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Mathematical Biosciences and Engineering

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

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  • © 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)
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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