Multi-strain COVID-19 dynamics with vaccination strategies: Mathematical modeling and case study

The emergence of alpha, beta, gamma, and delta COVID-19 variants has posed important challenges to global health. Understanding the transmission dynamics and evaluating the impact of vaccination strategies are critical for effective pandemic management. The present study develops a novel mathematical model that incorporates time-dependent vaccination rates to analyze the spread of these four COVID-19 variants, utilizing India as a case study. We assess the model’s positivity, boundedness, and disease-free equilibrium, as well as we calculate basic reproduction numbers. A sensitivity analysis is conducted to evaluate the impact of key parameters on transmission dynamics. Using optimal control theory, we evaluate three strategies: continuous vaccination of susceptible individuals, public awareness campaigns to reduce contact rates, and quarantine/hospitalization of infected individuals. Numerical simulations over a 300-day period demonstrate that the combined strategy — continuous vaccination, public awareness campaigns, and quarantine/hospitalization —leads to the greatest reduction in infections across all four variants. This is confirmed by the incremental cost-effectiveness ratio and provides practical insights for optimizing pandemic response. The model extends prior research by integrating real-world vaccination data with multi-strain COVID-19 dynamics, offering a comprehensive framework that can guide policymakers in managing future outbreaks. Our study emphasizes the necessity of synergistic public health strategies, and highlights their practical relevance for epidemic management in regions with high population density and limited healthcare resources.