Mathematical modeling with optimal control analysis of social media addiction

Abstract

In this paper, we developed a deterministic mathematical model of social media addiction (SMA) with an optimal control strategy. Major qualitative analysis like the social media addiction free equilibrium point (E0), endemic equilibrium point (E∗), basic reproduction number (R0), were computed. From the stability analysis, we found that the social media addiction free equilibrium point (SMAFEP) is locally asymptotically stable if R0<1. The global asymptotic stablity of SMAFEP is stablished using Castillo-Chavez theorem. If R0>1 the unique endemic equilibruim is locally assymptotically stable. Also using Center Manifold theorem, the model exhabits a forward bifurcation at R0=1. The sensitivity of model parameters is done using the normalized forward sensitivity index definition. Secondly, we introduced two time dependent controls on the basic model and formulated an optimal control model. Then, we used the Pontryagin’s maximum principle to find the optimal system of the model. Numerical simulations, on the optimal control problem using the fourth-order Range-Kutta forward-backward sweep method, on the suggested strategies for SMA is performed. We found that to effectively control SMA at a specified period of time, stakeholders and policymakers must apply the integrated control strategies C.