一类媒介传染病模型动力学性态分析

摘要

A vector-borne epidemic model with constant input for host and exponential growth for mosquito was built.The basic reproduction number R0 of the model was obtained by using the next generation of generator matrix,and the existence and stability of equilibria were discussed.Furthermore,the results show that if R0>1 ,the model has a unique endemic equilibrium and is locally asymptotically stable,if R0<1 ,there may have two,one or no epidemic equilibrium.When the system has two endemic equilibria,one of them is a saddle node and another is a stable node.By numerical simulation,the conclusion was validated.%建立了宿主常数输入以及蚊子指数出生的媒介传染病模型，利用下一代生成矩阵法得到了模型的基本再生数R0，讨论了平衡点的存在性和稳定性。并且证明了当R0＞1时，系统存在唯一的正平衡点且局部渐近稳定；当R0＜1时，无病平衡点局部渐近稳定，且系统可能存在2个、1个或0个正平衡点。 当系统存在2个正平衡点时，1个为鞍点，1个为稳定结点。并通过数值模拟进行了验证。