Effect of time delay on pattern dynamics in a spatial epidemic model

被引：21

作者：

Wang, Yi ^{[1
]}

Cao, Jinde ^{[1
,4
]}

Sun, Gui-Quan ^{[2
,3
]}

Li, Jing ^{[3
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

[2] Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Shanxi, Peoples R China

[3] North Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China

[4] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2014年 / 412卷

基金：

中国国家自然科学基金;

关键词：

Epidemic model; Nonlinear incidence rate; Time delay; Turing instability; Patterns; NOISE; DIFFUSION; BEHAVIOR; TRANSMISSION; VIRUSES; MEASLES; SYSTEM; RATES;

D O I：

10.1016/j.physa.2014.06.038

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Time delay, accounting for constant incubation period or sojourn times in an infective state, widely exists in most biological systems like epidemiological models. However, the effect of time delay on spatial epidemic models is not well understood. In this paper, spatial pattern of an epidemic model with both nonlinear incidence rate and time delay is investigated. In particular, we mainly focus on the effect of time delay on the formation of spatial pattern. Through mathematical analysis, we gain the conditions for Hopf bifurcation and Turing bifurcation, and find exact Turing space in parameter space. Furthermore, numerical results show that time delay has a significant effect on pattern formation. The simulation results may enrich the finding of patterns and may well capture some key features in the epidemic models. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：137 / 148

页数：12

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