On a Five-Dimensional Nonautonomous Schistosomiasis Model with Latent Period

Abstract

A five-dimensional nonautonomous schistosomiasis model which include latent period is proposed and studied. By constructing several auxiliary functions and using some skills, we obtain some sufficient conditions for the extinction and permanence (uniform persistence) of infectious population of the model. New threshold values of integral form are obtained. For the corresponding autonomous schistosomiasis model, our results are consistent with the past results. For the periodic and almost periodic cases, some corollaries for the extinction and permanence of the disease are established. In order to illustrate our theoretical analysis, some numerical simulations are presented.