具有水平传播和噬菌体-细菌相互作用的部分退化反应-扩散霍乱模型的动力学

IF 0.8 4区 数学 Q2 MATHEMATICS
Zhenxiang Hu, Shengfu Wang, L. Nie
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引用次数: 0

摘要

为了讨论空间异质性、水平传播、环境病毒和噬菌体对霍乱弧菌传播的影响,我们提出了一个具有耦合反应扩散方程和常微分方程的霍乱模型。我们建立了该模型的适定性,包括全局正解的存在性、半流的渐近光滑性和全局吸引子的存在性。得到了基本繁殖数R0,以描述疾病的持续和灭绝。即当R0≤1时,无病稳态是全局渐近稳定的,而当R0≤1时,无病稳态是不稳定的。而且,这种疾病是持续性的模型在这种情况下具有无噬菌体和存在噬菌体的地方性稳定状态。进一步讨论了空间均匀模型中无噬菌体和有噬菌体的地方性稳态的全局渐近稳定性。最后,通过数值算例说明了本文的主要理论结果和开放性问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dynamics of a partially degenerate reaction-diffusion cholera model with horizontal transmission and phage-bacteria interaction
We propose a cholera model with coupled reaction-diffusion equations and ordinary differential equations for discussing the effects of spatial heterogeneity, horizontal transmission, environmental viruses and phages on the spread of vibrio cholerae. We establish the well-posedness of this model which includes the existence of unique global positive solution, asymptotic smoothness of semiflow, and existence of a global attractor. The basic reproduction number R0 is obtained to describe the persistence and extinction of the disease. That is, the disease-free steady state is globally asymptotically stable for R0≤1, while it is unstable for R0>1. And, the disease is persistence and the model has the phage-free and phage-present endemic steady states in this case. Further, the global asymptotic stability of phage-free and phage-present endemic steady states are discussed for spatially homogeneous model. Finally, some numerical examples are displayed in order to illustrate the main theoretical results and our opening questions.
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来源期刊
Electronic Journal of Differential Equations
Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.50
自引率
14.30%
发文量
1
审稿时长
3 months
期刊介绍: All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.
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