媒介具有Logistic增长的WNV模型动力学性态分析

Dynamics Analysis of a WNV Model with Logistic Growth of Vector

建立了宿主具有常数出生率以及蚊子具有Logistic增长的西尼罗河病毒(WNV)的传染病模型.利用van den Driessche和Watmough的方法,得到了模型的基本再生数,进而讨论了平衡点的存在性和稳定性,并且证明了当因病死亡率大于恢复率时,若基本再生数大于1,则系统存在唯一的正平衡点且是局部渐近稳定的,若基本再生数小于1,则系统存在两个正平衡点,其中一个为鞍点.当因病死亡率小于恢复率时,若基本再生数大于1,则系统存在唯一的正平衡点且是局部渐近稳定的,若基本再生数小于1,则系统不存在正平衡点.

The WNV epidemic model with constant birth rate for host and Logistic growth for mosquito was built.The basic reproduction number of the model was obtained by using the method of van den Driessche and Watmough,and the existence and stability of equilibria were discussed.Then the results of the study show that when disease-induced death rate is greater than recovery rate,if the basic reproduction number is greater than 1,then the system has a unique epidemic equilibrium and is locally asymptotically stable,if the basic reproduction number is less than 1,then the system have two epidemic equilibria,one of them is a saddle point;when disease-induced death rate is less than recovery rate,if the basic reproduction number is greater than 1,then the system has a unique epidemic equilibrium and is locally asymptotically stable,if the basic reproduction number is less than 1,there is no endemic equilibrium.