Stability and Optimal Control in a Mathematical Model of Online Game Addiction

Abstract

In this paper, we constructed an online game addiction model(including sus-
ceptible, infective, professional and quitting compartments). We also consid-
er that the direct transfer from the susceptible individuals to the professional
individuals. Some properties of the model are derived by the basic reproduc-
tion number R 0 and stability of all kinds of equilibria is obtained. Then we
use Pontriagin’s maximum principle to solve the optimal control strategy.
Finally, Numerical simulations are also conducted in the analytic results.