University of Tabriz Computational Methods for Differential Equations 2345-3982 10 3 2022 07 01 Backward bifurcation in a two strain model of heroin addiction 656 673 13344 10.22034/cmde.2021.44619.1881 EN Reza Memarbashi Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran. Atena Ghasemabadi Esfarayen University of Technology, Esfarayen, North Khorasan, Iran. Zahra Ebadi Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran. Journal Article 2021 02 17 Among the various causes of heroin addiction, the use of prescription opioids is one of the main reasons. In this article, we introduce and analyze a two-strain epidemic model with the superinfection for modeling the effect of prescribed opioids abuse on heroin addiction. Our model contains the impact of relapse of individuals under treatment/rehabilitation to drug abuse in each strain. We extract the basic reproductive ratio, the invasion numbers and study the occurrence of backward bifurcation in strain dominance equilibria, i.e., boundary equilibria. Also, we explore both the local and global stability of DFE and boundary equilibria under suitable conditions. Furthermore, we study the existence of the coexistence equilibrium point. We prove that when R0 < 1, the coexistence equilibrium point can exist, i.e., backward bifurcation occurs in coexistence equilibria. Finally, we use numerical simulation to describe the obtained analytical results.  https://cmde.tabrizu.ac.ir/article_13344_2e6fd9d3c835ce55ea84c49f19926a7c.pdf