Dynamics of positive solutions to SIR and SEIR epidemic models with saturated incidence rates

被引：80
|
作者：
Liu, Zhenjie [1 ,2 ]
机构：
[1] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China
[2] Harbin Univ, Dept Math, Harbin 150086, Heilongjiang, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2013年 / 14卷 / 03期
基金：
高等学校博士学科点专项科研基金;
关键词：
Epidemiological model; Coincidence degree; Ito's formula; Stochastic Lyapunov function; Asymptotic behavior; PERIODIC-SOLUTIONS; GLOBAL STABILITY; DELAYED SIR; EXISTENCE;
D O I：
10.1016/j.nonrwa.2012.09.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we obtain sufficient criteria for the existence of periodic solutions to deterministic SIR and SEIR epidemic models with modified saturation incidence rates by means of using the continuation theorem based on coincidence degree theory, and we show that the solution is unique and globally stable. Second, we discuss their corresponding stochastic epidemic models with random perturbation have a unique global positive solution respectively, and we utilize stochastic Lyapunov functions to investigate the asymptotic behavior of the solution. (C) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1286 / 1299
页数：14
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