关于日本血吸虫病动力学模型的周期解

Periodic Solutions of Schistosomiasis Japonicum Dynamical Models

日本血吸虫病是在我国广为流传的传染病和寄生虫病,对人体的健康造成了极其严重的危害,关于日本血吸虫病的传播动力学模型引起了广泛的讨论。在吴建宏等建立的双宿主日本血吸虫病的自治动力学模型的基础上,考虑到湖泊型地区钉螺数量的季节性变化因素,本文考察了相应的非自治的传播动力学模型,研究了其周期解的稳定性,并在此基础上进行了数值模拟。研究表明,在一定的参数条件下,无论开始时疾病传播情况如何,疾病终将趋于消亡;否则,在一定的初始条件下,疾病传播形成周期性的地方病。数值模拟发现,在一定的参数条件下,钉螺数量的季节性变化振幅充分大时,可使疾病趋于消亡;此外,同时对患病的人与牛进行治疗,也有利于使疾病消亡。本文中还研究了Barbour双宿主模型的非自治动力学模型,不仅对其周期解的稳定性进行了讨论,还得到该系统周期解的存在性条件。

Japonicum is a widely spread infectious disease in China that has been jeopardizing human health for a long time. Numerous dynamic models were built up to study the mechanism of its transmission. Wu 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 carried out for further illustrations. The result shows that, with certain parameters, the disease will vanish eventually regardless of the original condition; otherwise, under certain initial condition,it will develop into periodic endemic disease. It also shows that, with certain parameters, when theswing 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 of the asymptotic stability of its periodic solutions.