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

Pages: 1019 - 1034, Volume 8, Issue 4, October 2011

doi:10.3934/mbe.2011.8.1019       Abstract        References        Full Text (451.3K)       Related Articles

Andrey V. Melnik - Department of Applied Mathematics and Computer Science, Samara Nayanova Academia, Molodogvardeyskaya 196, 443001, Samara, Russian Federation (email)
Andrei Korobeinikov - MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland (email)

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.

Keywords:  Infectious disease, endemic equilibrium state, global stability, mass action, direct Lyapunov method, Lyapunov function, compartment model, HIV.
Mathematics Subject Classification:  Primary: 92D30; Secondary: 34D20.

Received: October 2010;      Accepted: March 2011;      Published: August 2011.

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