Optimal control of information epidemics modeled as Maki Thompson rumors

Kandhway, Kundan and Kuri, Joy (2014) Optimal control of information epidemics modeled as Maki Thompson rumors. In: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 19 (12). pp. 4135-4147.

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Abstract

We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin's Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas. We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns. (C) 2014 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Publication:	COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Publisher:	ELSEVIER SCIENCE BV
Additional Information:	Copy right for this article belongs to the ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Keywords:	Maki Thompson rumor model; Optimal control; Pontryagin's Minimum Principle; Social networks
Department/Centre:	Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Date Deposited:	21 Aug 2014 10:26
Last Modified:	21 Aug 2014 10:26
URI:	http://eprints.iisc.ac.in/id/eprint/49610

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