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

Andrey V. Melnik; Andrei Korobeinikov

doi:10.3934/mbe.2011.8.1019

Article Contents

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

Andrey V. Melnik^1, and
Andrei Korobeinikov^2,

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: September 30, 2010

Revised: February 28, 2011

Published: July 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 92D30; Secondary: 34D20.

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