Geodesic
Decision Making Procedure in Optimal Control Problem for the SIR Model
Contributions to game theory and management, Tome 6 (2013), pp. 189-199 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this work we join on classical SIR model to describe influenza epidemic in urban population with procedure of making decision. We suppose that agent in urban population makes a choice: whether or not to participate in vaccination company. Each decision involve different costs and indirectly influence on the population state. We formulated an optimal control problem to study the optimal behavior during epidemic period and vaccination company. All theoretical results are also supported by the numerical simulations.
Keywords: SIR model, vaccination problem, evolutionary games, optimal control, epidemic process. 
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Elena Gubar; Ekaterina Zhitkova. Decision Making Procedure in Optimal Control Problem for the SIR Model. Contributions to game theory and management, Tome 6 (2013), pp. 189-199. http://geodesic.mathdoc.fr/item/CGTM_2013_6_a12/

[1] Behncke H., “Optimal control of deterministic epidemics”, Optim. Control Appl. Meth., 21 (2000), 269–285 | DOI | MR | Zbl

[2] Bonhoeffer S., May R. M., Shaw G. M., Nowak M. A., “Virus dynamics and drug therapy”, Proc. Natl. Acad. Sci. USA, 94 (1997), 6971–6976 | DOI

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

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

[5] Gjorgjieva J., Smith K., Chowell G., Sanchez F., Snyder J., Castillo-Chavez C., “The role of vaccination in the control of SARS”, Mathematical Biosciences and Engineering, 2:4 (2005), 753–769 | DOI | MR | Zbl

[6] Gubar E., Zhitkova E., Fotina L., Nikitina I., “Two Models of the Influenza Epidemic”, Contributions to game theory and management, 4, 2011, 107–120

[7] Karpuhin G. I. (ed.), Gripp, Medicina, Leningrad, 1986

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

[9] Kermack W. O., Mc KendrickA. G., “A contribution to themathematical theory of epidemics”, Proceedings of the Royal Society. Ser. A, 115:771 (1927), 700–721 | DOI | Zbl

[10] Khouzani M. H. R., Sarkar S., Altman E., “Optimal Control of Epidemic Evolution”, Proceedings of IEEE INFOCOM, 2011

[11] Khouzani M. H. R., Sarkar S., Altman E., “Dispatch then stop: Optimal dissemination of security patches in mobile wireless networks”, Proc. of 48th IEEE Conference on Decisions and Control (CDC), 2010, 2354–2359

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

[13] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V. Mishchenko E. F., The Mathematical Theory of Optimal Processes, Interscience, 1962 | MR

[14] Sandholm W. H., Dokumaci E., Franchetti F., Dynamo: Diagrams for Evolutionary Game Dynamics, version 0.2.5, , 2010 http://www.ssc.wisc.edu/w̃hs/dynamo

[15] Kolesin I. D., Zhitkova E. M., Matematicheskie modeli epidemiy, SPbU, 2004