Modelling COVID-19 Dynamics with a Double Dose Vaccination Strategy in India and Its Potential Influence on the Emergence of Future Diseases

Abstract

COVID-19 is a contagious disease responsible for millions of deaths annually and represents a significant global public health challenge. Despite ongoing vaccination efforts, the current COVID-19 situation remains worrisome. This study examines a COVID-19 model incorporating a double-dose vaccination strategy to manage the outbreak in India. We conducted a fundamental qualitative analysis of this mathematical model, investigating conditions for positive invariance and boundedness with appropriate initial conditions. We estimated the basic reproduction number () for disease transmission and identified two equilibrium points: the disease-free equilibrium and the disease-endemic equilibrium. Using the Routh-Hurwitz criteria, we assessed the stability of these equilibria. The disease can be eradicated if ; otherwise, it persists in the population. To complement the qualitative analysis, we performed numerical simulations using MATLAB and estimated model parameters. Sensitivity analysis was conducted to explore the relationship between model parameters and mild and critical cases. The simulations demonstrated that a complete vaccination program significantly reduces mild and critical cases and could potentially eradicate the virus from the community. The insights from our analysis may assist public health professionals in implementing the most effective strategies to control the virus outbreak in India.