Guo, Youming; Li, Tingting Optimal control and stability analysis of an online game addiction model with two stages. (English) Zbl 1446.49002 Math. Methods Appl. Sci. 43, No. 7, 4391-4408 (2020). Summary: In this paper, we establish a mathematical model of online game addiction with two stages to research the dynamic properties of it. The existence of all equilibria is obtained, and the basic reproduction number is calculated by the method of next-generation matrix. The global asymptotic stability of disease-free equilibrium (DFE) is proved by comparison principle, and the global asymptotic stability of endemic equilibrium (EE) is proved by constructing an appropriate Lyapunov function. Then we use the Pontryagin’s maximum principle to find the optimal solution of the model, so that the number of infected people can be minimized. In numerical simulation, firstly, we validate the global stability of DFE and EE. Secondly, we consider three kind of control measures (treatment, isolation, and education) and divide them into four cases. The models with control and without control are solved numerically by using forward and backward sweep Runge-Kutta method. In order to achieve the best control effect, we suggest that three kind of measures should be used simultaneously according to the optimal control strategy. Cited in 8 Documents MSC: 49J15 Existence theories for optimal control problems involving ordinary differential equations 49K15 Optimality conditions for problems involving ordinary differential equations 92D30 Epidemiology Keywords:forward and backward sweep method; game addiction model; Lyapunov function; optimal control; two stages; disease-free equilibrium; endemic equilibrium PDFBibTeX XMLCite \textit{Y. Guo} and \textit{T. Li}, Math. Methods Appl. Sci. 43, No. 7, 4391--4408 (2020; Zbl 1446.49002) Full Text: DOI