SPATIOTEMPORAL DYNAMICS OF A REACTION-DIFFUSION SCHISTOSOMIASIS MODEL WITH SEASONAL AND NONLOCAL TRANSMISSIONS

Schistosomiasis is a kind of parasitic disease that is mainly caused by schistosomiasis japonicum parasitism. Spatial diffusion, spatial heterogeneity, nonlocal effective contact (this property can be described by some integral functions), and seasonal patterns have been identified in the infection mechanism of schistosomiasis. In this paper, we formulated a spatial diffusion schistosomiasis model with seasonal and nonlocal transmissions to investigate the impact of interesting factors on the transmission dynamics of schistosomiasis. We derived the functional expression of the next generation operator, R(x), and defined the basic reproduction number, R-0, as the spectral radius of R(x). We also showed that the threshold dynamics of the system are determined by R-0. Specifically the schistosomiasis-free periodic steady state is global attractive when R-0 < 1 and the uniform persistence of the disease holds for R-0 > 1. Numerical simulations were conducted to verified the theoretical results and investigate the influences of factor factors on schistosomiasis transmissions. Our works suggest that schistosomiasis is less prevalent in regions where rivers have fast currents than in those with slow currents. Thus, government departments should consider the spatial heterogeneity and take corresponding control measures for different river and lake basins.