A Heroin Epidemic Model With The Impact Of Vaccination

Heroin and other opioid drugs are used by tens of millions of people around the world,resulting in hundreds of thousands of deaths each year.Heroin abuse is considered as an epidemic.Following the successful clinical trials of a vaccine that blocks the pleasure induced by heroin,vaccine therapy is expected to become an important way for heroin users to quit drugs in the future.In this paper,we propose a heroin epidemic model with heroin vaccine in order to understand the mechanism of heroin transmission and the role of heroin vaccine in controlling the spread of heroin.By using the theory and method in differential equations and infectious disease modeling,we define the basic reproduction number?₀of the model and study the existence and stability of equilibria.In particular,the model system without vaccine may undergo backward bifurcation,while the heroin persistent equilibrium is globally asymptotically stable under certain condition as the reproduction number is greater than one.Numerical simulations suggest that the heroin vaccine plays an important role in heroin transmission control.