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This article is cited in 2 scientific papers (total in 2 papers)
Computational Mathematics
Deterministic and stochastic models of infection spread and testing in an isolated contingent
A. V. Chigareva, M. A. Zhuravkova, V. A. Chigarevb a Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
b Belarusian National Technical University, 65 Niezaliežnasci Avenue, Minsk 220013, Belarus
Abstract:
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.
Received: 14.04.2021 Revised: 26.04.2021 Accepted: 29.09.2021
Citation:
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, 3 (2021), 57–67
Linking options:
https://www.mathnet.ru/eng/bgumi17 https://www.mathnet.ru/eng/bgumi/v3/p57
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