具有非线性恢复率的媒介传染病模型性态分析  

Dynamics Analysis of Vector Borne Diseases with Nonlinear Recovery Rate

作　　者：杨扬 李桂花[1] YANG Yang;LI Gui-hua(School of Science, North Universifty of China, Taiyuan 030051, China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2021年第2期102-106,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11801340);山西省留学回国人员科技活动择优资助项目;山西省自然科学基金资助项目(201901D111179)。

摘　　要：建立了宿主种群具有非线性恢复率的媒介传染病模型并研究了系统的动力学性态.首先计算出系统的基本再生数,并给出无病平衡点稳定性条件,进一步证明了系统可能存在两个、一个或没有正平衡点.若系统存在两个正平衡点,则染病者数量较小的平衡点为鞍型,染病者数量较大的平衡点是稳定的或不稳定的,并给出系统经历Hopf分支的条件.最后通过数值模拟发现系统存在鞍结点分支、Hopf分支及Bogdanov-Takens分支.研究结果将为控制媒介传染病的传播提供理论依据.In this paper,we built the model of vector borne diseases with nonlinear recovery rate in host population and studied the dynamic behaviors of the system.Firstly,we gave the basic reproduction number.Furthermore,we gave the stability conditions of the disease-free equilibrium.In the system,there may exist two,one or no positive equilibria.If there are two positive equilibria,one of the small numbers of infected population is a saddle type.The other one is stable or unstable.Thus,the system undergoes Hopf bifurcation.At last,by numerical simulation we find that system undergoes saddle-node bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation.The results will be helpful for the planning of recurrent disease control in the public security authorities.

关 键 词：非线性恢复率 媒介传染病 基本再生数 HOPF分支 

分 类 号：O175.1[理学—数学]