This paper presents a comparative analysis of deterministic and stochastic computational modeling approaches for the optimal control of COVID-19. We formulate a compartmental epidemic model with perturbation by white noise that incorporates various factors influencing disease transmission. By incorporating stochastic effects, the model accounts for uncertainties inherent in real-world epidemic data. We establish the mathematical properties of the model, such as well-posedness and the existence of stationary distributions, which are crucial for understanding long-term epidemic dynamics. Moreover, the study presents an optimal control strategies to mitigate the epidemic's impact, both in deterministic and stochastic sceneries. Reported data from Algeria are used to parameterize the model, ensuring its relevance and applicability to practical satiation. Through numerical simulations, the study provides insights into the effectiveness of different control measures in managing COVID-19 outbreaks. This research contributes to advancing our understanding of epidemic dynamics and informs decision-making processes for epidemic controlling interventions.

Department of Clinical Laboratory Sciences College of Applied Medical Sciences King Khalid University Abha Saudi Arabia

Department of Mathematics University of Peshawar Peshawar KP 25000 Pakistan

Faculty of Education Nangrahar University Nangrahar Afghanistan

IT4Innovations VSB Technical University of Ostrava Ostrava Czech Republic

Jadara University Research Center Jadara University Jadara Jordan

Laboratory of Mathematics Modeling and Applications University of Adrar Adrar Algeria

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