Filomat · 2019 · 31 citations · 17 references
Natural SciencesBehavioral SciencesEconomicsCompartmental ModelingDynamical SystemsGame TheoryAddictionBehavioral ModelingControl TheoryNash EquilibriumOptimal ControlStability TheoryGame AddictionMinimax TheoremNash Equilibrium ProblemsOptimal Control In GamesPontryagin Maximum PrinciplePontryagin's Maximum PrincipleReplicator DynamicsStability Of Equilibria
In this paper, we construct an online game addiction model(including susceptible, infective, professional and quitting compartments). We also consider that the direct transfer from the susceptible individuals to the professional individuals. Some properties of the model are derived by the basic reproduction number R0 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.
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The Mathematical Theory of Optimal Processes
M. L. Chambers, L. S. Pontryagin, V. G. Boltyanskiĭ et al. · OR · 1965 · 3.3K citations