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Том 16   Выпуск 2   Год 2021
Логинов К.К., Перцев Н.В.

Прямое статистическое моделирование распространения эпидемии на основе стадия-зависимой стохастической модели

Математическая биология и биоинформатика. 2021;16(2):169-200.

doi: 10.17537/2021.16.169.

Список литературы

  1. Daley D.J., Gani J. Epidemic Modelling: An Introduction. Cambridge Studies in Mathematical Biology 15. Cambridge University press; 1999. 213 p.
  2. Anderson R.M., May R.M. Infektsionnye bolezni cheloveka. Dinamika i kontrol'. Moscow; 2004. 784 p. (Translation of: Roy M. Anderson, Robert M. May. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press; 1991.)
  3. Grenfell B.T., Bjornstad O.N., Finkenstadt B.F. Dynamics of measles epidemics: scaling noise, determinism and predictability with the TSIR model. Ecological Monographs. 2002;72(2):185-202. doi: 10.1890/0012-9615(2002)072[0185:DOMESN]2.0.CO;2
  4. Akhtar S., Carpenter T.E., Rathi S.K. A chain-binomial model for intra-household spread of Mycobacterium tuberculosis in a low socio-economic setting in Pakistan. Epidemiol Infect. 2007;135(1):27-33. doi: 10.1017/S0950268806006364
  5. Mastikhin A.V. Final distribution for Gani epidemic Markov processes. Mathematical Notes. 2007;82:787-797. doi: 10.1134/S0001434607110223
  6. Sloot P.M.A., Ivanov S.V., Boukhanovsky A.V., D.A.M.C. Van De Vijver, Boucher C.A.B. Stochastic simulation of HIV population dynamics through complex network modeling. International Journal of Computer Mathematics. 2008;85(8):1175-1187. doi: 10.1080/00207160701750583
  7. Pertsev N.V., Leonenko V.N. Stochastic individual-based model of spreadof tuberculosis. Russ. J. Numer. Anal. Math. Modelling. 2009;24(4):341-360. doi: 10.1515/RJNAMM.2009.021
  8. Nishiura H. Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009). Biomed. Eng. Online. 2011;10(15). doi: 10.1186/1475-925X-10-15
  9. Yuan Y., Belair J. Threshold dynamics in an SEIRS model with latency and temporary immunity. J. Math. Biol. 2014;69,:875-904. doi: 10.1007/s00285-013-0720-4
  10. Vlad A.I., Sannikova T.E., Romanyukha A.A. Transmission of Acute Respiratory Infections in a City: Agent-Based Approach. Mathematical Biology and Bioinformatics. 2020;15(2):338-356 (in Russ.). doi: 10.17537/2020.15.338
  11. Krivorotko O.I., Kabanikhin S.I., Zyatkov N.Yu., Prikhodko A.Yu., Prokhoshin N.M., Shishlenin M.A. Mathematical modeling and forecasting of COVID-19 in Moscow and Novosibirsk region. Siberian Journal of Numerical Mathematics. 2020;4:395-414 (in Russ.). doi: 10.15372/SJNM20200404
  12. Maleki M., Mahmoudi M.R., Heydari M.H., Kim-Hung Pho. Modeling and forecasting the spread and death rate of coronavirus (COVID-19) in the world using time series models. Chaos, Solitons and Fractals. 2020;140:110151. doi: 10.1016/j.chaos.2020.110151
  13. Das R.C. Forecasting incidences of COVID-19 using Box-Jenkins method for the period July 12-Septembert 11, 2020: A study on highly affected countries. Chaos, Solitons and Fractals. 2020;140:110248. doi: 10.1016/j.chaos.2020.110248
  14. Feroze N. Forecasting the patterns of COVID-19 and causal impacts of lockdown in top five affected countries using Bayesian Structural Time Series Models. Chaos, Solitons and Fractals. 2020;140:110196. doi: 10.1016/j.chaos.2020.110196
  15. Fu X., Ying Q., Zeng T., Long T., Wang Y. Simulating and forecasting the cumulative confirmed cases of SARS-CoV-2 in China by Boltzmann function-based regression analyses. Journal of Infection. 2020;80:602-605. doi: 10.1101/2020.02.16.20023564
  16. Kucharski A., Russell T., Diamond C., Liu Y., Edmunds J., Funk S., Eggo R.M. Early dynamics of transmission and control of COVID-19: a mathematical modelling study. Lancet Infect Dis. 2020;20:553-558. doi: 10.1016/S1473-3099(20)30144-4
  17. Nguemdjo U., Meno F., Dongfack A., Ventelou B. Simulating the progression of the COVID-19 disease in Cameroon using SIR models. PLoS ONE. 2020;15(8):e0237832. doi: 10.1371/journal.pone.0237832
