Analysis of the Covid-19 Mathematical Model Based on Vaccine Data: A Descriptive Approach to Eradicate the Outbreak

This article presents an overview of vaccine effects and analyses a case study of the COVID-19 outbreaks and the effectiveness of vaccinations in Bangladesh. We have conceptually and numerically explored the model. We determined the reproduction number (R0) using the next-generation matrix methodology. We have evaluated the model's local stability for disease-free and endemic equilibria, determined by the basic reproduction number. We calculated sensitivity indices to examine the parameters' impact on the reproduction number. We present an SVIR model to simulate the impact of the vaccination process, solve it using the fourth-order Runge-Kutta technique, and validate our findings using fourth-order polynomial regression. The results suggest that the COVID-19 situation will improve if a significant proportion of individuals in Bangladesh are vaccinated (2 doses of the available vaccine). In the end, the numerical simulation provides a clear picture of the rising and falling tendency of this disease's spread in parallel with vaccination, as shown by the parameters in the mathematical model. From the perspective of Bangladesh, this study highlights the effect of the COVID-19 vaccine.