Abstract
Consideration was given to the possibility of applying the vector optimization methods and the optimal control theory to construction of the economy modes of maintaining the collective immunity to the infectious agent with allowance for the population psychology and medico-social effects of vaccination. Described was a population immunization model taking into account the natural immunization component. Cases of single and double vaccination with determination of their optimal modes were examined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Infektsionnye bolezni. Rukovodstvo (Manual for Infectious Diseases), Moscow: Meditsinskaya Literatura, 2014.
Medunitsin, N.V. and Yakovleva, T.V., Improvement of the Approaches to the Vaccinal Prevention, Epidemiol. Vaktsinoprofilakt., 2012, No. 3, pp. 70–78
Kolesin, I.D. and Tendera, M.F., Optimization of Anti-Influenza Prophylaxis, Autom. Remote Control, 1998, Vol. 59, no 3, pp. 412–417
Kolesin, I.D. and Zhitkova, E.M., Optimization of Students’ Anti-epidemic Prophylaxis, Autom. Remote Control, 2008, Vol. 69, No. 7, pp. 1216–1222.
Müller, J., Optimal Vaccination Patterns in Age-structured Populations, SIAM J. Appl. Math., 1998, Vol. 59, pp. 222–241
Kribs-Zaleta, C.M. and Martcheva, M., Vaccination Strategies and Backward Bifurcation in an Agesince- infection Structured Model, Math. Biosci., 2002, Vol. 177, pp. 317–332
Kribs-Zaleta, C.M. and Velasco-Hernandez, J.X., A Simple Vaccination Model with Multiple Endemic States, Math. Biosci., 2000, Vol. 164, pp. 183–201
Moghadas, S.M. and Gumel, A.B., A Mathematical Study of a Model for Childhood Diseases with Non-permanent Immunity, J. Comput. Appl. Math., 2003, Vol. 157, pp. 347–363
Hansen, E. and Day, T., Optimal Control of Epidemics with Limited Resources, J. Math. Biol., 2011, Vol. 62, pp. 423–451
Onyango, N.O. and Müller, J., Determination of Optimal Vaccination Strategies Using an Orbital Stability Threshold from Periodically Driven Systems, J. Math. Biol., 2014, Vol. 68, pp. 763–784
Gubar, E., Zhitkova, E., Fotina, L., and Nikitina, I., Two Models of the Influenza Epidemic Contributions to Game Theory and Management, in Collected Papers Presented at the Fourth Int. Conf. Game Theory and Management (GTM2011), vol. V, St. Petersburg: Graduate School of Management, 2012, pp. 107–120
Smorodintsev, A.A., Gripp i ego profilaktika (Grippe and Its Prophylaxis), St. Petersburg: Meditsina, 1984.
Bukrinskaya, A.G., Virusologiya (Virology), Moscow: Meditsina, 1986.
Mashunin, Yu.K., Metody i modeli vektornoi optimizatsii (Methods and Models of Vector Optimization), Moscow: Nauka, 1986.
Moiseev, N.N., Matematicheskie zadachi sistemnogo analiza (Mathematical Problems of System Analysis), Moscow: Nauka, 1981.
Gripp (Grippe), Karpukhin, G.I., Ed., Leningrad: Meditsina, 1986.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.D. Kolesin, E.M. Zhitkova, 2016, published in Avtomatika i Telemekhanika, 2016, No. 6, pp. 109–120.
This paper was recommended for publication by A.I. Mikhal’skii, a member of the Editorial Board
Rights and permissions
About this article
Cite this article
Kolesin, I.D., Zhitkova, E.M. Optimization of immunocorrection of collective immunity. Autom Remote Control 77, 1031–1040 (2016). https://doi.org/10.1134/S0005117916060072
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117916060072