Stability Analysis and Optimal Control of Social Media Hoax Propagation Mathematical Model with Forgetting Mechanism

Hoax is an information or explanation with unconfirmed truth. Nowadays, social media is the most used media in hoax propagation. If no action is taken, hoax propagation can cause serious problems. In this paper, a mathematical model representing social media hoax propagation with forgetting mechanism is analyzed in order to study the dynamics of social media hoax propagation in real life. Based on the analysis result, we obtain two equilibria, namely, non-endemic equilibrium and endemic equilibrium whose local stabilities depend on the basic reproduction number or R₀. Social media hoax propagation occurs when R₀ > 1 and does not occur when R₀ < 1. Based on the sensitivity analysis result, the probability that a hoax is considered attractive and the forgetting rate of social media users against hoaxes are the most influential parameters on the dynamics of social media hoax propagation. Next, in order to minimize the number of hoax spreaders and hoax contents on social media, three control variables, namely, anti-hoax campaign, punishment for hoax spreaders, and hoax deletion by authorized parties, are imposed to the mathematical model. The optimal control problem in this paper is solved by using Pontryagin Maximum Principle. The numerical simulation result shows that the bundle implementation of three control strategies is the most effective scenario to minimize the number of hoax spreaders and hoax contents on social media.