Abstract
In the context of vaccination, we develop a novel mathematical model to examine the Omicron type of coronavirus illness. The system's mathematical analysis based on its equilibrium points shall be obtained. The threshold quantity is used to investigate the system's local and global asymptotical analysis. The Omicron vaccination model shown to be stable locally asymptotically if . The system is globally asymptotically stable at the disease-free equilibrium for a special case when if . We estimate the model parameters based on the observed data and show that the threshold is in the absence of vaccination. The model has the phenomenon of backward bifurcation under certain conditions. Herd immunity analysis is obtained and it turns out that the herd immunity threshold for the South African population is 74%. The impact of vaccination on disease dynamics is also shown and discussed. Further, we have given some graphical results showing the community's disease reduction.
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