COMPARTMENTAL SEVIR MODEL FOR COVID-19 WITH VACCINATION CONTROL
DOI:
https://doi.org/10.69980/6kkg2x81Keywords:
SEVIR model, COVID-19, Vaccination, Basic reproduction number, Equilibrium, Stability analysis, Boundedness, Optimal Control, Disease-induced mortalityAbstract
The ongoing evolution of COVID-19 necessitates advanced mathematical models to capture key epidemiological features such as vaccination efficacy and asymptomatic spread. This paper introduces a new SEVIR model (Susceptible-Exposed-Vaccinated-Infectious-Recovered), Which diverges from traditional SEIR frameworks by integrating a vaccinated compartment with partial immunity. Unlike prior models with dual infectious classes based on severity, this model emphasizes vaccination dynamics and differential transmission rates. We describe the model compartments, parameters, and differential equations, providing a comprehensive overview of its structure and implications for pandemic control. The basic reproduction number R0 is derived, and the existence together with the stability properties of both the disease-free equilibrium and the endemic equilibrium are analyzed. Furthermore, we investigate the role of optimal control strategies involving vaccination and treatment, aiming to reduce the number of infections while minimizing associated intervention costs. The analytical results are supported with numerical simulations, and the main insights obtained from the study are summarized at the conclusion of the paper.
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