Debunking Rumor in the Presence of Time Delays and Saturated Rates: An Optimal Control Approach

Abstract The rapid diffusion of rumors in a large population may yield serious consequences. Debunking rumors by releasing clarifying messages is a common means of containing rumor spreading. In the process of rumor spreading, there exist time delays and saturated effects. This paper addresses the problem of debunking a rumor in the presence of four time delays and four saturated rates. First, a novel controlled rumor spreading model is advised. Thereby, the original problem is reduced to an optimal control model. The optimality system for the optimal control model is deduced. An iterative algorithm for solving the optimal control model is presented. The convergence and superiority of the algorithm are validated through computer experiments. The possibility of estimating some key factors in the optimal control model is explored. Finally, the robustness of the algorithm to the initial conditions, the time delays, and the decay indices, is corroborated through simulation experiments. This work contributes to effective rumor debunking.