Математическая модель по среднесрочным прогнозам COVID-19 в Казахстане
DOI:
https://doi.org/10.26577/JMMCS.2021.v111.i3.08Ключевые слова:
обратные задачи, идентификация, дифференциальная эволюцияАннотация
В работе сформулирована и решена задача идентификации неизвестных параметров математической модели распространения инфекции COVID-19 в Казахстане, по дополнительной статистической информации об инфицированных, выздоровевших и летальных случаях. Рассматриваемая модель, входящая в семейство модифицированных моделей на базе модели SIR, разработанной У. Кермаком и А. Маккендриком в 1927 году, представлена в виде системы из 5 нелинейных обыкновенных дифференциальных уравнений, описывающая вариационный переход индивидуумов из одной группы в другую. За счет решения обратной задачи, сведенной к решению оптимизационной задачи минимизации функционала, алгоритмом дифференциальной эволюции, предложенной Райнером Сторном и Кеннетом Прайсом в 1995 году на основе простых эволюционной задач биологии, были уточнены параметры модели и построен прогноз инфицированных, выздоровевших и умерших индивидуумов среди населения страны. Алгоритм дифференциальной эволюции включает в себя генерацию популяций вероятных решений случайно созданных в предварительно определенном пространстве, выборку критерия остановки алгоритма, мутацию, скрещивание и отбор.
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[12] Krivorotko O.I., Kabanikhin S.I., Zyat’kov N. and others, "Mathematical Modeling and Forecasting of COVID-19 in Moscow and Novosibirsk Region" , Numerical Analysis and Applications 13-4 (2020): 332-348.
[13] Margenov S., Popivanov N., Ugrinova I., Harizanov S., Hristov T., "Mathematical and computer modeling of COVID-19 transmission dynamics in Bulgaria by time-depended inverse SEIR model" , AIP Conference Proceedings 2333 (2021).
[14] Cooper I., Mondal A., Antonopoulos C., "A SIR model assumption for the spread of COVID-19 in different communities" , Chaos, Solitons and Fractals 139 (2020): 1-15.
[15] Lima L., "Modeling based in the stochastic dynamics for the time evolution of the COVID-19" , Preprint (2020): 1-4.
[16] Paticchio A., Scarlatti T., Mattheakis M., Protopapas P., Brambilla M., "Semi-supervised Neural Networks solve an inverse problem for modeling Covid-19 spread" , Preprint (2020): 1-6.
[17] Lasry J.-M., Lions P.-L., "Mean field games" , Jpn. J. Math. 2-1 (2007): 229-260.
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[19] Krivorot’ko O.I., Kabanihin S.I., Zyat’kov N.YU., Prihod’ko A.YU., Prohoshin N.M., SHishlenin M.A.,
"Matematicheskoe modelirovanie i prognozirovanie COVID-19 v Moskve i Novosibirskoj oblasti" , URL:
https://arxiv.org/pdf/2006.12619.pdfLi (2020) [in Russian].
[20] Wang B. Y., Peng R., Zhou C., Zhan Y., Liu Z., et al., "Mathematical Modeling and Epidemic Prediction of COVID-19 and Its Significance to Epidemic Prevention and Control Measures " , Ann. Infect. Dis. Epidemiol. 5, no.1 (2020): 10-52.
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[22] Price K.V., Storn R. and Lampinen J.A., Differential Evolution (Nat. Comput. Ser., Springer, Berlin. 2004).
[23] Storn R., Differential evolution research: Trends and open questions, in: Advances in Differential Evolution (Stud.Comput. Intell. 143. Springer, Berlin. 2004): 1-31.
[24] Storn R., Price K., Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces (Report no. TR 012, International Computer Science Institute, Berkeley. 1995).
[25] Storn R., Price K., "Differential evolution: A simple and efficient heuristic for global optimization over continuous spaces" , J. Global Optim. 11, no. 4 (1997): 341-359.
[26] Qing A., Diferential Evolution: Fundamentals and Applications in Electrical Engineering JohnWiley & Sons, NewYork.2009).
Загрузки
Как цитировать
Kabanikhin, S. I., Bektemesov, M. A., & Bektemessov, J. M. (2021). Математическая модель по среднесрочным прогнозам COVID-19 в Казахстане. Вестник КазНУ. Серия математика, механика, информатика, 111(3), 95–106. https://doi.org/10.26577/JMMCS.2021.v111.i3.08
Выпуск
Раздел
Прикладная математика
