Analisis Stabilitas dan Kontrol Optimal Model Matematika Kecanduan Game Online

putri karimah - Universitas Negeri Padang
Muhammad Subhan - Universitas Negeri Padang

Abstract


The purpose of this study is to see how the analysis of stability and optimal control of the mathematical model of online game addiction so that the problem of addiction to online games can be resolved in the future. The author conducted a stability analysis of the model equilibrium point where there are two equilibrium points and also obtained the basic reproduction number R_0=(〖(k〗_2+μ)k_1 β+〖(1-k〗_1)(δ+μ)α+〖(1-k〗_1)β(1-γ)k_2)/(〖(k〗_2+μ)(δ+μ) ). By using Pontryagin's maximum principle, optimal control of the control variables is obtained, namely 〖k_1〗^*=min{1,maks(0,1/c_1  (λ_2-λ_3 )S((αI+βP)/N))} dan 〖k_2〗^*=min{1,maks(0,1/c_2  ((λ_2-λ_3 )I+〖(λ〗_3-λ_4)γI))}.

The purpose of this study is to see how the analysis of stability and optimal control of the mathematical model of online game addiction so that the problem of addiction to online games can be resolved in the future. The author conducted a stability analysis of the model equilibrium point where there are two equilibrium points and also obtained the basic reproduction number . By using Pontryagin's maximum principle, optimal control of the control variables is obtained, namely  dan.


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References


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DOI: http://dx.doi.org/10.24036/unpjomath.v7i3.12605