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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Stochastic Dynamics of the COVID-19 Epidemic Via a New Mathematical Model

Discontinuity, Nonlinearity, and Complexity 12(3) (2023) 511--537 | DOI:10.5890/DNC.2023.09.004

I.M. Elbaz$^{1,2}$, M.A. Sohaly$^2$, H. El-Metwally$^2$

$^1$ Basic Sciences Department, Faculty of Engineering, The British University in Egypt, Cairo, Egypt

$^{2}$ Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

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Abstract

This work considers a new stochastic mathematical model for the transmission dynamics of the coronavirus COVID-19 by providing the healthy compartment together with the quarantine/isolation compartment. In the deterministic model, global stability conditions of the disease-free equilibrium $E_0$ and the endemic equilibrium $E_\star$ are derived in terms of the threshold quantity $R_0^d$. Based on the chaotic behavior, we develop and analyze a four-dimensional stochastic COVID-19 epidemic model. Uniqueness, boundedness, and positiveness of the proposed stochastic model are investigated in a biologically feasible region. In terms of the stochastic basic reproduction number $R_0^s$ of the stochastic model, extinction and persistence of the COVID-19 disease are derived. Our theoretical findings are supported by some numerical simulations. The sensitivity of the model with respect to the parameters involved in the system is studied to investigate the most sensitive parameter towards the highest number of infected individuals. We confirm the stability analysis by showing the elasticity of $R_0^s$ with respect to the variation of each parameter. We present real data of a case study with the first wave of the COVID-19 epidemic in the United Kingdom. We compare our numerical results with the real data.

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