Impulsive Control of Rumours

摘要: In this paper we introduce an impulsive control model of a rumour process. The subpopulation of spreaders is classified into two groups, subscribers and nonsubscribers. A subscriber spreader is one who receives a broadcast of a rumour and starts spreading it, a nonsubscriber spreader one who changes 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 those stiflers who once were spreaders (Scenario 2). It is shown that with either scenario the optimal time for the second broadcast is always at the end of the process started by the first broadcast. We consider also the case of several broadcasts.