Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function

In this research, we investigate the global properties of the heroin epidemic model with time distributed delay and nonlinear incidence function. We show that the system has threshold dynamics in terms of R₀, and we prove, a Lyapunov function, that for R₀<1 the drug-free equilibrium is globally asymptotically stable. For R₀>1, we give the persistence result of the heroin consumption. We also show the global stability of the endemic equilibrium for R₀>1 using a suitable Lyapunov function. The mathematical results are illustrated by numerically simulations.