一类非线性SEIRS传染病传播数学模型

A Kind of Nonlinear SEIRS Epidemic Spread Mathematic Model

研究了一类具有非线性发生率的易感者-暴露类-患病者-恢复者-易感者(SEIRS)传染病模型。利用Routh-Hurwitz判别法,分析了无病平衡点与地方病平衡点的局部渐近稳定性;采用Lyapunov-LaSalle不变原理,分析了无病平衡点的全局渐近稳定性;运用持久性理论证明了模型的持久性,并给出了地方病平衡点全局渐近稳定的猜想。最后通过数值模拟验证了结论与猜想。

A susceptible-exposure-infected-recovery-susceptible( SEIRS) epidemic model with nonlinear saturated incidence rate was proposed. Local asymptotic property of the disease-free equilibrium and endemic equilibrium was studied by using Routh-Hurwitz criterion. Global asymptotic property of the disease-free equilibrium was researched by using Lyapunov-La Salle invariance principle. The persistence of the model was proved by using persistence theory and an assumption about the global asymptotic stability of the endemic equilibrium was obtained. Finally,some numerical simulations were given to verify the theoretical results and assumption.