Stationary distribution of stochastic COVID-19 epidemic model with control strategies

Rukhsar Ikram; Ghulam Hussain; Inayat Khan; Amir Khan; Gul Zaman; Aeshah A. Raezah; Rukhsar Ikram; Ghulam Hussain; Inayat Khan; Amir Khan; Gul Zaman; Aeshah A. Raezah

doi:10.3934/math.20241468

AIMS Mathematics

2024, Volume 9, Issue 11: 30413-30442. doi: 10.3934/math.20241468

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Research article Special Issues

Stationary distribution of stochastic COVID-19 epidemic model with control strategies

1.
Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan
2.
Department of Mathematics, University of Malakand, Lower Dir Khyber Pakhtunkhawa, Pakistan
3.
Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia

Received: 21 August 2024 Revised: 10 October 2024 Accepted: 15 October 2024 Published: 25 October 2024
MSC : 92D30, 93E20

In this research article, we investigated a coronavirus (COVID-19) epidemic model with random perturbations, which was mainly constituted of five major classes: the susceptible population, the exposed class, the infected population, the quarantine class, and the population that has recovered. We studied the problem under consideration in order to derive at least one, and only one, nonlocal solution within the positive feasible region. The Lyapunov function was used to develop the necessary result of existence for ergodic stationary distribution and the conditions for the disease's extinction. According to our findings, the influence of Brownian motion and noise effects on epidemic transmission were powerful. The infection may diminish or eradicate if the noise is excessive. To illustrate our proposed scheme, we numerically simulated all classes' findings.
- Stationary distribution,
- extinction,
- stochastic epidemic model,
- optimal control
Citation: Rukhsar Ikram, Ghulam Hussain, Inayat Khan, Amir Khan, Gul Zaman, Aeshah A. Raezah. Stationary distribution of stochastic COVID-19 epidemic model with control strategies[J]. AIMS Mathematics, 2024, 9(11): 30413-30442. doi: 10.3934/math.20241468

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Abstract

In this research article, we investigated a coronavirus (COVID-19) epidemic model with random perturbations, which was mainly constituted of five major classes: the susceptible population, the exposed class, the infected population, the quarantine class, and the population that has recovered. We studied the problem under consideration in order to derive at least one, and only one, nonlocal solution within the positive feasible region. The Lyapunov function was used to develop the necessary result of existence for ergodic stationary distribution and the conditions for the disease's extinction. According to our findings, the influence of Brownian motion and noise effects on epidemic transmission were powerful. The infection may diminish or eradicate if the noise is excessive. To illustrate our proposed scheme, we numerically simulated all classes' findings.

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