两菌株的传染病反应扩散模型的动力学分析
首发时间:2021-04-15
摘要:基于传染病传播过程不常局限于单一菌株,~提出了一类带有两菌株的传病反应扩散模型. 首先分析得到了模型解的适定性, 通过定义基本再生数, 研究了模型的阈值动力学性质.~然后对模型的正稳态解作出了先验估计, 利用 LaSalle 不变原理得到了半平凡稳态解的全局稳定性. 同时研究了当扩散系数趋于~0~时, 模型的正稳态解的渐近分布.~最后通过数值模拟验证了理论的正确性.
关键词: 应用数学 反应扩散 基本再生数 渐近分布 先验估计 阈值动力学
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Dynamics analysis on a two-strain SIS epidemic model with diffusion
Abstract:Based on the spread of infectious diseases rarely confined to a single strain, a type of infectious disease reaction diffusion model with two strains is proposed. Firstly, the well po- sedness of the model solution is analyzed, and the threshold dynamics of the model are studi- ed by defining the basic reproduction number. A priori estimate is analyzed for the steady-st- ate solution of the model, and the global stability of the semi-trivial steady-state solution is o- btained by the LaSalle invariance principle. Moreover, asymptotic profiles of the steady-state solu- tion of the model is studied when the diffusion coefficient tends to 0. Finally, the correc- tness of the theory is verified by numerical simulation.
Keywords: Applied mathematics Reaction diffusion Basic reproduction number Asymp- totic profiles Priori estimation Threshold dynamics
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