Dynamic behaviors of a class of HIV compartmental models

Based on heterogeneities in drug efficacy (either spatial or phenotypic), two HIV compartmental models were proposed in Callaway and Perelson (2002) 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 R0⩽1 (for which the infection equilibrium does not exist), the infection-free equilibrium is globally asymptotically stable; while when R0>1 (for which the infection equilibrium exists), the infection equilibrium is globally asymptotically stable.