Schistosomiasis Kinetic Model Of Non-autonomous

Schistosomiasis is recognized as a major public health problem in Peoples’ Republic of China. In recentyears, more investigations on mathematical model of schistosomiasis transmission have been undertaken in orderto assess and predict the effects of various control strategies to elimination of the disease. Nevertheless, seasonalfluctuations may have potential impact on the transmission of schistosomiasis. In this paper, we mainly studynon-autonomous schistosomiasis models. The main content of this paper is arranged as follows:In the first chapter, we briefly introduces tansmission of schistosomiasis. Then, the domestic and interna-tional research status of schistosomiasis at present are reviewed. Finally, the main work and the organization ofthis paper are given.In the second chapter, the seasonal variation modified Barbour’s one-host model is studied. We use theoperator theory in Functional Analysis and the monodromy matrix of the linear periodic system theories to derivethe basic reproduction number and demonstrate that the disease dies out for R0<1, whereas it is permanent forR0>1. Then, based on the annual report data, estimation of parameters and computer numerical simulation, wecalculate the basic reproduction numbers to investigate the effectiveness of the current control strategy adoptedin Liaonan, Bailu and Wenquan villages of Xingzi county. The annual report data included the data from2003to2010.In the third chapter, the seasonal variation modified Barbour’s two-host model is studied. Using the samemethod as in the previous section we obtain the basic reproduction number R0, and prove that R0=1is athreshold condition which can be used to distinguish the permanence and the extinction of the disease. We alsotake Liaonan village in Xingzi county for example, the values of the basic reproduction number for this areaare obtained by numerical calculation to evaluate the effects of application of the control strategy, and comparethese values to the one-host model.In the forth chapter, we investigate a nonautonomous schistosomiasis model with incubation period. Byconstructing proper auxiliary function, the sufficient conditions for the persistence and extinction of the modelare established.