Mathematical Biosciences and Engineering, 2011, 8(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

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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Keywords global stability; mass action; compartment model; direct Lyapunov method; Lyapunov function; endemic equilibrium state; Infectious disease; HIV.

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


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