Optimal Control Strategies for an Advertisement Viral Diffusion

  • João N. C. Gonçalves
  • Helena Sofia Rodrigues
  • M. Teresa T. Monteiro
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 223)


The process of diffusing viral marketing campaigns through social networks can be modeled under concepts of mathematical epidemiology. Based on a Susceptible-Infected-Recovered (SIR) epidemiological model, the benefits of optimal control theory on the diffusion of a real viral advertisement are studied. Two optimal control strategies that could help marketers to maximize the spread of information and minimize the costs associated to it in optimal time windows are analyzed and compared. The uniqueness of optimality system is proved. Numerical simulations show that high investment costs in publicity strategies do not imply high overall levels of information diffusion. This paper contributes to the current literature by studying a viral marketing campaign using real numerical data.


Optimal control theory Viral marketing SIR epidemiological model Information diffusion strategies 



The authors would like to acknowledge the comments and suggestions from the reviewers, which improved the quality of the paper. This work was supported in part by the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013; and through Algoritmi R&D Center, under COMPETE: POCI-01-0145-FEDER-007043 within the Project Scope: UID/CEC/00319/2013.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • João N. C. Gonçalves
    • 1
  • Helena Sofia Rodrigues
    • 2
    • 3
  • M. Teresa T. Monteiro
    • 1
  1. 1.Department of Production and Systems, Algoritmi R&D CenterUniversity of MinhoBragaPortugal
  2. 2.School of Business StudiesPolytechnic Institute of Viana do CasteloValençaPortugal
  3. 3.Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA)University of AveiroAveiroPortugal

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