  18. Zaplotnik Z., Gavric A., Medic L. Simulation of the COVID-19 epidemic on the social network of Slovenia: Estimating the intrinsic forecast uncertainty. PLoS ONE. 2020;15(8):e0238090. doi: 10.1371/journal.pone.0238090
  19. Atangana A., Araz S.I. Mathematical model of COVID-19 spread in Turkey and South Africa: Theory, methods and application. Advances in Difference Equations. 2020;2020(1):1-89. doi: 10.1186/s13662-020-03095-w
  20. Levashkin S.P., Agapov S.N., Zakharova O.I., Ivanov K.N., Kuzmina E.S., Sokolovsky V.A., Monasova A.S., Vorobiev A.V., Apeshin D.N. Study of SEIRD Adaptive-Compartmental Model of COVID-19 Epidemic Spread in Russian Federation Using Optimization Methods. Mathematical Biology and Bioinformatics. 2021;16(1):136-151 (in Russ.). doi: 10.17537/2021.16.136
  21. Vinitsky S.I., Gusev A.A., Chuluunbaatar G., Derbov V.L., Krassovitskiy P.M., Pen’kov F.M. Reduced sir model of COVID-19 pandemic. Computational Mathematics and Mathematical Physics. 2021;61(3):376-387. doi: 10.1134/S0965542521030155
  22. Abidemi A., Zainuddin Z.M., Aziz N.A.B. Impact of control interventions on COVID-19 population dynamics in Malaysia: a mathematical study. Eur. Phys. J. Plus. 2021;136(237). doi: 10.1140/epjp/s13360-021-01205-5
  23. Kavitha C., Gowrisankar A., Banerjee S. The second and third waves in India: when will the pandemic be culminated? Eur. Phys. J. Plus. 2021;136(596). doi: 10.1140/epjp/s13360-021-01586-7
  24. Pertsev N.V., Pichugin B.J. Vestnik voronezhskogo gosudarstvennogo tekhnicheskogo universiteta (Bulletin of Voronezh State Technical University). 2006;2(5):70-76 (in Russ.).
  25. Pertsev N.V., Pichugin B.J. An individual-based stochastic model of the spread of tuberculosis. J. Appl. Ind. Math. 2010;4(3):359-370. doi: 10.1134/S1990478910030087
  26. Leonenko V.N., Pertsev N.V., Artzrouni M. Using high performance algorithms for the hybrid simulation of disease dynamics on CPU and GPU. Procedia Computer Science. 2015;51:150-159. doi: 10.1016/j.procs.2015.05.214
  27. Pichugin B.J., Pertsev N.V., Topchii V.A., Loginov K.K. Stochastic modeling of age-structed population with time and size dependence of immigration rate. Russ. J. Numer. Anal. Math. Modelling. 2018;33(5):289-299. doi: 10.1515/rnam-2018-0024
  28. Pertsev N.V., Loginov K.K., Topchii V.A. Analysis of a stage-dependent epidemic model based on a non-Markov random process. J. Appl. Industr. Math. 2020;14:(3):566-580. doi: 10.33048/sibjim.2020.23.309
  29. Marchenko M.A., Mikhailov G.A. Parallel realization of statistical simulation and random number generators. Russ. J. Numer. Anal. Math. Modelling. 2002;17:113-124. doi: 10.1515/rnam-2002-0107
  30. Mikhailov G.A., Voitishek A.V. Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo (Numerical statistical modeling. Monte Carlo Methods). Moscow; 2006. 368 p. (in Russ.).
  31. Marchenko M. PARMONC – A Software Library for Massively Parallel Stochastic Simulation. In: Parallel Computing Technologies. PaCT 2011. Lecture Notes in Computer Science. Ed. Malyshkin V.: Springer, Berlin, Heidelberg; 2011. V. 6873. P. 302-316. doi: 10.1007/978-3-642-23178-0_27
  32. Cramér H. Matematicheskie metody statistiki. Moscow; 1975. 648 p. (Translation of: Harald Cramér. Mathematical Methods of Statistics. Princeton University Press; 1946. (Princeton Mathematical Series; V. 9)).
  33. Marchuk G.I. Mathematical Models in Immunology. Computational Methods and Experiments. Moscow: Nauka; 1991. 304 p. (in Russ.).
  34. Bocharov G., Volpert V., Ludewig B., Meyerhans A. Mathematical Immunology of Virus Infections. Cham: Springer; 2018. 245 p. doi: 10.1007/978-3-319-72317-4
Содержание Оригинальная статья
Мат. биол. и биоинф.
2021;16(2):169-200
doi: 10.17537/2021.16.169
опубликована на рус. яз.

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Аннотация (англ.)
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