Dynamics of a stochastic COVID-19 epidemic in the presence of white noise

Volume 39, Issue 1, pp 90--104 https://dx.doi.org/10.22436/jmcs.039.01.06

Publication Date: March 12, 2025 Submission Date: July 27, 2024 Revision Date: August 15, 2024 Accteptance Date: September 11, 2024

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Authors

S. Hussain - Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 2440, Saudi Arabia. E. N. Madi - Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Besut Campus, Terengganu, Malaysia. N. Iqbal - Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 2440, Saudi Arabia. I. A. R. Moghrabi - Information Systems and Technology Department, Kuwait Technical College, Kuwait. - Department of Computer Science, College of Arts and Sciences, University Central Asia, Naryn, Kyrgyz Republic. I. M. Sulaiman - Institute of Strategic Industrial Decision Modelling, School of Quantitative sciences, Universiti Utara Malaysia, 06010, Sintok, Kedah, Malaysia. - Faculty of Education and Arts, Sohar University, Sohar 311, Oman.

Abstract

This paper presents a stochastic mathematical model to enhance the understanding of COVID-19 dynamics, addressing limitations often found in deterministic frameworks that may overlook critical random fluctuations in disease spread. By introducing white noise perturbations, this model provides a more realistic representation of epidemic dynamics, allowing for a detailed analysis of the effects of stochasticity on disease transmission. In comparison to existing deterministic models, our approach captures the inherent unpredictability in epidemic behavior more effectively. Our numerical simulations reveal that COVID-19 eradication occurs when the threshold parameter \(\mathscr{R}{\text{r}}^* < 1\), while persistence is observed when \(\mathscr{R}{\text{r}}^* > 1\). These findings underscore the importance of considering stochastic elements in epidemic modeling and highlight the superiority of stochastic models in capturing the complexities of real-world scenarios. By offering a more nuanced understanding of disease dynamics, this research contributes valuable insights that could inform more effective public health strategies.

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Keywords

• Stochastic model
• numerical scheme
• white noise
• existence and persistence
• COVID-19

MSC

•  26A33
•  34A08
•  35R11

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