Some Approaches of Using Stochastic Models of Epidemiology to the Problem of COVID-19

Atoyev, K., Bogdanov, O., Knopov, P., & Korkhin, A. (2024). Some Approaches of Using Stochastic Models of Epidemiology to the Problem of COVID-19. In: Nexus of Sustainability. Eds. Zagrorodny, A., Bogdanov, V., & Zaporozhets, A., pp. 211-227 Springer. 10.1007/978-3-031-66764-0_10.

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Abstract

The chapter proposes a method for modeling the epidemic dynamics, which allows to fit the epidemic model to known time series of indicators, and not to unknown continuous functions of time. The methodology for constructing an epidemic dynamics model is based on taking into account the delayed influence of some variables on others in the form of distributed lag models. The construction of such models is based on the dual nature of non-negative integer random variables. Their distribution can also be considered as an impulse transition function of a discrete system. This consideration makes it possible to obtain a general view of such a distribution law and construct a dynamics model in the form of blocks that reproduce the lag, given by transfer functions, and blocks of the interaction of variables in the form of their products. The proposed approach makes it possible to obtain various models and analyze them as linear dynamic systems with time-varying coefficients. Statements about the relationship between the transfer functions of different blocks are proved. It is shown that the discrete analogue of the SIR model follows from the obtained general model with discrete time. A theorem is proved on a sufficient condition for the stability of a population to infection in relation to the general form of a model with discrete time. Based on the theoretical solutions obtained, various models were built as examples, taking into account the latent period as well as quarantine measures. Their stability was proven. The problem of identifying one such model based on the data on one wave of coronavirus in relation to Ukraine was formulated and solved. Two evaluation criteria are analyzed. The resulting model has satisfactory accuracy despite the high noise level. As a result of the evaluation, unobservable values such as the duration of the latent period, wait time for the test results, and the proportion of asymptomatic diseases were determined.

Item Type:	Book Section
Research Programs:	Advancing Systems Analysis (ASA) Advancing Systems Analysis (ASA) > Cooperation and Transformative Governance (CAT)
Depositing User:	Luke Kirwan
Date Deposited:	27 Nov 2024 11:55
Last Modified:	27 Nov 2024 11:55
URI:	https://pure.iiasa.ac.at/20147

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