具有双接种的病毒变异传染病模型稳定性分析

Stability analysis of an epidemic model of virus mutation with two vaccinations

研究了一类具有双接种和病毒自发变异的传染病模型,采用第二代生成矩阵法求得系统的基本再生数并证明了各个平衡点的存在性,进而通过Hurwitz判别法得到无病平衡点与边界平衡点的局部渐近稳定性,并借助Lyapunov函数和LaSalle不变集原理证明了无病平衡点与边界平衡点全局渐近稳定的充分条件,利用数值模拟验证了结论的正确性。

This paper proposes an epidemic model of virus mutation with two vaccinations.The basic regeneration number is found by using the next generation matrix method system and the existence of each equilibrium point is proved.Then,the local asymptotic stability of the infection-free and boundary equilibria are carried out through the use of Hurwitz criteria,and the sufficient conditions for global asymptotic stability of the infection-free and boundary equilibria are determined through Lyapunov functions and the LaSalle invariant set.Finally,some numerical simulations are given to demonstrate the obtained results.