Optimal Control Strategies Depending on Interest Level for the Spread of Rumor

Abstract

Many media channels such as broadcast, newspaper, and social networks diffuse a variety of information which can cause spread of many rumors. There are social damage and economic damage due to the spread of rumors. Thus one needs to establish strategies for controlling the rumors. We first propose rumor model with three control strategies for preventing the spread of rumor, (1) announcing the truth before ignorant receives rumor, (2) punishing spreaders, and (3) deleting information of the rumor in media, and consider optimal control problems to minimize the number of spreaders while minimizing the cost of three control strategies for preventing the spread of rumors. The analysis of optimal control problems is conducted as Pontryagin’s Maximum Principle. Furthermore, adapted optimal control is performed to investigate the effect of three controls under isoperimetric constraints. By using numerical simulations, we compare the number of spreaders before and after applying the three controls and confirm when and how each control should be applied with respect to the interest level of rumor. The lower the interest level of rumor is, the greater the number of spreaders drops after the three controls are applied. In terms of timing of three controls, control (1) should be applied in the early stage of rumor spreading and control (2) is required when the rumors spread the most. After the rumors spread the most, control (3) is needed. Commonly the higher the interest level is, the more controls (1) and (2) are required. On the other hand, control (3) is needed a lot when the interest level is low.