A LQ Vaccine Communication Game
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.
KeywordsDifferential 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.
- Alexéev, V., Tikhomirov, V., & Fomine, S. (1982). Commande optimale. Moscou: Éditions MIR.Google Scholar
- Brekke, K. R., Cellini, R., Siciliani, L., & Straume, O. R. (2017). Differential games in health-care markets: Models of quality competition with fixed prices. In J. Apaloo & B. Viscolani (Eds.), Advances in dynamic and mean field games. Annals of the International Society of dynamic games (Vol. 15, pp. 145–167). Cham: Birkhäuser.Google Scholar
- Engwerda, J. C. (2005) LQ dynamic optimization and differential games. Chichester: Wiley.Google Scholar
- Gasparini, R., Panatto, D., Lai, P. L., & Amicizia, D. (2015). The “urban myth” of the association between neurological disorders and vaccinations. Journal of Preventive Medicine and Hygiene, 56, e1–e8.Google Scholar
- Guerra, R., Ricciardi, W., & Siliquini, R. (2017). Vaccinazioni: Stato dell’arte, falsi miti e prospettive. Quaderni del Ministero della Salute, 27. Vaccinations: State of the art, false myths and perspectives, Report of the Italian Health Ministry.Google Scholar
- Hotez, P. J. (2017). How the Anti-Vaxxers are winning. The New York Times. The Opinion Pages, February 8 (p. A25).Google Scholar
- Ozawa, S., Portnoy, A., Getaneh, H., Clark, S., Knoll, M., Bishai, D., Yang, H. K., & Patwardhan, P. D. (2016). Modeling the economic burden of adult vaccine-preventable diseases in the United States. Health Affairs, published online October 12.Google Scholar
- Seierstad, A., & Sydsæter, K. (1987). Optimal control theory with economic applications. Amsterdam: North-Holland.Google Scholar
- World Health Organization. (2016, June 7). Addressing vaccine hesitancy. http://www.who.int/immunization/programmes_systems/vaccine_hesitancy/en/