Mathematical modeling of schistosomiasis

New models for schistosomiasis are developed. Two major types of models are established. The first type includes two models, and these models incorporate several realistic features including drug treatment for human hosts, an infection age in snail hosts, density-dependent birth rate of snails, negative binomial distribution of schistosomes within human hosts, disease-induced mortality in both human and snail hosts. The second type includes several human groups sharing a water resource, preserves most of the characteristics of the first type except the age-structure of the infected snails, and incorporates migrations between human groups. The existence, uniqueness, and well-posedness of these models are proved. The basic reproductive numbers are defined. With this threshold, the qualitative and quantitative mathematical properties of these models are studied. The biological consequences are also discussed. Numerical simulations help examine the dynamics and suggest some properties of these models that we were unable to prove mathematically. One of them shows that one model may have a bifurcation at which the unique equilibrium changes the stability and stable periodic solutions exist.