Complete threshold dynamics of a reaction–diffusion schistosomiasis model in different time-evolving domains

The significance of river and lake regions in the propagation of schistosomiasis cannot be overlooked, as this disease is transmitted predominantly through water. In this paper, we focus on the complete dynamics of a reaction–diffusion model for schistosomiasis, which accounts for domain that evolve over time. By employing theories of asymptotically autonomous and nonautonomous semiflows, we delineate the global dynamics of the system within domains that are fixed, asymptotically periodic, and bounded, with the dynamics being dictated by the basic reproduction number. Utilizing the sub-and supersolutions method alongside the comparison principle, we substantiate the threshold dynamics of the system in asymptotically unbounded domains. In numerical simulation part, we explore the influence of the evolving domain on the schistosomiasis transmission by comparing the basic reproduction numbers across various domains. Our findings reveal that the asymptotic growth and periodic changes in the size of these areas are pivotal in the transmission of schistosomiasis, with the growth of the regional evolution ratio being particularly conducive to the spread of the disease. These insights suggest that it is imperative for prevention and control authorities to enhance their schistosomiasis countermeasures, especially during the rainy seasons when the risk of transmission is significantly increased.