The Susceptible-Isolated-Infected-Recovered-Vaccinated (SIqIRV) deterministic model is examined in this paper. This model considers a nonlinear force of quarantine, infection and care, where vaccinated individuals lose their immunity after a period of time and become susceptible to infection. Isolation is the main key to bringforth the SIq IRV model. The fundamentals of reproduction number calculated using this model is an outbreak threshold that decides whether or not a disease can spread. The infection free steady state solutions are locally and globally found to be asymptotically stable when R 0 < 1. Infection persistent steady state solutions are also found to be locally asymptotically stable when R 0 > 1. At the end, computational simulations were run to confirm and support our theoretical findings.

In this paper, a fractional order nonlinear model for Omicron, known as B.1.1.529 SARS-Cov-2 variant, is proposed. The COVID-19 vaccine and quarantine are inserted to ensure the safety of host population in the model. The fundamentals of positivity and boundedness of the model solution are simulated. The reproduction number is estimated to determine whether or not the epidemic will spread further in Tamilnadu, India. Real Omicron variant pandemic data from Tamilnadu, India, are validated. The fractional-order generalization of the proposed model, along with real data-based numerical simulations, is the novelty of this study.

In this study, an epidemic mathematical model for Omicron, denoted as B.1.1.529 SARS-Cov-2 Variant, is constructed. Covid-19 vaccines are considered here to ensure the host population’s safety across the model. The fundamentals of positivity and boundedness in this model have been investigated and validated. The reproduction number was calculated to determine whether or not the disease would spread further in Tamilnadu. Infection-free steady-state solutions that exist are asymptotically stable locally when R 0 < 1 and globally when R 0 > 1. Also Infection-present steady-state solutions that are locally stable are discovered when R 0 < 1. Finally, the current Omicron variant pandemic data from Tamilnadu, India, is validated.