Numerical Analysis of Stochastic COVID-19 Epidemic Model with the Vaccine Intervention

Abstract

The Pandemic, COVID-19, has left a great impact on every aspect of life around the globe. It paved the way for crises in all major sectors including health and economics. Therefore, that raise the necessity of an appropriate mathematical models to foresee the intensity and spread of COVID-19 variant. The study puts forward the mathematical investigation and examination of a stochastic COVID-19 model by considering viral latent period into account. The model consists eight compartments: susceptible, exposed, infected, recovered-exposed, recovered, dead population, quarantined, and vaccinated humans. The study compares the deterministic and stochastic COVID-19 models to examine their numerical behaviour. The results depict that the deterministic model does not constitutes the real world uncertainties while the stochastic model provides a more representation of COVID-19 transmission. To substantiate our results, real data of infected individuals after vaccination (from November 2022 to January 2023 in Spain) are used for model evaluation. Various numerical methods, including stochastic Runge-Kutta method, stochastic Non-standard Finite Difference (SNSFD) method and the stochastic Euler method, are applied. The results show, for the step sizes the SNSFD method portrays stable numerical behaviour and is less sensitive to step size variation as compared to other numerical methods (Stochastic Euler and Stochastic Runge-Kutta) considered. This study provides insight into the uncertain nature of pandemic outbreaks and may contribute to understanding of intervention and vaccination strategies.