The Asymptotic Behavior Research For Several Types Of Nonautonomou Schistosomiasis Mathematical Model

Schistosomiasis is a parasitic disease caused by blood flukes of the genus Schistosoma. Schistosomiasisis one of the most prevalent parasitic diseases all over the world. Mathematical modeling has become animportant tool in analyzing the spread and control of infectious diseases. Nevertheless, seasonalfluctuations may have potential impact on the transmission of schistosomiasis. Hence, in this paper, threekinds of nonautonomous schistosomiasis models are studied. The main contents can be summarized asfollows:In the first chapter, we introduce the ecological background of schistosomiasis. Then, we introduce thepurpose and significance of the schistosomiasis dynamics, and also review the research achievements andprogress of the schistosomiasis dynamics. Finally, the main works of this paper are given.In the second chapter, a nonautonomous schistosomiasis system is established. We take into account thesaturation incidence rate and all coefficients varying with time. As well as, the long-time behavior of anonautonomous schistosomiasis epidemic model is discussed. Under quite weak assumptions, sufficientconditions for the permanence and extinction of infectious population of disease are obtained. Numericalsimulations which support our theoretical analysis are also given.In the third chapter, we investigate a nonautonomous schistosomiasis model in a periodic environment.We obtain a threshold value between the extinction and the uniform persistence. Our main results show thatthe disease persists if the threshold value is larger than unity. It was also proved that there exists a positiveperiodic solution. Numerical simulations which support our theoretical analysis are also given.In the forth chapter, we propose a modified version of Barbour’s model with implusive effect andperiodic variation in transmission. We establish the basic reproductive number and its calculation for ourimpulsive nonautonomous schistosomiasis model. Sufficient conditions for the global asymptotic stabilityof the disease-free periodic solution are obtained. Finally, we also take Liaonan village in Xingzi county forexample, the values of the basic reproductive number for this area are obtained by numerical calculation toevaluate the effects of application of the control strategy.