Periodic Solutions Of Schistosomiasis Japonicum

Wu, Liu and Zhuo (1987, [1]) have proposed an autonomous dual-host model for the transmission dynamics of the schistosomiasis japonicum, in this paper, based on their model, a corresponding non-autonomous transmission model for the lake type districts is considered by accounting for the seasonal variation of snails numbers. The asymptotic stability of periodic solutions is studied and a numerical simulation is used for further illustrations. The result shows that, with certain parameters, the disease will vanish eventually regardless of the original condition; otherwise, for certain original condition, it will develop into periodic endemic disease. It also shows that, with certain parameters, when the swing of periodical variation of snails aggregates to a certain number, the disease will disappear; and, curing the infected cow and people at the same time is more effective for disease control. On the other hand, the non-autonomous situation of Barbour dual-host model is studied and the existence conditions for positive periodic solutions is given based on the study on the asymptotic stability of its periodic solutions.