STATIONARY DISTRIBUTION AND EXTINCTION OF STOCHASTIC CORONAVIRUS (COVID-19) EPIDEMIC MODEL

Amir Khan, Hedayat Ullah (), Mostafa Zahri (), Usa Wannasingha Humphries, Touria Karite (), Abdullahi Yusuf, Hakeem Ullah and Mehreen Fiza
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Amir Khan: Department of Mathematics, University of Swat, KPK, Pakistan§Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT), Faculty of Science, 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Hedayat Ullah: ��Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan
Mostafa Zahri: ��Department of Mathematics, Research Group MASEP, University of Sharjah, UAE
Usa Wannasingha Humphries: �Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT), Faculty of Science, 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Touria Karite: �LISA Laboratory, Department of Electrical Engineering and Informatics, National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Fez, Morocco
Abdullahi Yusuf: ��Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey**Department of Mathematics, Near East University TRNC, Mersin, Turkey
Hakeem Ullah: ��Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan
Mehreen Fiza: ��Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-15

Abstract: The aim of this paper is to model corona-virus (COVID-19) taking into account random perturbations. The suggested model is composed of four different classes i.e. the susceptible population, the smart lockdown class, the infectious population, and the recovered population. We investigate the proposed problem for the derivation of at least one unique solution in the positive feasible region of nonlocal solution. For one stationary ergodic distribution, the necessary result of existence is developed by applying the Lyapunov function and the condition for the extinction of the disease is also established. The obtained results show that the effect of Brownian motion and noise terms on the transmission of the epidemic is very high. If the noise is large the infection may decrease or vanish. For validation of our obtained scheme, the results for all the classes of the problem have been simulated numerically.

Keywords: Stochastic Model; Epidemiology; COVID-19; SQIR Model; Lyapunov Function; Milstein Scheme (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400503

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