Левашкин С.П.1,2, Агапов С.Н.1, Захарова О.И.1, Иванов К.Н.1, Кузьмина Е.С.1, Соколовский В.А.1, Монасова А.С.1, Воробьев А.В.1, Апешин Д.Н.1
Исследование адаптивно-компартментной модели распространения КОВИД-19 в некоторых регионах РФ методами оптимизации
Математическая биология и биоинформатика. 2021;16(1):136-151.
doi: 10.17537/2021.16.136.
Список литературы
- Bernoulli D. Essai d’une nouvelle analyse de la mortalité causée par la petite vérole et des avantages de l’inoculum pour la prévenir. Mém. Math. Phys. Acad. Roy. Sci. Paris. 1760:1–45.
- Farr W. Progress of epidemics. 2d Report of the regist. London: General of England and Wales, 1840.
- En'ko P.L. Vrach (DOCTOR). 1889;46–48 (in Russ.).
- Ross R., Hudson H.P. An application of the theory of probabilities to the study of a priori pathometry. Proc. R. Soc. Lond. 1916-1917;A 93:212-240. doi: 10.1098/rspa.1917.0015
- Bailey N. Matematika v biologii i meditsine. Moscow, 1970. 326 p. (Translation of: Bailey N.T.J. The mathematical approach to biology and medicine. Wiley, 1967).
- Baroian O.V., Rvachev L.A. Matematika i epidemiologiia (Mathematics and Epidemiology). Moscow, 1977. 63 p. (in Russ.).
- Boev B.V. In: Epidemiologicheskaia kibernetika: modeli, informatsiia, eksperimenty (Epidemiological Cybernetics: Models, Information, Experiments). 1991:6–13. (in Russ.).
- Anderson R.M., May R.M. Infectious Diseases of Humans. Dynamics and Control. Oxford: Oxford University Press, 1991.
- Macdonald G. The measurement of malaria transmission. Proc. R. Soc. Med. 1955;48(4):295–302. doi: 10.1177/003591575504800409
- Hoppensteadt F. An age dependent epidemic model. Journal of the Franklin Institute. 1974:325–333. doi: 10.1016/0016-0032(74)90037-4
- Gupur G., Li Xue-Zhi, Zhu Guang-Tian. Threshold and Stability Results for an Age-Structured Epidemic Model. Computers and Mathematics with Applications. 2001;42:883–907. doi: 10.1016/S0898-1221(01)00206-1
- Park T. Age-dependence in epidemic models of vector-borne infections. Huntsville: The University of Alabama, 2004.
- Giordano G., Blanchini F., Bruno R., Colaneri P., Di Filippo A., Di Matteo A., Colaneri M. Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. Nature Medicine. 2020;26:855–860. doi: 10.1038/s41591-020-0883-7
- Bukin Iu.S., Dzhioev Iu.P., Bondariuk A.N., Tkachev S.E., Zlobin V.I. Primenenie universal'noi matematicheskoi modeli epidemicheskogo protsessa «SRID» dlia prognoza razvitiia epidemii COVID-19 v gorode Moskva (Application of the universal mathematical model of the epidemic process "SRID" to predict the development of the COVID-19 epidemic in the city of Moscow): preprint. 2020. 21 p. (in Russ.). doi: 10.24108/preprints-3112045
- Derrode S., Gauchon R., Ponthus N., Rigotti C., Pothier C., Volpert V., Loisel S., Bertoglio J.-P., Roy P. Piecewise estimation of R0 by a simple SEIR model. Application to COVID-19 in French regions and departments until June 30. Université Lyon 1 - Claude Bernard. 2020. https://www.semanticscholar.org/paper/Piecewise-estimation-of-R0-by-a-simple-SEIR-model.-Derrode-Gauchon/7394add56a191e2fed3121c2d935d7f3f278320a#paper-header (accessed 14.05.2020).
- Kochańczyk M., Grabowski F., Lipniacki T. Super-spreading events initiated the exponential growth phase of COVID-19 with ℛ0 higher than initially estimated. Biology, Medicine. Royal Society Open Science. 2020. Article No. 200786. doi: 10.1098/rsos.200786
- Wang X., Tang T., Cao L., Aihara K., Guo Q. Inferring key epidemiological parameters and transmission dinamics of COVID-19 based on a modifiend SEIR model. Math. Model. Nat. Phenom. 2020;15:74. Article No. 2020050. doi: 10.1051/mmnp/2020050
- Grigorieva E.V., Khailov E. N., Korobeinikov A. Optimal quarantine strategies for COVID-19 control models. arXiv:2004.10614 [math.OC] 2020. 21 p. http://arxiv.org/abs/2004.10614v3 (accessed 14.05.2020).
