Two Modes of Vaccination Program in Controlled SIR Model

Authors

  • Elena Gubar Saint Petersburg State University
  • Ekaterina Zhitkova Saint Petersburg State University
  • Ekaterina Kupchinenko Saint Petersburg State University
  • Natalia Petriakova Saint Petersburg State University

Abstract

The problem of forming herd immunity to an infectious disease, i.e. influenza, which is optimal to the population, is often considered as a modification of the classical Susceptible-Infected-Recovery model. However the annual vaccination of the total population is quite expensive and is not obligatory for every individual. Any agent in population has a choice: whether or not to participate in the vaccination program. So each epidemic season society confronts a dilemma: how to maintain the necessary immunization level which is subject to individual choice. Apparently each available alternative incurs different costs and benefits for an individual agent and the population in total. We compare social and individual benefits and expenses in two cases: optimal vaccination policy is used to preserve the optimal herd immunity; agents participate in the vaccination campaign, considering only individual benefits. It's supposed that agent choices do not depend only on the cost generated by agents' choices during the epidemic period. Agents also take into account all available information, received from neighbors, media and former experience. Every agent compares it's own preferences and the alternatives, chosen by neighbors and can update its choice every season. We study the influence of information about previous epidemics on the decision making process. We investigate an optimal control problem to study the optimal vaccination behavior during an epidemic period based on classical Susceptible-Infected-Recovery model and present a procedure for making vaccination decisions.

Keywords:

SIR model, vaccination problem, evolutionary games, optimal control, epidemic process

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References

Behncke, H. (2000). Optimal control of deterministic epidemics, Optim. Control Appl. Meth., no. 21, pp. 269–285.

Bonhoeffer, S., May, R. M., Shaw, G. M., and M. A. Nowak (1997). Virus dynamics and drug therapy, it Proc. Natl. Acad. Sci. USA, vol. 94, pp. 6971-6976.

Conn, M. (2006). Handbook of Models for Human Aging Elsevier Academic Press, London (ed.).

Fu, F., D.I. Rosenbloom, L. Wang and M. A. Nowak (2010). Imitation dynamics of vaccination behaviour on social networks. Proceedings of the Royal Society. Proc. R.Soc. B., 278, 42–49.

Gjorgjieva, J, Smith, K., Chowell, G., Sanchez, F., Snyder, J. and C. Castillo-Chavez (2005). The role of vaccination in the control of SARS, Mathematical Biosciences and Engineering, 2(4), 753–769.

Gubar, E., Zhitkova, E. (2013). Decision making procedure in optimal control problem for the sir model. Contributions to game theory and management, 6, 189–199.

Gubar, E., Fotina, L., Nikitina, I., Zhitkova, E. (2012). Two models of the influenza epidemic Contributions to Game Theory and Management, 5, 107–120.

Gubar, E., Zhu, Q. (2013) Optimal Control of Influenza Epidemic Model with Virus Mutations Proceedings of the European Control Conference. Proceedings of ECC13, Zurich: European Control Association, 2013, p. 3125-3130.

Khatri, S., Rael, R., J. Hyman (2003). The Role of Network Topology on the Initial Growth Rate of Influenza Epidemic. Technical report BU-1643-M.

Kermack, W. O. and A. G. Mc Kendrick (1927). A contribution to themathematical theory of epidemics, in Proceedings of the Royal Society. Ser. A. V. 115, No. A771. p.700–721.

Khouzani, M. H. R., Sarkar, S., Altman, E. (2010). Dispatch then stop: Optimal dissemination of security patches in mobile wireless networks. CDC: 2354–2359.

Khouzani, M. H. R., Sarkar, S., and E. Altman (2011). Optimal Control of Epidemic Evolution, in Proceedings of IEEE INFOCOM.

Mehlhorn, H. et al. (2008). Encyclopedia of Parasitology. Third Edition Springer-Verlag Berlin Heidelberg, New York (eds).

Pontryagin, L. S., V. G. Boltyanskii, R. V. Gamkrelidze et E. F. Mishchenko (1962). The Mathematical Theory of Optimal Processes, Interscience.

Traulsen, A., Pacheco, J. M., Nowak, M. A. (2007). Pairwise comparison and selection temperature in evolutionary game dynamics.J. Theor. Biol.246, 522-529.

Kolesin, I., Gubar, E., Zhitkova, E. (2014). Strategies of control in medical and social systems. Unipress, SPbSU, St.Petersburg. SPbU.

Sandholm, W. H. (2011). Population Games and Evolutionary Dynamics, MIT.

Sandholm, W. H., E. Dokumaci, and F. Franchetti (2010). Dynamo: Diagrams for Evolutionary Game Dynamics, version 0.2.5. http://www.ssc.wisc.edu/whs/dynamo.

Weibull, J. (1995). Evolutionary Game Theory — Cambridge, MA: The M.I.T.Press.

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Published

2022-05-24

How to Cite

Gubar, E., Zhitkova, E., Kupchinenko, E. ., & Petriakova, N. . (2022). Two Modes of Vaccination Program in Controlled SIR Model. Contributions to Game Theory and Management, 8. Retrieved from https://gametheory.spbu.ru/article/view/13451

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