Dynamics of an SAITS alcoholism model on unweighted and weighted networks

A novel SAITS alcoholism model on networks is introduced, in which alcoholics are divided into light problem alcoholics and heavy problem alcoholics. Susceptible individuals can enter into the compartment of heavy problem alcoholics directly by contacting with light problem alcoholics or heavy problem alcoholics and the heavy problem alcoholics who receive treatment can relapse into the compartment of heavy problem alcoholics are also considered. First, the dynamics of our model on unweighted networks, including the basic reproduction number, existence and stability of equilibria are studied. Second, the models with fixed weighted and adaptive weighted networks are introduced and investigated. At last, some simulations are presented to illustrate and extend our results. Our results show that it is very important to treat alcoholics to quit the drinking.