A LQ Vaccine Communication Game

  • Alessandra BurattoEmail author
  • Luca Grosset
  • Bruno Viscolani
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 280)


The vaccination issue is a crucial problem nowadays. We see the presence of an anti-vaccination movement, which takes actions to spread the idea that vaccines are ineffective and even dangerous. We propose a model for this public health problem using the differential game framework and aspire to help understanding the effectiveness of communication policies. One player of the game is the health-care system, which aims to minimize the number of unvaccinated people at minimum cost. The second player is a pharmaceutical firm, which produces and sells a given type of vaccine, and wants to maximize its profit. To pursue their objectives, the two players run suitable vaccination advertising campaigns. We study the open-loop Nash equilibrium advertising strategies of the two players and observe that the communication policy of the pharmaceutical firm helps the health-care system to decrease the number of unvaccinated people.


Differential games Vaccine communication policy Advertising 



The authors thank two anonymous referees for their interesting comments and suggestions. The third author wants to thank D. Bonandini for instructive talks on the vaccination problem in Italy.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Alessandra Buratto
    • 1
    Email author
  • Luca Grosset
    • 1
  • Bruno Viscolani
    • 1
  1. 1.Department of Mathematics Tullio Levi-CivitaUniversity of PadovaPadovaItaly

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