- Zhou X., Ma X.-d., Hong N., Su L., Ma Y., He J., Jiang H., Liu C., Shan G., Zhu W., Zhang S., Long Y. Forecasting the Worldwide Spread of COVID-19 based on Logistic Model and SEIR Model. 2020. Medicine, Geography. medRxiv. Article No. 20044289. doi: 10.1101/2020.03.26.20044289
- Lin Q., Zhao S., Gao D., Lou Y., Yang S., Musa S. S., Wang M.H., Cai Y., Wang W., Yang L., He D. A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action. International Journal of Infectious Diseases. doi: 10.1016/j.ijid.2020.02.058
- Zamir M., Abdeljawad T., Nadeem F., Wahid A., Yousef A. An optimal control analysis of a COVID-19 model Author links open overlay panel. Alexandria Engineering Journal. 2021;60(3):2875-2884. doi: 10.1016/j.aej.2021.01.022
- Okhuese V.A., Mathematical predictions for COVID-19 as a global pandemic. medRxiv. 2020. doi: 10.1101/2020.03.19.20038794
- Zeng Y., Guo X., Deng Q., Luo S., Zhang H. Forecasting of COVID-19: spread with dynamic transmission rate. Journal of Safety Science and Resilience. 2020;1(2):91-96. doi: 10.1016/j.jnlssr.2020.07.003
- Tomchin D.A., Fradkov A.L. Prognozirovanie rasprostraneniia virusa COVID-19 v Rossii na osnove prostykh matematicheskikh modelei epidemii (Predicting the spread of the COVID-19 virus in Russia based on simple mathematical models of epidemics). St. Petersburg, 2020. 17 p. (in Russ.).
- Mamo D.K. Model the transmission dynamics of COVID-19 propagation with public health intervention. Results in Applied Mathematics. 2020;7. Article No. 100123. doi: 10.1016/j.rinam.2020.100123
- Garba S.M., Lubuma J.M.-S., Tsanou B. Modeling the transmission dynamics of the COVID-19 Pandemic in South Africa. Mathematical Biosciences. 2020;328. Article No. 108441. doi: 10.1016/j.mbs.2020.108441
- Aghdaoui H., Tilioua M., Sooppy Nisar K., Khan I. A Fractional Epidemic Model with Mittag-Leffler Kernel for COVID-19. Mathematical Biology and Bioinformatics. 2021;16(1):39-56. doi: 10.17537/2021.16.39
- Kondratyev M. Forecasting methods and models of disease spread. Computer Research and Modeling. 2013;5(5):863-882.(in Russ.). doi: 10.20537/2076-7633-2013-5-5-863-882
- Vasil'ev F.P. Metody optimizatsii (Optimization Methods). Moscow, 2002 (in Russ.).
- Krivorotko O., Kabanikhin S., Zyatkov N., Prikhod’ko A., Prokhoshin N., Shishlenin M. Mathematical modeling and prediction of COVID-19 in Moscow and Novosibirsk region. Numerical Analysis and Applications. 2020;13:332–348. doi: 10.1134/S1995423920040047
- He D., Dushoff J., Day T., Ma J., Earn D. J.-D. Inferring the causes of the three waves of the 1918 influenza pandemic in England and Wales. Proceedings of the Royal Society B: Biological Sciences. 2013. doi: 10.1098/rspb.2013.1345
- BlackBoxOptim.jl. https://github.com/robertfeldt/BlackBoxOptim.jl (accessed 14.05.2020).
- Samorodskaia I.V. Medvestnik. 2020. https://medvestnik.ru/content/medarticles/Problemy-diagnostiki-i-ucheta-zabolevaemosti-COVID-19.html (accessed 14.05.2020) (in Russ.).
- WHO. Clinical management of COVID-19: interim guidance, 27 May 2020. 2020. https://apps.who.int/iris/handle/10665/332196 (accessed 14.05.2020).
- Anderson R.M., May R.M. Directly transmitted infectious diseases: Control by vaccination. Science. 1982:1053-1060. doi: 10.1126/science.7063839
- Roberts M., Heesterbeek H. Bluff your way in epidemic models. Trends in Microbiology. 1993;1(9):343–348. doi: 10.1016/0966-842X(93)90075-3
- Ferguson N.M., Keeling M.J., Edmunds W.J., Gani R., Grenfell B.T., Anderson R.M., Leach S. Planning for smallpox outbreaks. Nature. 2003;425(6959):681–685. doi: 10.1038/nature02007
- Frost I., Craig J., Osena G., Hauck S., Kalanxhi E., Schueller E., Gatalo O., Yan-y Y., Tseng K., Lin G., Klein E. Modeling COVID-19 Transmission in Africa: Country-wise Projections of Total and Severe Infections Under Different Lockdown Scenarios. medRxiv. 2020. Article No. 20188102. doi: 10.1101/2020.09.04.20188102
- Bertozzi A.L., Franco E., Mohler G., Short M.B., Sledge D. The challenges of modeling and forecasting the spread of COVID-19. PNAS. 2020;117(29):16732-16738. doi: 10.1073/pnas.2006520117
|
|
|