The analysis of the SIRS alcoholism models with relapse on weighted networks

Two SIRS alcoholism models with relapse on networks with fixed and adaptive weight are introduced. The spread of alcoholism threshold [Formula: see text] is calculated by the next generation matrix method. For the model with fixed weight, we prove that when [Formula: see text] the alcohol free equilibrium is globally asymptotically stable, then the drinking crowd gradually disappear. When [Formula: see text], the alcoholism equilibrium is global attractivity, then the density of alcoholics will remain in a stable value. For the model with adaptive weight, we only make some numerical simulations. We also give two effective strategies. Our results show that the treatment of recuperator for stopping relapsing and preventing the susceptible people to drink are two effective measures to eliminate alcoholism problem, and preventing the susceptible people to drink is more effective when the proportion of recuperator to accept treatment is equal to the proportion of susceptible people to refuse drinking alcohol.