects when biting of insect vectors is non-homogeneous between susceptible and infective hosts, we consider a generalization of the Ross malaria model (which is a type of model applicable not only to malaria transmission), allowing both for increased or decreased attractiveness of infective hosts, but disregarding other kinds of heterogeneity which have e.g. been dealt with by Hasibeder and Dye (1988). We characterize the degree of heterogeneity between susceptible and infective hosts by one single parameter and, unlike the analysis in Kingsolver (1987), we start at the level of individuals:

Let π₁(X) denote the proportion of adequate contacts (bites or blood meals facilitating transmission) of infective vectors which they have with susceptible hosts, and π₂(X) the proportion of adequate contacts of uninfected vectors which they have with infective hosts.