Global stability for a delayed multi-group SIRS epidemic model with cure rate and incomplete recovery rate

被引：5
|
作者：
Muroya, Yoshiaki [1 ]
Kuniya, Toshikazu [2 ]
机构：
[1] Waseda Univ, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan
[2] Kobe Univ, Grad Sch Syst Informat, Nada Ku, Kobe, Hyogo 6578501, Japan
来源：
INTERNATIONAL JOURNAL OF BIOMATHEMATICS | 2015年 / 8卷 / 04期
基金：
日本学术振兴会;
关键词：
Multi-group SIRS epidemic model; delay; permanence; global stability; Lyapunov functional; BEHAVIOR;
D O I：
10.1142/S1793524515500485
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, by applying Lyapunov functional approach, we establish a sufficient condition on the global stability of a "delayed" multi-group SIRS epidemic model with cure rate and incomplete recovery rate which does not depend on the delays and is an extension of the "light drug model" studied in the recent paper [Muroya, Li and Kuniya, Complete global analysis of an SIRS epidemic model with graded cure rate and incomplete recovery rate, J. Math. Anal. Appl. 410 (2014) 719-732] to a multi-group model. Applying a Lyapunov functional on total population of each compartment, we offer new techniques for the delayed system, how to prove the permanence, the existence of the endemic equilibrium and the global stability of disease-free equilibrium for the reproduction number (R) over tilde (0) <= 1 and endemic equilibrium for (R) over tilde (0) > 1.
引用
收藏
页数：30
相关论文
共 50 条
  • [1] GLOBAL STABILITY OF A DELAYED MULTI-GROUP SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATES AND RELAPSE OF INFECTION
    Muroya, Yoshiaki
    Kuniya, Toshikazu
    Enatsu, Yoichi
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (09): : 3057 - 3091
  • [2] Global stability for a multi-group SIRS epidemic model with varying population sizes
    Muroya, Yoshiaki
    Enatsu, Yoichi
    Kuniya, Toshikazu
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (03) : 1693 - 1704
  • [3] Stability of a delayed SIRS epidemic model with a nonlinear incidence rate
    Xu, Rui
    Ma, Zhien
    CHAOS SOLITONS & FRACTALS, 2009, 41 (05) : 2319 - 2325
  • [4] GLOBAL BEHAVIORS FOR A CLASS OF MULTI-GROUP SIRS EPIDEMIC MODELS WITH NONLINEAR INCIDENCE RATE
    Tang, Qian
    Teng, Zhidong
    Jiang, Haijun
    TAIWANESE JOURNAL OF MATHEMATICS, 2015, 19 (05): : 1509 - 1532
  • [5] Global stability of a multi-group delayed epidemic model with logistic growth
    Almuqati, B. M.
    AIMS MATHEMATICS, 2023, 8 (10): : 23046 - 23061
  • [6] Complete global analysis of an SIRS epidemic model with graded cure and incomplete recovery rates
    Muroya, Yoshiaki
    Li, Huaixing
    Kuniya, Toshikazu
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 410 (02) : 719 - 732
  • [7] Epidemic dynamics on a delayed multi-group heroin epidemic model with nonlinear incidence rate
    Liu, Xianning
    Wang, Jinliang
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (05): : 2149 - 2160
  • [8] GLOBAL DYNAMICS OF A MULTI-GROUP EPIDEMIC MODEL WITH GENERAL RELAPSE DISTRIBUTION AND NONLINEAR INCIDENCE RATE
    Wang, Jinliang
    Zu, Jian
    Liu, Xianning
    Huang, Gang
    Zhang, Jimin
    JOURNAL OF BIOLOGICAL SYSTEMS, 2012, 20 (03) : 235 - 258
  • [9] GLOBAL STABILITY OF A MULTI-GROUP SIS EPIDEMIC MODEL FOR POPULATION MIGRATION
    Kuniya, Toshikazu
    Muroya, Yoshiaki
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2014, 19 (04): : 1105 - 1118
  • [10] Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate
    Muroya, Yoshiaki
    Enatsu, Yoichi
    Nakata, Yukihiko
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 377 (01) : 1 - 14
12345