Positive steady states in an epidemic model with nonlinear incidence rate

被引：8

作者：

Gao, Xiaoyan ^{[1
,2
]}

Cai, Yongli ^{[2
]}

Rao, Feng ^{[3
]}

Fu, Shengmao ^{[1
]}

Wang, Weiming ^{[2
]}

机构：

[1] Northwest Normal Univ, Sch Math & Stat, Lanzhou 730070, Gansu, Peoples R China

[2] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Peoples R China

[3] Nanjing Tech Univ, Sch Phys & Math Sci, Nanjing 211816, Jiangsu, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 75卷 / 02期

基金：

美国国家科学基金会;

关键词：

Nonconstant positive steady state; Bifurcation; Turing instability; Nonlinear incidence rate; REACTION-DIFFUSION MODEL; HARRISON REACTION SCHEME; CROSS-DIFFUSION; SPATIOTEMPORAL PATTERNS; STATIONARY SOLUTIONS; TURING PATTERNS; BIFURCATION; SYSTEM; DYNAMICS;

D O I：

10.1016/j.camwa.2017.09.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a diffusive epidemic model with nonlinear incidence rate under homogeneous Neumann boundary condition. The value of this study lies in two aspects. Mathematically, we show the stability of the constant positive steady state solution, the existence and nonexistence, the local and global structure of nonconstant positive steady states. And epidemiologically, we find that the system exhibits Turing patterns controlled by diffusion. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：424 / 443

页数：20

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