Global stability of an SI epidemic model with feedback controls in a patchy environment

被引：33

作者：

Li, Hong-Li ^{[1
]}

Zhang, Long ^{[1
]}

Teng, Zhidong ^{[1
]}

Jiang, Yao-Lin ^{[1
,2
]}

Muhammadhaji, Ahmadjan ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Xi An Jiao Tong Univ, Dept Math, Xian 710049, Shaanxi, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 321卷

基金：

中国国家自然科学基金;

关键词：

Global stability; SI epidemic model; Feedback controls; Patchy environment; Basic reproduction number; Lyapunov function; PREDATOR-PREY MODEL; DYNAMICS; DISEASE; SYSTEM; DELAYS;

D O I：

10.1016/j.amc.2017.10.057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate an SI epidemic model with feedback controls in a patchy environment where individuals in each patch can disperse among n (n >= 2) patches. We derive the basic reproduction number R-0 and prove that the disease-free equilibrium is globally asymptotically stable if R-0 <= 1. In the case of R-0 > 1, we derive sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory. Numerical simulations are carried out to support our theoretical results. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：372 / 384

页数：13

共 36 条

[1]

Aizerman M. A., 1964, Absolute Stability of Regulator Systems

[2]

[Anonymous], 1979, NONNEGATIVE MATRICES

[3]

[Anonymous], 1993, Internat. J. Math. Math. Sci., DOI [10.1155/S0161171293000213, DOI 10.1155/S0161171293000213]

[4]

[Anonymous], 1974, MODELS ECOLOGY

[5]

[Anonymous], 2012, ELECT J DIFFERENTIAL

[6]

Bhatia N. P, 1967, Lecture Notes in Mathematics, V1, P113

[7] Models for transmission of disease with immigration of infectives [J].

Brauer, F ;

van den Driessche, P .

MATHEMATICAL BIOSCIENCES, 2001, 171 (02) :143-154

[8] Global stability of an SI epidemic model with feedback controls [J].

Chen, Lijuan ;

Sun, Jitao .

APPLIED MATHEMATICS LETTERS, 2014, 28 :53-55

[9] Global asymptotical stability of a Logistic model with feedback control [J].

Fan, Yong-Hong ;

Wang, Lin-Lin .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (04) :2686-2697

[10] Threshold dynamics of a nonlinear multi-group epidemic model with two infinite distributed delays [J].

Feng, Xiaomei ;

Wang, Kai ;

Zhang, Fengqin ;

Teng, Zhidong .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (07) :2762-2771

← 1 2 3 4 →