Analysis on a Spatial SIS Epidemic Model with Saturated Incidence Function in Advective Environments: I. Conserved Total Population

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Xiaodan Chen, Renhao Cui
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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2522-2544, December 2023.
Abstract. This paper concerns the qualitative analysis on a reaction-diffusion SIS (susceptible-infected-susceptible) epidemic model governed by the saturated incidence infection mechanism in advective environments. A variational expression of the basic reproduction number [math] was derived and the global dynamics of the system in terms of [math] was established: the disease-free equilibrium is unique and linearly stable if [math] and at least an endemic equilibrium exists if [math]. More precisely, we explore qualitative properties of the basic reproduction number and investigate the spatial distribution of the individuals with respect to the dispersal and advection. We find that the concentration phenomenon occurs when the advection is large and the infectious disease will be eradicated for the small dispersal of infected individual. Our theoretical results may shed some new insight into the infectious disease prediction and control strategy.
具有饱和发病函数的平流环境空间 SIS 流行病模型分析:I. 保持不变的总人口
SIAM 应用数学杂志》,第 83 卷第 6 期,第 2522-2544 页,2023 年 12 月。 摘要本文对平流环境下受饱和感染机制控制的反应-扩散 SIS(易感-感染-易感)流行病模型进行定性分析。推导出了基本繁殖数[math]的变分表达式,并用[math]建立了系统的全局动力学:如果[math],则无病平衡是唯一和线性稳定的;如果[math],则至少存在一个流行平衡。更确切地说,我们探讨了基本繁殖数的定性特性,并研究了个体在扩散和平流方面的空间分布。我们发现,当平流较大时,会出现集中现象,而对于感染个体的小规模扩散,传染病将被根除。我们的理论结果可以为传染病预测和控制策略提供一些新的启示。
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
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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