Geodesic
Direct statistical modeling of spread of epidemic based on a stage-dependent stochastic model
Matematičeskaâ biologiâ i bioinformatika, Tome 16 (2021), pp. 169-200.

Voir la notice de l'article provenant de la source Math-Net.Ru

A stochastic stage-dependent model of  spread of an epidemic in a certain region is presented. The model is written in the form of a continuous-discrete random process that takes into account the passage of individuals through various stages of an infectious disease. Within the framework of the model, the population of the region is represented in the form of cohorts of individuals, structured according to immunological, clinical, epidemiological and demographic criteria. All cohorts make up two blocks. Individuals belonging to the cohorts of the first block are considered indistinguishable within a fixed cohort and have the same type of parametric description. Individuals belonging to the cohorts of the second block differ from each other by the time of admission to a particular cohort and by the time of stay in this cohort. An algorithm for statistical modeling of the dynamics of cohorts of individuals based on the Monte Carlo method is developed. A numerical study of the dynamics of cohorts of individuals was conducted for sets of parameters reflecting different variants of transmission of infection between individuals. 
@article{MBB_2021_16_a3,
     author = {K. K. Loginov and N. V. Pertsev},
     title = {Direct statistical modeling of spread of epidemic based on a stage-dependent stochastic model},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {169--200},
     publisher = {mathdoc},
     volume = {16},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2021_16_a3/}
}
TY  - JOUR
AU  - K. K. Loginov
AU  - N. V. Pertsev
TI  - Direct statistical modeling of spread of epidemic based on a stage-dependent stochastic model
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2021
SP  - 169
EP  - 200
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2021_16_a3/
LA  - ru
ID  - MBB_2021_16_a3
ER  - 
%0 Journal Article
%A K. K. Loginov
%A N. V. Pertsev
%T Direct statistical modeling of spread of epidemic based on a stage-dependent stochastic model
%J Matematičeskaâ biologiâ i bioinformatika
%D 2021
%P 169-200
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2021_16_a3/
%G ru
%F MBB_2021_16_a3
K. K. Loginov; N. V. Pertsev. Direct statistical modeling of spread of epidemic based on a stage-dependent stochastic model. Matematičeskaâ biologiâ i bioinformatika, Tome 16 (2021), pp. 169-200. http://geodesic.mathdoc.fr/item/MBB_2021_16_a3/

[1] D. J. Daley, J. Gani, Epidemic Modelling: An Introduction, Cambridge Studies in Mathematical Biology, 15, Cambridge University press, 1999, 213 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1688203'>1688203</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0922.92022'>0922.92022</ext-link>

[2] Roy M. Anderson, Robert M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, 1991, 784 pp.

[3] B. T. Grenfell, O. N. Bjornstad, B. F. Finkenstadt, “Dynamics of measles epidemics: scaling noise, determinism and predictability with the TSIR model”, Ecological Monographs, 72:2 (2002), 185–202 <ext-link ext-link-type='doi' href='https://doi.org/10.1890/0012-9615(2002)072[0185:DOMESN]2.0.CO;2'>10.1890/0012-9615(2002)072[0185:DOMESN]2.0.CO;2</ext-link>

[4] S. Akhtar, T. E. Carpenter, S. K. Rathi, “A chain-binomial model for intra-household spread of Mycobacterium tuberculosis in a low socio-economic setting in Pakistan”, Epidemiol Infect., 135:1 (2007), 27–33 <ext-link ext-link-type='doi' href='https://doi.org/10.1017/S0950268806006364'>10.1017/S0950268806006364</ext-link>

[5] A. V. Mastikhin, “Final distribution for Gani epidemic Markov processes”, Mathematical Notes, 82 (2007), 787–797 <ext-link ext-link-type='doi' href='https://doi.org/10.1134/S0001434607110223'>10.1134/S0001434607110223</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2399966'>2399966</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1151.60038'>1151.60038</ext-link>

[6] P. M.A. Sloot, S. V. Ivanov, A. V. Boukhanovsky, D. A.M. C. Van De Vijver, C. A.B. Boucher, “Stochastic simulation of HIV population dynamics through complex network modeling”, International Journal of Computer Mathematics, 85:8 (2008), 1175–1187 <ext-link ext-link-type='doi' href='https://doi.org/10.1080/00207160701750583'>10.1080/00207160701750583</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2442563'>2442563</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1142.92029'>1142.92029</ext-link>

[7] N. V. Pertsev, V. N. Leonenko, “Stochastic individual-based model of spreadof tuberculosis”, Russ. J. Numer. Anal. Math. Modelling, 24:4 (2009), 341–360 <ext-link ext-link-type='doi' href='https://doi.org/10.1515/RJNAMM.2009.021'>10.1515/RJNAMM.2009.021</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2548948'>2548948</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1167.92022'>1167.92022</ext-link>

