Threshold dynamics of a reaction-diffusion-advection schistosomiasis model with seasonality

This paper proposes a reaction-diffusion-advection schistosomiasis model with seasonality based on the life cycle of schistosomiasis (humans, eggs, snails, and cercariae). Using the next generation operator theory, we define the basic reproduction number R₀ that characterizes the transmission potential of schistosomiasis, and further reveal the threshold dynamics of the system through the monotone dynamical system theory. Specifically, if R₀≤1, the disease-free periodic solution is globally asymptotically stable, meaning that schistosomiasis will die out; if R₀'1, the system admits a unique positive periodic solution that is globally asymptotically stable, indicating that the disease will break out. Numerically, we use data from Ourinhos, Brazil, to analyze the impact of diffusion rates, spatial heterogeneity, advection rates, and seasonality on the transmission of schistosomiasis.