A multiple-strain pathogen model with diffusion on the space of Radon measures

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-10-28 DOI:10.1016/j.cnsns.2024.108402

Azmy S. Ackleh , Nicolas Saintier , Aijun Zhang

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引用次数: 0

Abstract

We formulate a multiple strain Susceptible–Infectious–Susceptible (SIS) pathogen model with diffusion on the space of Radon measures which has the advantage of unifying discrete and continuous strain spaces under one framework. We first establish the well-posedness of this model. Then we study the long-time behavior for the case of discrete strain spaces. We define the basic reproduction number for each strain. We establish the existence of a disease-free equilibrium and a strain-specific endemic equilibrium which defines a competitive exclusion equilibrium where the density of individuals at one strain is positive and the density at the remaining strains is zero. We study the stability of these equilibria under the assumption that the disease transmission and recovery rates are spatially homogeneous or under the assumption that the diffusion rate of the susceptible individuals is equal to the diffusion rate of the infected individuals. We then extend some of these long-time behavior results from the discrete strain space case to the continuous strain space case.

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在拉顿测量空间上具有扩散作用的多菌株病原体模型

我们提出了一个多菌株易感-感染-易感（SIS）病原体模型，该模型在拉顿计量空间上具有扩散性，其优点是将离散和连续菌株空间统一在一个框架下。我们首先建立了该模型的良好拟合性。然后，我们研究离散应变空间的长期行为。我们定义了每个菌株的基本繁殖数。我们确定了无病均衡和菌株特有的流行均衡的存在，后者定义了竞争性排斥均衡，即一个菌株的个体密度为正，其余菌株的个体密度为零。我们研究了在疾病传播率和恢复率空间均一的假设下，或在易感个体的扩散率等于受感染个体的扩散率的假设下，这些均衡的稳定性。然后，我们将离散应变空间情况下的一些长期行为结果扩展到连续应变空间情况下。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.