Enhancing transmission control of the COVID-19 epidemic in India: optimal strategies and approaches

The COVID-19 pandemic has rapidly spread worldwide, leading to devastating consequences for public health, the global economy, and society as a whole. This research paper provides a comprehensive review of the dynamics and control strategies employed to combat the transmission of COVID-19. Our approach involves developing a classic SEIQR model, specifically tailored to the context of India. In our analysis, we take into account both two susceptible states and the impact of quarantine measures to better understand the intricate dynamics of the virus's transmission. We employ the next-generation matrix method to calculate the reproduction number to evaluate the extent of the virus's spread. We also statistically validate the stability results by utilizing the reproduction number and further analyze global stability through analytical methods and numerical simulations. In addition, we perform an optimal control analysis. This analysis utilizes four control parameters to investigate the impact of implementing control measures on the number of infected and exposed individuals. We examine the impacts of adjusting these control parameters by investigating how the number of infected and exposed individuals changes when we increase or decrease them. We compare scenarios with and without control measures to analyze the differences. We compared the results of the proposed model to the previous study and found that it effectively reduces the number of infections.