%0 Journal Article %A LIU Feng %T Stability analysis of a drug abuse epidemic model %D 2019 %R 10.11772/j.issn.1001-9081.2018102215 %J Journal of Computer Applications %P 1534-1539 %V 39 %N 5 %X The recovered drug users maybe become susceptible to drug again, but this possibility is neglected in the existing drug abuse epidemic model in which the drug users are assumed to be permanently immune to drugs after recovery. Aiming at the problem, the evolution process of drug abuse population was analyzed with considering both community treatment and isolation therapy, and a drug abuse epidemic model based on temporary immunity was proposed. Furthermore, the basic reproduction number of the proposed model was calculated and the existence and stability of the proposed model equilibrium were discussed. It is shown that the proposed model has a drug free equilibrium which is locally asymptotically stable and a unique endemic equilibrium when the basic reproduction number is less and more than unity respectively. And the global stability of the endemic equilibrium was proved by using a geometric approach. Otherwise, the proposed model has the phenomenon of backward bifurcation under certain conditions when the basic reproduction number is equal to unity. The above results were verified by the numerical simulations. The results indicate that the prevalence of drug abuse can be effectively inhibited by increasing the rate of isolation therapy, improving the effect of community treatment and reducing the infection rate. %U http://www.joca.cn/EN/10.11772/j.issn.1001-9081.2018102215