Traveling waves of a diffusive SIR epidemic model with a class of nonlinear incidence rates and distributed delay

被引：39

作者：

Bai, Zhenguo ^{[1
]}

Zhang, Shengli ^{[1
]}

机构：

[1] Xidian Univ, Sch Math & Stat, Xian 710071, Shaanxi, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2015年 / 22卷 / 1-3期

基金：

中国国家自然科学基金;

关键词：

Traveling wave solutions; Diffusive SIR model; Distributed delay; Schauder's fixed point theorem; VECTOR-DISEASE-MODEL; MONOSTABLE EQUATIONS; ASYMPTOTIC SPEED; EXISTENCE; SYSTEMS; FRONTS; SPREAD; PROPAGATION; STABILITY; INFLUENZA;

D O I：

10.1016/j.cnsns.2014.07.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the traveling waves of a diffusive SIR epidemic model with a class of nonlinear incidence rates of the form beta S(x,t) integral(h)(0) f(tau)g(I(x,t - tau))d tau. We find that the existence of traveling waves is determined by the basic reproduction number of the corresponding spatial- homogenous delay differential equations and the minimal wave speed. The existence proof is to introduce an auxiliary system and apply Schauder's fixed point theorem. The non- existence of traveling waves is obtained by two- sided Laplace transform. (C) 2014 Elsevier B. V. All rights reserved.

引用

页码：1370 / 1381

页数：12

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