Dynamics of a two-strain disease model with general incidence function and treatment

In this paper, we investigate the global dynamics of a Two-Strain Disease Model with a general nonlinear incidence rate and treatment term. The two basic reproduction numbers, [Formula: see text] associated to the drug-susceptible strain and [Formula: see text] associated to the drug resistant strain, are derived using the next generation matrix method. We give a complete study of the existence and global stability of the steady states for the model so that we discuss four cases: the trivial steady state [Formula: see text], the endemic equilibrium [Formula: see text] regarding the drug-susceptible strain, the endemic equilibrium [Formula: see text] concerning the drug resistant strain, and the coexistence equilibrium [Formula: see text] relative to both drug-susceptible and drug-resistant strains. By using Lyapunov theory, we prove the global stability of the equilibria under some hypothesis on the basic reproduction numbers and the general incidence rate. Moreover, we prove that epidemics occur regarding any strain when the associated basic reproduction number remains above one. We also study the sensitivity of parameters that influence the basic reproduction number [Formula: see text]. Finally, to illustrate our analytical results, we give some numerical simulations using the ode45 Matlab routine.