Dynamic behaviors of a class of HIV compartmental models. (English) Zbl 1352.92143
Summary: Based on heterogeneities in drug efficacy (either spatial or phenotypic), two HIV compartmental models were proposed in [D. S. Callaway and A. S. Perelson, Bull. Math. Biol. 64, No. 1, 29–64 (2002; Zbl 1334.92227)] to study the HIV virus dynamics under drug treatment. In this paper, we provide a global analysis on the two models, including the positivity and boundedness of solutions and the global stability of equilibrium solutions. In particular, we show that when the basic reproduction number \(R_0\leqslant 1\) (for which the infection equilibrium does not exist), the infection-free equilibrium is globally asymptotically stable; while when \(R_0>1\) (for which the infection equilibrium exists), the infection equilibrium is globally asymptotically stable.
Keywords:
HIV compartmental model; global stability; Lyapunov function; LaSalle’s invariance principleCitations:
Zbl 1334.92227References:
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