关于日本血吸虫病动力学模型的周期解

发布时间：2018-07-23 12:27

【摘要】：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。
[Abstract]:Schistosomiasis japonicum (Schistosomiasis japonicum) is a widespread infectious and parasitic disease in China, which has caused great harm to human health. The transmission dynamics model of schistosomiasis japonicum has been widely discussed. Based on the autonomous kinetic model of schistosomiasis japonicum by Wu Jian-hong et al., considering the seasonal variation of snail population in lake area, the corresponding non-autonomous transmission dynamics model was investigated in this paper. The stability of the periodic solution is studied and the numerical simulation is carried out. The results show that under certain parameter conditions, no matter how the disease spreads at the beginning, the disease will eventually die out; otherwise, under certain initial conditions, the disease transmission will form a periodic endemic disease. Numerical simulation shows that the disease tends to die out when the amplitude of seasonal variation of snail population is large enough under certain parameter conditions. In addition, the treatment of infected people and cattle is also beneficial to the extinction of disease. In this paper, we also study the nonautonomous dynamic model of the Barbour double host model. Not only the stability of the periodic solution is discussed, but also the existence condition of the periodic solution of the system is obtained.
【作者单位】：复旦大学数学科学学院;
【基金】：国家自然科学基金重点项目(10531030;10701053)
【分类号】：R532.21

【共引文献】