Mathematical modeling of containing the spread of heroin addiction via awareness program

As many countries are hit by the social economic impact of heroin addiction, there is an urgent need to have an effective awareness program that focuses on educating the population on the danger of heroin addiction and helping the heroin-users quit. This paper aims to study the effect of the awareness program on the spread of heroin dependence using a mathematical model with distributed delay. First, we show the existence threshold parameter (Formula presented.), which we call the basic reproduction number of the spread of heroin use. We prove, via the Lyapunov direct method, that the drug-free equilibrium is globally asymptotically stable if (Formula presented.). If (Formula presented.), the drug dependence persists, and the drug equilibrium is globally asymptotically stable. We give three possible scenarios to find the optimal awareness program strategy that puts the heroin epidemic under control. These scenarios take into consideration the reachability of the population, the immunity against heroin addiction, and the effectiveness of the program to contain the use of heroin in the population and bring (Formula presented.) below one.