(untitled) (Contemporary Mathematics, 2024)
In this work, we introduce a new SEVIR epidemic model to analyze the dynamics of infectious diseases by incorporating the key compartments such as susceptible, exposed, vaccinated, infected, and recovered populations. We add the vaccination compartment in the current model and calculate the consequences concerning the disease spreading; it is significantly relevant at the present day considering the general policies of worldwide vaccinations. For a stringent assessment of stability, it should involve derivation of a basic reproduction number, as this parameter characterizes whether an infection will be spread at all. Our results demonstrate that when we have R0 < 1, the disease-free equilibrium is locally asymptotically stable, which implies that an infection will eventually die out. We also identify two distinguished disease-dependent equilibrium points for the first time, giving much deeper insight into long term behavior of the disease. Numerical simulations show the efficacy of vaccination toward reducing the newly infected individuals and suggest the model can predict stabilization for all compartments over time. The exposed and recovered population increases and stabilizes as the susceptible, infected, and vaccinated populations decline. In this regard, these are valuable insights into the progression of epidemics and put emphasis on vaccination programs. Our model provides a perspective on disease control by taking into account the interplay between vaccination and infection dynamics. It can be very useful for predicting future outbreaks and can guide public health policy. Future work will extend the model by adding quarantine measures to further hone our understanding of disease transmission.