The rapid and widespread transmission of COVID-19 has necessitated the development and implementation of effective control measures. Vaccination has emerged as a key tool in combating the pandemic. This article introduces a novel approach to modeling the dynamics of COVID-19 transmission by integrating vaccination strategies into the susceptible-infected-recovered (SIR) framework using viability theory. We have defined a set of constraints including a guaranteed level of vaccination, we analyze the impact of different vaccination rates on curbing the spread of the virus. Our findings reveal the significant role of vaccination in reducing transmission and offer valuable insights into optimizing vaccination campaigns. The viability-based SIR model provides a comprehensive framework for policymakers and healthcare professionals to devise targeted strategies and allocate resources effectively in the battle against COVID-19.
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