Schistosomiasis model with treatment, habitat modification and biological control

Schistosomiasis is a parasitic disease caused by Schistosoma worm infection. Some species of snails can serve as the intermediate hosts for the parasite. Numerous interventions have been performed to repress the snail population. One of them is the use of molluscicide. Nevertheless, it is debated that molluscicide intervention has negative impacts on the ecosystem. To investigate the impact of more environmentally friendly interventions, we develop a schistosomiasis model with treatment, habitat modification and biological control. The biological control agent examined in our model is a snail predator. Moreover, to investigate the impact of snail habitat modification, we assume that the snail population grows logistically. We show that all solutions of our model are non-negative and bounded. We also study the existence and stability conditions of equilibrium points. The basic reproduction numbers are determined using the next-generation operator. Linearization combined with the Routh-Hurwitz criterion is used to prove the local stability condition of disease-free equilibrium points. Bifurcation theory is applied to investigate the local stability condition of the endemic equilibrium points. To examine the global behavior of our model, we use asymptotically autonomous system theory and construct a Lyapunov function. We perform several numerical simulations to validate and support our deductive results. Our results show that early treatment can reduce the basic reproduction number and schistosomiasis cases. In addition, modifying snail habitat and releasing the snail predator at the snail habitat can reduce schistosomiasis prevalence. We suggest using snail predators which can hunt and kill snails effectively as a biological control agent.