Stability of an SAIRS alcoholism model on scale-free networks

A new SAIRS alcoholism model with birth and death on complex heterogeneous networks is proposed. The total population of our model is partitioned into four compartments: the susceptible individual, the light problem alcoholic, the heavy problem alcoholic and the recovered individual. The spread of alcoholism threshold R-0 is calculated by the next generation matrix method. When R-0 < 1, the alcohol free equilibrium is globally asymptotically stable, then the alcoholics will disappear. When R-0 > 1, the alcoholism equilibrium is global attractivity, then the number of alcoholics will remain stable and alcoholism will become endemic. Furthermore, the modified SAIRS alcoholism model on weighted contact network is introduced. Dynamical behavior of the modified model is also studied. Numerical simulations are also presented to verify and extend theoretical results. Our results show that it is very important to treat alcoholics to control the spread of the alcoholism. (C) 2017 Elsevier B.V. All rights reserved.