Global stability of HIV-1 and HIV-2 model with drug resistance compartment

Abstract

In this paper we propose a new mathematical model describing the dynamics of the human immunodeficiency virus 1 and 2 with drug resistant compartment. We proved the positivity and boundedness of solutions with non-negative initial conditions. The dynamical system admits four equilibrium states: free equilibrium disease, one endemic equilibrium of each strain and one of the two strains. Two basic reproduction numbers are calculated. The global stability of the four equilibrium points is proved by using suitable Lyapunov functions. Numerical simulations were carried out to illustrate our results and a parameter sensitivity analysis completed this work.