Vaccination strategies against SARS-CoV-2: evaluating the impact of coverage and efficacy using a mathematical model

The COVID-19 pandemic, caused by the SARS-CoV-2 virus, has necessitated rapid and widespread vaccination efforts to mitigate its impact on global health systems and economies. This study formulates a non-linear deterministic SVEIIAR model to evaluate the effect of different vaccination strategies on the transmission dynamics of SARS-CoV-2. The model explores the potential outcomes of varying vaccination scenarios by incorporating key parameters such as vaccine coverage, efficacy and transmission rate. The proposed mathematical model is analyzed for its positivity, existence, boundedness and uniqueness of the solution. Stability analysis is performed for both the Disease-Free Equilibrium (DFE) and Endemic Equilibrium (EE), utilizing Lyapunov functions to assess both local and global stability. Numerical Simulation highlight the critical thresholds for vaccine coverage and efficacy required to achieve herd immunity and significantly reduce infection rates. Sensitivity analyses reveal that increasing vaccination rates and efficacy are crucial for reducing the basic reproduction number \(R_0\) $R_0$ particularly in the presence of emerging variants with higher transmissibility. This research provides valuable insights for public health policymakers to optimize vaccination strategies and effectively control the spread of COVID-19.