Contribution of the 2021 COVID-19 Vaccination Regime to COVID-19 Transmission and Control in South Africa: A Mathematical Modeling Perspective
This study assesses the impact of COVID-19 vaccines through an epidemiological model that quantifies their role in pandemic control. We analyze an SIR-based model incorporating vaccination effects and calculate the basic reproduction number, $\mathcal{R}_0$. Our findings indicate that under conditions of imperfect vaccination and non-permanent immunity from recovery, a backward bifurcation may occur when $\mathcal{R}_0<1$. Conversely, with full immunity from vaccination and lasting immunity post-recovery, the disease-free equilibrium is globally asymptotically stable for $\mathcal{R}_0<1$. Numerical simulations support these theoretical results. The model is calibrated using South African data from Johns Hopkins University, covering the period from February 17 to August 5, 2021. Results show that vaccine effectiveness in preventing infection was below 50\%, consistent with the CDC's February 2024 report indicating an improved infection-protection rate of 54\% for newly produced vaccines. Additionally, our findings demonstrate that vaccines significantly enhanced recovery rates and reduced both mortality and recovery time, aligning with CDC reports. A sensitivity analysis highlights key parameters affecting $\mathcal{R}_0$, offering insights for policymakers on optimizing vaccination strategies.