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Stability analysis of an HIV/AIDS epidemic model with treatment
L. Cai, X. Li, , B. Guo
Published in
2009
Volume: 229
   
Issue: 1
Pages: 313 - 323
Abstract
An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number ℜ0. If ℜ0 ≤ 1, the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if ℜ0 > 1. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results. © 2008 Elsevier B.V. All rights reserved.
About the journal
JournalJournal of Computational and Applied Mathematics
ISSN03770427