Document Type : Research Article
Authors
1
Center for Basic Sciences, Pt. Ravishankar Shukla University, Raipur, Chhattisgarh.
2
School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur, Chhattisgarh.
3
Department of Mathematics, Government Kachna Dhurwa College, Chhura, Chhattisgarh.
4
College of Trades, Technology, and Hospitality, Victoria University, Footscray, Victoria 3011, Australia.
10.22067/ijnao.2026.98939.1878
Abstract
The COVID-19 pandemic, caused by the SARS-CoV-2 virus, has led to the emergence of multiple variants, including Alpha, Beta, Gamma, Delta, and Omicron, each exhibiting distinct transmissibility and severity profiles. In this context, a new deterministic mathematical model has been developed as an extension of Thakur and Sahu \cite{thakur25}, designed to capture the dynamics of COVID-19 transmission while incorporating the effects of both the first and second doses of vaccination.
The model is examined using the theory of dynamical systems. The basic reproduction number is derived, and both the local stability of the disease-free and endemic equilibria, as well as the global stability of the disease-free equilibrium, are established. The model is calibrated using data from India's third wave of the COVID-19 pandemic. Sensitivity analysis, employing Partial Rank Correlation Coefficients (PRCC) and Normalised Forward Sensitivity Indices (NFIs), identifies vaccination rates as key parameters driving disease dynamics. Findings reveal that the Omicron variant has the potential to cause large-scale outbreaks even with ongoing vaccination campaigns. The study emphasizes the need for sustained high vaccination coverage and the continued implementation of non-pharmaceutical interventions to control the pandemic effectively. Furthermore, the model is extended to an optimal control framework, concluding that dynamically adjusting five targeted control measures offers the most effective strategy for reducing infections while minimizing associated costs.
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