Spatiotemporal dynamics of a periodic reaction–advection–diffusion schistosomiasis model with intrinsic and infection incubation periods

To study the impact of seasonal variations, individual diffusion, and advection in rivers on the transmission of schistosomiasis, in this paper, we present a periodic reaction–advection–diffusion schistosomiasis model which incorporates spatial heterogeneity, infection and intrinsic incubation periods. We first prove the well-posedness of the system, and then derive the basic reproduction number \(R_0\) $R_0$ and show it is a dynamics threshold: the disease-free periodic solution is globally attractive when \(R_0<1\) $R_0<1$ , otherwise, the disease will be persist. Moreover, in space homogenous case, we prove that the global attractively of the endemic equilibrium by constructing Lyapunov functional. Numerical simulations are conducted to investigate the influence of some key factors on the disease. Our works suggestion: (1) timely eradication of snails in the river is one of the most effective means to prevent the outbreak of the disease; (2) neglecting the periodic time delays caused by seasonal factors will overestimate or underestimate the prevalence of schistosomiasis; (3) The transmission of schistosomiasis has an inverse relationship with cercariaes(miracidias) diffusion and advection rates.