How to run a campaign: Optimal control of SIS and SIR information epidemics

Kandhway, Kundan and Kuri, Joy (2014) How to run a campaign: Optimal control of SIS and SIR information epidemics. In: APPLIED MATHEMATICS AND COMPUTATION, 231 . pp. 79-92.

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Abstract

Information spreading in a population can be modeled as an epidemic. Campaigners (e.g., election campaign managers, companies marketing products or movies) are interested in spreading a message by a given deadline, using limited resources. In this paper, we formulate the above situation as an optimal control problem and the solution (using Pontryagin's Maximum Principle) prescribes an optimal resource allocation over the time of the campaign. We consider two different scenarios-in the first, the campaigner can adjust a direct control (over time) which allows her to recruit individuals from the population (at some cost) to act as spreaders for the Susceptible-Infected-Susceptible (SIS) epidemic model. In the second case, we allow the campaigner to adjust the effective spreading rate by incentivizing the infected in the Susceptible-Infected-Recovered (SIR) model, in addition to the direct recruitment. We consider time varying information spreading rate in our formulation to model the changing interest level of individuals in the campaign, as the deadline is reached. In both the cases, we show the existence of a solution and its uniqueness for sufficiently small campaign deadlines. For the fixed spreading rate, we show the effectiveness of the optimal control strategy against the constant control strategy, a heuristic control strategy and no control. We show the sensitivity of the optimal control to the spreading rate profile when it is time varying. (C) 2014 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	APPLIED MATHEMATICS AND COMPUTATION
Publisher:	ELSEVIER SCIENCE INC
Additional Information:	Copyright for this article belongs to the ELSEVIER SCIENCE INC, USA
Keywords:	Information epidemics; Optimal control; Pontryagin's maximum principle; Social networks; Susceptible-infected-recovered (SIR); Susceptible-infected-susceptible (SIS)
Department/Centre:	Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Date Deposited:	11 May 2014 06:38
Last Modified:	11 May 2014 06:38
URI:	http://eprints.iisc.ac.in/id/eprint/48907

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