Deterministic and stochastic models of infection spread and testing in an isolated contingent

  • Anatoliy V. Chigarev Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Michael A. Zhuravkov Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-7420-5821
  • Vitaliy A. Chigarev Belarusian National Technical University, 65 Niezaliežnasci Avenue, Minsk 220013, Belarus
DOI: https://doi.org/10.33581/2520-6508-2021-3-57-67

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.

Author Biographies

Anatoliy V. Chigarev, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

doctor of science (physics and mathematics), full professor; professor at the department of bio- and nanomechanics, faculty of mechanics and mathematics

Michael A. Zhuravkov, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

doctor of science (physics and mathematics), full professor; head of the department of theoretical and applied mechanics, faculty of mechanics and mathematics

Vitaliy A. Chigarev, Belarusian National Technical University, 65 Niezaliežnasci Avenue, Minsk 220013, Belarus

PhD (physics and mathematics); associate professor at the department of theoretical and structural mechanics, faculty of engineering

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Published
2021-11-19
Keywords: mathematical model, epidemic, estimation, posterior probability, SIR model
How to Cite
Chigarev, A. V., Zhuravkov, M. A., & Chigarev, V. A. (2021). Deterministic and stochastic models of infection spread and testing in an isolated contingent. Journal of the Belarusian State University. Mathematics and Informatics, 3, 57-67. https://doi.org/10.33581/2520-6508-2021-3-57-67
Issue
No 3 (2021): Journal of the Belarusian State University. Mathematics and Informatics
Section
Computational Mathematics

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