This study develops mathematical model for the B.1.1.529 SARS-CoV-2 Omicron Variant of COVID-19. This model examines and evaluates the essentials of positivity and boundedness. The reproduction number \(R_0\) is determined as \(\rho (FV^{-1}) =\nu _3 \big ( \frac{\Gamma (\nu _8 + \nu _1 -1)}{(\nu _1+ \nu _2)(\nu _8+\nu _1)}+\frac{(\nu _4 -\nu _8 - \nu _1)(\nu _6(\nu _8+\nu _1) +\nu _1)}{\nu _9(\nu _8+\nu _1)}\big ) \big (\frac{1}{(\nu _1+\nu _{10}+\nu _{12}-\nu _7)}\big )\) to find out whether the disease spreads further in Tamil Nadu. To protect the safety of the host population, this model incorporates COVID-19 vaccinations and quarantine measures. Our findings indicate that infection-free steady-state solutions are asymptotically stable both locally and globally when \(R_0<1\) , while infection-present steady-state solutions are also locally stable. The current pandemic Omicron variant data from Tamil Nadu, India, have been validated. Also, the error analysis was performed on the original data.
