Geodesic
Deterministic and stochastic models of infection spread and testing in an isolated contingent
Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2021), pp. 57-67.

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The mathematical SIR model generalisation for description of the infectious process dynamics development by adding a testing model is considered. The proposed procedure requires the expansion of states’ space dimension due to variables that cannot be measured directly, but allow you to more adequately describe the processes that occur in real situations. Further generalisation of the SIR model is considered by taking into account randomness in state estimates, forecasting, which is achieved by applying the stochastic differential equations methods associated with the application of the Fokker – Planck – Kolmogorov equations for posterior probabilities. As COVID-19 practice has shown, the widespread use of modern means of identification, diagnosis and monitoring does not guarantee the receipt of adequate information about the individual’s condition in the population. When modelling real epidemic processes in the initial stages, it is advisable to use heuristic modelling methods, and then refine the model using mathematical modelling methods using stochastic, uncertain-fuzzy methods that allow you to take into account the fact that flow, decision-making and control occurs in systems with incomplete information. To develop more realistic models, spatial kinetics must be taken into account, which, in turn, requires the use of systems models with distributed parameters (for example, models of continua mechanics). Obviously, realistic models of epidemics and their control should include models of economic, sociodynamics. The problems of forecasting epidemics and their development will be no less difficult than the problems of climate change forecasting, weather forecast and earthquake prediction.
Keywords: mathematical model; epidemic; estimation; posterior probability; SIR model. 
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A. V. Chigarev; M. A. Zhuravkov; V. A. Chigarev. Deterministic and stochastic models of infection spread and testing in an isolated contingent. Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2021), pp. 57-67. http://geodesic.mathdoc.fr/item/BGUMI_2021_3_a4/

[1] S. D. Varfolomeev, K. G. Gurevich, “Biokinetika”, Grand, Moskva, 1999, 716

[2] R. R. Akhmerov, “Ocherki po teorii obyknovennykh differentsialnykh uravnenii. Differentsialnye uravneniya v biologii, khimii, meditsine. Osnovy teorii obyknovennykh differentsialnykh uravnenii”, Institut vychislitelnykh tekhnologii Sibirskogo otdeleniya RAN, Novosibirsk, 2002 | DOI | Zbl

[3] Dzh. Marri, “Nelineinye differentsialnye uravneniya v biologii. Lektsii o modelyakh”, Mir, Moskva, 1983, 397

[4] B. Eastman, C. Meaner, M. Przedborski, M. Kohandel, “Mathematical modeling of COVID-19 containment strategies with consideration for limited medical resources”, 2020 | DOI | Zbl

[5] E. Dong, H. Du, L. Gardner, “An interactive web-based dashboard to track COVID-19 in real time. The Lancet Infectious Diseases”, 20(5), 2020, 533–534 | DOI

[6] E. Seidzh, D. Mels, “Teoriya otsenivaniya i ee primenenie v svyazi i upravlenii”, Statisticheskaya teoriya svyazi, 6, Svyaz, Moskva, 1976, 496

[7] D. L. Snyder, “The state-variable approach to continuous estimation with applications to analog communication theory”, MIT Press, Cambridge, 1969, 114 | Zbl

[8] G. Khaken, “Sinergetika. Ierarkhii neustoichivostei v samoorganizuyuschikhsya sistemakh i ustroistvakh”, Mir, Moskva, 1985, 424 | MR

[9] A. A. Funtov, “O priblizhennom analiticheskom reshenii uravnenii Lotki – Volterry”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 19(2) (2011), 89–92 | DOI | Zbl

[10] Yu. S. Kharin, V. A. Voloshko, O. V. Dernakova, V. I. Malyugin, A. Yu. Kharin, “Statisticheskoe prognozirovanie dinamiki epidemiologicheskikh pokazatelei zabolevaemosti COVID-19 v Respublike Belarus”, Zhurnal Belorusskogo gosudarstvennogo universiteta. Matematika. Informatika, 3 (2020), 36–50 | DOI

[11] R. O. Omorov, “Metod topologicheskoi grubosti dinamicheskikh sistem: prilozheniya k sinergeticheskim sistemam”, Nauchnotekhnicheskii vestnik informatsionnykh tekhnologii, mekhaniki, optiki, 20(2) (2020), 257–262 | DOI