Schistosomiasis models with density dependence and age of infection in snail dynamics

Abstract

New models for schistosomiasis are developed. These models incorporate several realistic features including drug treatment for human hosts, an infection age in snail hosts, density-dependent birth rate of snails, distribution of schistosomes within human hosts, and disease-induced mortality in both human and snail hosts. The qualitative and quantitative mathematical properties of the models are studied, their biological consequences and some control strategies are discussed, and the results of the new models are compared with those of simpler models. It is shown that the new model may have a bifurcation at which the unique endemic equilibrium changes the stability and stable periodic solutions exist. This is quite different from the simpler models. Explicit thresholds of treatment rate are established above which the infection will be controlled under certain levels. Evaluations of cost-effectiveness are also discussed by analyzing the sensitivity of the mean number of parasites per person to changes of other parameters.