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Zbl 1221.37204
Xu, Rui
Global dynamics of an HIV-1 infection model with distributed intracellular delays. (English)
[J] Comput. Math. Appl. 61, No. 9, 2799-2805 (2011). ISSN 0898-1221

Summary: In this paper, an HIV-1 infection model with distributed intracellular delays is investigated, where the intracellular delays account for the time the target cells are contacted by the virus particles and the time the contacted cells become actively infected meaning that the contacting virions enter cells and the time the virus has penetrated into a cell and the time the new virions are created within the cell and are released from the cell, respectively. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle's invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, the chronic-infection equilibrium is globally asymptotically stable.

MSC 2000:: *37N25 Dynamical systems in biology
92D30 Epidemiology
34D23 Global stability
34K20 Stability theory of functional-differential equations

Keywords: HIV-1 infection; intracellular delay; stability; Lasalle's invariance principle

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Zentralblatt MATH Berlin [Germany]