Abstract
This paper presents classification and analysis of the mathematical models of the spread of COVID-19 in different groups of population such as family, school, office (3–100 people), town (100–5000 people), city, region (0.5–15 million people), country, continent, and the world. The classification covers major types of models (time-series, differential, imitation ones, neural networks models and their combinations). The time-series models are based on analysis of time series using filtration, regression and network methods. The differential models are those derived from systems of ordinary and stochastic differential equations as well as partial differential equations. The imitation models include cellular automata and agent-based models. The fourth group in the classification consists of combinations of nonlinear Markov chains and optimal control theory, derived by methods of the mean-field game theory. COVID-19 is a novel and complicated disease, and the parameters of most models are, as a rule, unknown and estimated by solving inverse problems. The paper contains an analysis of major algorithms of solving inverse problems: stochastic optimization, nature-inspired algorithms (genetic, differential evolution, particle swarm, etc.), assimilation methods, big-data analysis, and machine learning.
Award Identifier / Grant number: 075-15-2022-281
Funding source: Siberian Branch, Russian Academy of Sciences
Award Identifier / Grant number: FWNF-2024-0001
Funding statement: The study of Olga Krivorotko was supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation (Sections 3–7). The study of Sergey Kabanikhin (introduction and Sections 2–3) was supported by the program for fundamental scientific research of the Siberian Branch of the Russian Academy of Sciences (project FWNF-2024-0001).
Acknowledgements
We are grateful to Dr. Cliff Kerr for his help in using Covasim package, Academician of RAS Aleksander Shananin, Profs. Gennady Bocharov and Maxim Shishlenin for their valuable comments and advice in the early stages of this study. Most of the computational results were obtained with the help of Dr. Nikolay Zyatkov.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- The inverse scattering problem for an inhomogeneous two-layered cavity
- Hölder stability estimates in determining the time-dependent coefficients of the heat equation from the Cauchy data set
- Complex turbulent exchange coefficient in Akerblom–Ekman model
- On the identification of Lamé parameters in linear isotropic elasticity via a weighted self-guided TV-regularization method
- Rough surfaces reconstruction via phase and phaseless data by a multi-frequency homotopy iteration method
- Determination of unknown shear force in transverse dynamic force microscopy from measured final data
- Inverting mechanical and variable-order parameters of the Euler–Bernoulli beam on viscoelastic foundation
- On the mean field games system with lateral Cauchy data via Carleman estimates
- Artificial intelligence for COVID-19 spread modeling
Artikel in diesem Heft
- Frontmatter
- The inverse scattering problem for an inhomogeneous two-layered cavity
- Hölder stability estimates in determining the time-dependent coefficients of the heat equation from the Cauchy data set
- Complex turbulent exchange coefficient in Akerblom–Ekman model
- On the identification of Lamé parameters in linear isotropic elasticity via a weighted self-guided TV-regularization method
- Rough surfaces reconstruction via phase and phaseless data by a multi-frequency homotopy iteration method
- Determination of unknown shear force in transverse dynamic force microscopy from measured final data
- Inverting mechanical and variable-order parameters of the Euler–Bernoulli beam on viscoelastic foundation
- On the mean field games system with lateral Cauchy data via Carleman estimates
- Artificial intelligence for COVID-19 spread modeling