ANZIAM J.
46 (2005), 379391

Impulsive control of rumours with two broadcasts


C. Yalcin Kaya
School of Mathematics and Statistics
University of South Australia
Mawson Lakes SA 5095
Australia
yalcin.kaya@unisa.edu.au





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.

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