Abstract: Background: Since 2020, when the Covid-19 outbreak began, researchers worldwide have been investigating its biological processes, transmission patterns, and the mathematical expression of this infectious disease. Multiple mathematical models have been presented thus far, with the simplest being the SIR model. The question now is whether the SIR model can provide a comprehensive representation of Covid-19 or if a more intricate model is necessary. With this in mind, the SEPAIVRD model has been developed. Objective: This study focuses on understanding the third wave of Covid-19 that began in mid-May 2021 in Bangladesh. To achieve this, we introduced three essential compartments in our model: Presymptomatic (P), Asymptomatic (A), and Vaccinated (V) classes. The Asymptomatic class will help us determine how close the population is to achieving herd immunity. The Presymptomatic class will provide insight into whether we can effectively control Covid-19 by identifying infected individuals over an extended period. Lastly, the Vaccinated class will allow us to explore how the Presymptomatic class affects those who have received the vaccine. The results of this study aim to address these questions. Findings: According to the study findings, an increase in vaccination rates could result in a decrease in the number of people getting infected every day, lessening the strain on healthcare resources and lowering the risk of transmission to others. Moreover, the research highlights the significance of using highly effective vaccines to combat COVID-19 cases and fatalities, particularly in areas with low vaccination rates. Additionally, implementing social distancing measures can be an effective approach to contain the spread of the virus by reducing the effective contact rate. Conclusion: The model presented in this study provides a comprehensive overview of Covid-19 transmission in Bangladesh. Furthermore, this model can be applied to other countries in South Asia and is therefore a valuable mathematical model for understanding Covid-19.