Global dynamics of a mathematical model for HTLV-I infection of CD4⁺ T-cells

Abstract

In this paper, a mathematical model for HILV-I infection of CD4⁺ T-cells is investigated. The force of infection is assumed be of a function in general form, and the resulting incidence term contains, as special cases, the bilinear and the saturation incidences. The model can be seen as an extension of the model [Wang et al. Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression, Math. Biosci. 179 (2002) 207-217; Song, Li, Global stability and periodic solution of a model for HTLV-I infection and ATL progression, Appl. Math. Comput. 180(1) (2006) 401-410]. Mathematical analysis establishes that the global dynamics of T-cells infection is completely determined by a basic reproduction number ${\mathfrak{R}}_0$. If ${\mathfrak{R}}_0⩽1$, the infection-free equilibrium is globally stable; if ${\mathfrak{R}}_0>1$, the unique infected equilibrium is globally stable in the interior of the feasible region.