[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, 10:15 (2011) <ext-link ext-link-type='doi' href='https://doi.org/10.1186/1475-925X-10-15'>10.1186/1475-925X-10-15</ext-link>

[9] Y. Yuan, J. Belair, “Threshold dynamics in an SEIRS model with latency and temporary immunity”, J. Math. Biol, 69 (2014), 875–904 <ext-link ext-link-type='doi' href='https://doi.org/10.1007/s00285--013--0720--4'>10.1007/s00285--013--0720--4</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=3259507'>3259507</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1345.92160'>1345.92160</ext-link>

[10] Vlad A.I., Sannikova T.E., Romanyukha A.A., “Modelirovanie rasprostraneniya respiratornykh virusnykh infektsii v gorode: multiagentnyi podkhod”, Matematicheskaya biologiya i bioinformatika, 15:2 (2020), 338–356 <ext-link ext-link-type='doi' href='https://doi.org/10.17537/2020.15.338'>10.17537/2020.15.338</ext-link>

[11] Krivorotko O.I., Kabanikhin S.I., Zyatkov N.Yu., Prikhodko A., Prokhoshin N., Shishlenin M.A., “Matematicheskoe modelirovanie i prognozirovanie COVID-19 v Moskve i Novosibirskoi oblasti”, Sibirskii zhurnal vychislitelnoi matematiki, 2020, no. 4, 395–414 <ext-link ext-link-type='doi' href='https://doi.org/10.15372/SJNM20200404'>10.15372/SJNM20200404</ext-link>

[12] M. Maleki, M. R. Mahmoudi, M. H. Heydari, 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, 140 (2020), 110151 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.chaos.2020.110151'>10.1016/j.chaos.2020.110151</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=4129019'>4129019</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1495.92091'>1495.92091</ext-link>

[13] R. C. Das, “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, 140 (2020), 110248 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.chaos.2020.110248'>10.1016/j.chaos.2020.110248</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=4142127'>4142127</ext-link>

[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, 140 (2020), 110196 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.chaos.2020.110196'>10.1016/j.chaos.2020.110196</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=4137087'>4137087</ext-link>

[15] X. Fu, Q. Ying, T. Zeng, T. Long, Y. Wang, “Simulating and forecasting the cumulative confirmed cases of SARS-CoV-2 in China by Boltzmann function-based regression analyses”, Journal of Infection, 80 (2020), 602–605 <ext-link ext-link-type='doi' href='https://doi.org/10.1101/2020.02.16.20023564'>10.1101/2020.02.16.20023564</ext-link>

[16] A. Kucharski, T. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk, R. M. Eggo, “Early dynamics of transmission and control of COVID-19: a mathematical modelling study”, Lancet Infect Dis, 20 (2020), 553–558 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/S1473-3099(20)30144-4'>10.1016/S1473-3099(20)30144-4</ext-link>

[17] U. Nguemdjo, F. Meno, A. Dongfack, B. Ventelou, “Simulating the progression of the COVID-19 disease in Cameroon using SIR models”, PLoS ONE, 15:8 (2020), e0237832 <ext-link ext-link-type='doi' href='https://doi.org/10.1371/journal.pone.0237832'>10.1371/journal.pone.0237832</ext-link>

[18] Z. Zaplotnik, A. Gavric, L. Medic, “Simulation of the COVID-19 epidemic on the social network of Slovenia: Estimating the intrinsic forecast uncertainty”, PLoS ONE, 15:8 (2020), e0238090 <ext-link ext-link-type='doi' href='https://doi.org/10.1371/journal.pone.0238090'>10.1371/journal.pone.0238090</ext-link>

[19] A. Atangana, S. I. Araz, “Mathematical model of COVID-19 spread in Turkey and South Africa: Theory, methods and application”, Advances in Difference Equations, 2020:1 (2020), 1–89 <ext-link ext-link-type='doi' href='https://doi.org/10.1186/s13662--020--03095-w'>10.1186/s13662--020--03095-w</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=4193431'>4193431</ext-link>

[20] Levashkin S.P., Agapov S.N., Zakharova O.I., Ivanov K.N., Kuzmina E.S., Sokolovskii V.A., Monasova A.S., Vorobev A.V., Apeshin D.N., “Issledovanie adaptivno-kompartmentnoi modeli rasprostraneniya KOVID-19 v nekotorykh regionakh RF metodami optimizatsii”, Matematicheskaya biologiya i bioinformatika, 16:1 (2021), 136–151 <ext-link ext-link-type='doi' href='https://doi.org/10.17537/2021.16.136'>10.17537/2021.16.136</ext-link>

