Impulsive control of rumours with two broadcasts

Abstract

In this paper we introduce an impulsive control model of a rumour process. The spreaders are classified as subscriber spreaders, who receive an initial broadcast of a rumour and start spreading it, and nonsubscriber spreaders who change from being an ignorant to being a spreader after encountering a spreader. There are two consecutive broadcasts. The first starts the rumour process. The objective is to time the second broadcast so that the final proportion of ignorants is minimised. The second broadcast reactivates as spreaders either the subscriber stiflers (Scenario 1) or all individuals who have been spreaders (Scenario 2). It is shown that with either scenario the optimal time for the second broadcast is always when the proportion of spreaders drops to zero.