论文标题
具有非线性入射的流行反应扩散模型的全球和局部渐近稳定性
Global and local asymptotic stability of an epidemic reaction-diffusion model with a nonlinear incidence
论文作者
论文摘要
本文的目的是研究反应的动力学 - 扩散SI（易感性易感性）流行模型，其非线性发病率描述了个体之间传染病的传播。我们证明所提出的模型在一个条件下具有两个稳态。通过分析特征值并使用Routh-Hurwitz标准和适当构建的Lyapunov功能，我们建立了非负恒定稳态的局部和全球渐近稳定性，其基本繁殖数量比统一大于Unity，并且由基本的再现数量比较小的案例相等的元素，而不是统一的均等，而不是统一。通过应用适当构建的Lyapunov功能，我们确定了PDE情况下全局稳定性的状况。最后，我们提出了一些数字示例，以说明和确认整个论文中获得的分析结果。
The aim of this paper is to study the dynamics of a reaction--diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We prove that the proposed model has two steady states under one condition. By analyzing the eigenvalues and using the Routh--Hurwitz criterion and an appropriately constructed Lyapunov functional, we establish the local and global asymptotic stability of the non negative constant steady states subject to the basic reproduction number being greater than unity and of the disease--free equilibrium subject to the basic reproduction number being smaller than or equal to unity in ODE case. By applying an appropriately constructed Lyapunov functional, we identify the condition of the global stability in the PDE case. Finally, we present some numerical examples illustrating and confirming the analytical results obtained throughout the paper.