[21] Vinnitskii S.I., Gusev A.A., Derbov V.L., Krasovitskii P.M., Penkov F.M., Chuluunbaatar G., “Redutsirovannaya model SIR pandemii COVID-19”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 61:3 (2021), 400–412 <ext-link ext-link-type='doi' href='https://doi.org/10.1134/S0965542521030155'>10.1134/S0965542521030155</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1466.92212'>1466.92212</ext-link>

[22] A. Abidemi, Z. M. Zainuddin, N. A.B. Aziz, “Impact of control interventions on COVID-19 population dynamics in Malaysia: a mathematical study”, Eur. Phys. J. Plus, 136(237) (2021) <ext-link ext-link-type='doi' href='https://doi.org/10.1140/epjp/s13360-021-01205-5'>10.1140/epjp/s13360-021-01205-5</ext-link>

[23] C. Kavitha, A. Gowrisankar, S. Banerjee, The second and third waves in India: when will the pandemic be culminated?, Eur. Phys. J. Plus, 136(596) (2021) <ext-link ext-link-type='doi' href='https://doi.org/10.1140/epjp/s13360-021-01586-7'>10.1140/epjp/s13360-021-01586-7</ext-link>

[24] Pertsev N.V., Pichugin B.Yu., “Primenenie metoda Monte-Karlo dlya modelirovaniya dinamiki soobschestv vzaimodeistvuyuschikh individuumov”, Vestnik voronezhskogo gosudarstvennogo tekhnicheskogo universiteta, 2:5 (2006), 70–76 <ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1170.35366'>1170.35366</ext-link>

[25] N. V. Pertsev, B. J. Pichugin, “An individual-based stochastic model of the spread of tuberculosis”, J. Appl. Ind. Math, 4:3 (2010), 359–370 <ext-link ext-link-type='doi' href='https://doi.org/10.1134/S1990478910030087'>10.1134/S1990478910030087</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2668089'>2668089</ext-link>

[26] V. N. Leonenko, N. V. Pertsev, M. Artzrouni, “Using high performance algorithms for the hybrid simulation of disease dynamics on CPU and GPU”, Procedia Computer Science, 51 (2015), 150–159 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.procs.2015.05.214'>10.1016/j.procs.2015.05.214</ext-link>

[27] B. J. Pichugin, N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Stochastic modeling of age-structed population with time and size dependence of immigration rate”, Russ. J. Numer. Anal. Math. Modelling, 33:5 (2018), 289–299 <ext-link ext-link-type='doi' href='https://doi.org/10.1515/rnam-2018--0024'>10.1515/rnam-2018--0024</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=3871489'>3871489</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1405.92237'>1405.92237</ext-link>

[28] Pertsev N.V., Loginov K.K., Topchii V.A., “Analiz stadiya-zavisimoi modeli epidemii, postroennoi na osnove nemarkovskogo sluchainogo protsessa”, Sibirskii zhurnal industrialnoi matematiki, 23:3 (2020), 105–122 <ext-link ext-link-type='doi' href='https://doi.org/10.33048/sibjim.2020.23.309'>10.33048/sibjim.2020.23.309</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1505.92221'>1505.92221</ext-link>

[29] M. A. Marchenko, G. A. Mikhailov, “Parallel realization of statistical simulation and random number generators”, Russ. J. Numer. Anal. Math. Modelling, 17 (2002), 113–124 <ext-link ext-link-type='doi' href='https://doi.org/10.1515/rnam-2002--0107'>10.1515/rnam-2002--0107</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1890359'>1890359</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0999.65001'>0999.65001</ext-link>

[30] G. A. Mikhailov, A. V. Voitishek, Numerical statistical modeling. Monte Carlo Methods, M., 2006, 368 pp. (in Russ.)

[31] Marchenko M., “PARMONC A Software Library for Massively Parallel Stochastic Simulation”, Parallel Computing Technologies. PaCT 2011, Lecture Notes in Computer Science, 6873, ed. Malyshkin V., Springer, Berlin–Heidelberg, 2011, 302–316 <ext-link ext-link-type='doi' href='https://doi.org/10.1007/978-3-642-23178-0_27'>10.1007/978-3-642-23178-0_27</ext-link>

[32] Kramer G., Matematicheskie metody statistiki, Mir, M., 1975, 648 pp.

[33] Marchuk G.I., Matematicheskie modeli v immunologii. Vychislitelnye metody i eksperimenty, Nauka, M., 1991, 304 pp.

[34] G. Bocharov, V. Volpert, B. Ludewig, A. Meyerhans, Mathematical Immunology of Virus Infections, Springer, Cham, 2018, 245 pp. <ext-link ext-link-type='doi' href='https://doi.org/10.1007/978-3-319-72317-4'>10.1007/978-3-319-72317-4</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=3793193'>3793193</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1401.92002'>1401.92002</ext-link>