Debunking rumor in the presence of time delays and saturated rates: An optimal control approach

The rapid diffusion of a false rumor in a large population may possibly yield serious consequences. Releasing clarifying messages against the rumor is a common measure of containing rumor spreading. There exist time delays in rumor spreading, which have notable influence on the velocity and range of rumor spreading. In the presence of time delays, the problem of effectively releasing rumor-clarifying messages is addressed. First, a controlled rumor spreading model, in which four time delays are taken into account, is advised. Building on this, the original problem boils down to a delayed optimal control model. By invoking Pontryagin minimum principle, the associated optimality system is deduced. Thereby, the control model is solved algorithmically. Next, the effectiveness of the proposed algorithm is validated. Finally, the influence of the time delays is examined. This work contributes to effective rumor control.