Loading [Contrib]/a11y/accessibility-menu.js
Search Advanced

Mathematical Biosciences and Engineering

2011, Volume 8, Issue 4: 1019-1034. doi: 10.3934/mbe.2011.8.1019
Previous Article Next Article

Global asymptotic properties of staged models with multiple progression pathways for infectious diseases

  • 1.
    Department of Applied Mathematics and Computer Science, Samara Nayanova Academia, Molodogvardeyskaya 196, 443001, Samara
  • 2.
    MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick
  • Received: 01 October 2010 Accepted: 29 June 2018 Published: 01 August 2011

  • MSC : Primary: 92D30; Secondary: 34D20.

  • We consider global asymptotic properties of compartment staged-progression models for infectious diseases with long infectious period, where there are multiple alternative disease progression pathways and branching. For example, these models reflect cases when there is considerable difference in virulence, or when only a part of the infected individuals undergoes a treatment whereas the rest remains untreated. Using the direct Lyapunov method, we establish sufficient and necessary conditions for the existence and global stability of a unique endemic equilibrium state, and for the stability of an infection-free equilibrium state.

    Citation: Andrey V. Melnik, Andrei Korobeinikov. Global asymptotic properties of staged models with multiple progression pathways for infectious diseases[J]. Mathematical Biosciences and Engineering, 2011, 8(4): 1019-1034. doi: 10.3934/mbe.2011.8.1019

    Related Papers:

  • We consider global asymptotic properties of compartment staged-progression models for infectious diseases with long infectious period, where there are multiple alternative disease progression pathways and branching. For example, these models reflect cases when there is considerable difference in virulence, or when only a part of the infected individuals undergoes a treatment whereas the rest remains untreated. Using the direct Lyapunov method, we establish sufficient and necessary conditions for the existence and global stability of a unique endemic equilibrium state, and for the stability of an infection-free equilibrium state.


  • This article has been cited by:

    1. King-Yeung Lam, Xueying Wang, Tianran Zhang, Traveling Waves for a Class of Diffusive Disease-Transmission Models with Network Structures, 2018, 50, 0036-1410, 5719, 10.1137/17M1144258
    2. Gang Huang, Anping Liu, A note on global stability for a heroin epidemic model with distributed delay, 2013, 26, 08939659, 687, 10.1016/j.aml.2013.01.010
    3. Paul Georgescu, Hong Zhang, A Lyapunov functional for a SIRI model with nonlinear incidence of infection and relapse, 2013, 219, 00963003, 8496, 10.1016/j.amc.2013.02.044
    4. Leonid Shaikhet, Andrei Korobeinikov, Stability of a stochastic model for HIV-1 dynamics within a host, 2016, 95, 0003-6811, 1228, 10.1080/00036811.2015.1058363
    5. Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility, 2013, 10, 1551-0018, 369, 10.3934/mbe.2013.10.369
    6. Jianquan Li, Yanni Xiao, Fengqin Zhang, Yali Yang, An algebraic approach to proving the global stability of a class of epidemic models, 2012, 13, 14681218, 2006, 10.1016/j.nonrwa.2011.12.022
    7. Cruz Vargas-De-León, Global stability properties of age-dependent epidemic models with varying rates of recurrence, 2016, 39, 01704214, 2057, 10.1002/mma.3621
    8. Ellina V. Grigorieva, Evgenii N. Khailov, Andrei Korobeinikov, Optimal quarantine‐related strategies for COVID‐19 control models, 2021, 147, 0022-2526, 622, 10.1111/sapm.12393
    9. Zhimin Han, Yi Wang, Jinde Cao, Impact of contact heterogeneity on initial growth behavior of an epidemic: Complex network-based approach, 2023, 451, 00963003, 128021, 10.1016/j.amc.2023.128021
  • Reader Comments
  • © 2011 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(3020) PDF downloads(579) Cited by(9)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog