Optimal age control of bio-population dynamics

Volodymyr Kyrylych, Olha Milchenko

Анотація


The object of this paper is the problem of optimal control of a semi-linear system of two first-order hyperbolic equations with integral constraints. Using the method of characteristics and the maximum principle the necessary conditions for optimality are obtained.

Повний текст:

PDF (English)

Посилання


C. Almeder, J. P. Caulkins, G. Feichtinger, and G. Tragler, An age-structured single-state drug initiation model-cycles of grug epidemics and optimal prevention programs, Socio-Economic Planning Sciences 38 (2004), no. 1, 91-109. DOI: 10.1184/R1/6471008.v1

A. V. Arguchintsev, Optimal control of hyperbolic systems, Fizmatlit Publ, Moscow, 2007 (in Russian).

W. L. Chan and B. Z. Guo, Optimal birth control of population dynamics, J. Math. Anal. Appl. 144 (1989), no. 2, 532-552. DOI: 10.1016/0022-247x(89)90350-8

S. Chawla and S. Lenhart, Application of optimal control theory to bioremediation, J. Comput. Appl. Math. 114 (2000), no. 1, 81-102. DOI: 10.1016/S0377-0427(99)00290-3

A. L. Dawidowicz, A. Poskrobko, Matematyczne modele dynamiki populacji zalezne od wieku}, Metody matematyczne w zastosowaniach, 2014, Tom 2, pp. 39-58.

Н. В. Дерев'янко, В. М. Кирилич, Оптимальне керування гіперболічною системою напівлінійних рівнянь першого порядку з нескінченним горизонтом планування, Укр. мат. ж. 67 (2015), no. 2, 185-201; English version: T. O. Derev’yanko and V. M. Kyrylych, Problem of optimal control for a semilinear hyperbolic system of equations of the first order with infinite horizon planning, Ukr. Math. J. 67 (2015), no. 2, 211-229. DOI: 10.1007/s11253-015-1075-3

G. Feichtinger, G. Tragler, and V. M. Veliov, Optimality conditions for age-stractured control systems, J. Math. Anal. Appl. 288 (2003), no. 1, 47-68. DOI: 10.1016/j.jmaa.2003.07.001

N. Hritoneko and Y. Yatsenko, Mathematical modelling in economics, ccology and the environment, 2nd Ed., Springer Optimization and Its Applications 88, Springer 2013. DOI: 10.1007/978-1-4614-9311-2

A. G. M'Kendrick, Applications of mathematics to medical problems, Proc. Edinb. Math. Soc. 40 (1926), 98-130. DOI: 10.1017/S0013091500034428

S. P. Sethi and G. L. Thompson, Optimal control theory. Applications to Management Science and Economics, 2nd ed., New York, Springer, 2005.

V. Volterra, Variations and fluctuations of the number of individuals in animal species living together, In: Chapman, R. N., Ed., Animal Ecology, New York, McGraw-Hill, 1931. pp. 409-448. DOI: 10.1086/284409

J. von Foerster, Some remarks on changing populations, In: The Kinetics of Cellular Proliferation, ed. by F. Stohlman, Jr., Grune and Stratton, New York, 1955, pp. 382–407.




DOI: http://dx.doi.org/10.30970/vmm.2020.90.105-112

Посилання

  • Поки немає зовнішніх посилань.