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

Abstract

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 R01, we give the persistence result of the heroin consumption. We also show the global stability of the endemic equilibrium for R0>1using a suitable Lyapunov function. The mathematical results are illustrated by numerically simulations.

Keywords

• Lyapunov functional
• Uniform persistence
• Weak delay
• Global stability