关于日本血吸虫病动力学模型的周期解

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。

Geometric approach to the stability analysis of the periodic solution in a semi-continuous dynamic system

Integrated pest management （IPM） is a long-term management strategy and has been proved to be more effective in pest control. To well-understand the mechanism and effect of the action of IPM, the geometric theory of the involved semi-continuous dynamic systems is becoming more and more important. In this work, a geometric approach is applied to analyze the stability of the positive order-one periodic solution in semi-continuous dynamic systems. A stability criterion to test the stability of the order-one periodic solution is established. As an application, a stage-structure model involved chemical control is presented to show the efficiency of the proposed method. The sufficient conditions to insure the existence of the periodic solution are provided. In addition, the number and the stability of the periodic solutions are discussed accordingly. The simulations are carried out to verify the results.