Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay

Rukhsar Ikram; Amir Khan; Mostafa Zahri; Anwar Saeed; Mehmet Yavuz; Poom Kumam

doi:10.1016/j.compbiomed.2021.105115

Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay

Comput Biol Med. 2022 Feb:141:105115. doi: 10.1016/j.compbiomed.2021.105115. Epub 2021 Dec 9.

Authors

Rukhsar Ikram¹, Amir Khan², Mostafa Zahri³, Anwar Saeed⁴, Mehmet Yavuz⁵, Poom Kumam⁶

Affiliations

¹ Qurtuba University of Science and Information Technology Hayatabad Peshawar, Pakistan.
² Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10 140, Thailand; Department of Mathematics and Statistics, University of Swat, KP, Pakistan.
³ Department of Mathematics, Research Groups MASEP and BioInformatics FG, University of Sharjah, United Arab Emirates.
⁴ Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10 140, Thailand.
⁵ Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, TR10, Cornwall, UK; Department of Mathematics and Computer Sciences, Necmettin Erbakan University, 42090, Konya, Turkey. Electronic address: M.Yavuz@exeter.ac.uk.
⁶ Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10 140, Thailand; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40 402, Taiwan.

Abstract

We reformulate a stochastic epidemic model consisting of four human classes. We show that there exists a unique positive solution to the proposed model. The stochastic basic reproduction number R₀^s is established. A stationary distribution (SD) under several conditions is obtained by incorporating stochastic Lyapunov function. The extinction for the proposed disease model is obtained by using the local martingale theorem. The first order stochastic Runge-Kutta method is taken into account to depict the numerical simulations.

Keywords: Brownian motion; Delay; Extinction; Stationary distribution; Stochastic SIVR model.

MeSH terms

COVID-19*
Computer Simulation
Humans
Models, Biological
SARS-CoV-2
Stochastic Processes