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Impulsive control of rumours with two broadcasts

Published online by Cambridge University Press:  17 February 2009

Selma Belen ,
C. Yalçin Kaya  and
C. E. M. Pearce
Selma Belen
Affiliation:
School of Mathematics, The University of Adelaide, Adelaide SA 5005, Australia; e-mail: [email protected].
C. Yalçin Kaya
Affiliation:
School of Mathematics and Statistics, University of South Australia, Mawson Lakes SA 5095, Australia; e-mail: [email protected].
C. E. M. Pearce
Affiliation:
School of Mathematics, The University of Adelaide, Adelaide SA 5005, Australia; e-mail: [email protected].
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 3 , January 2005 , pp. 379 - 391
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions (Dover, New York, 1965).Google Scholar
[2]Belen, S. and Pearce, C. E. M., “Rumours with general initial conditions”, ANZIAM J. 45 (2004) 393–400.CrossRefGoogle Scholar
[3]Blaquière, A., “Impulsive optimal control with finite or infinite time horizon”, J. Optim. Theory Appl. 46 (1985) 431–439.CrossRefGoogle Scholar
[4]Frost, C., “Tales on the internet: making it up as you go along”, ASLIB Proc. 52 (2000) 5–10.CrossRefGoogle Scholar
[5]Pearce, C. E. M., Kaya, C. Y. and Belen, S., “Impulsive control of a sequence of rumour processes”, submitted.Google Scholar
[6]Rempala, R. and Zabczyk, J., “On the maximum principle fordeterministic impulse control problems”, J. Optim. Theory Appl. 59 (1988) 281–288.CrossRefGoogle Scholar