A comprehensive study of optimal control model simulation for COVID-19 infection with respect to multiple variants

Abstract

The COVID-19 virus is still spreading around the world. Several SARS-CoV-2 variants have been identified during this COVID-19 pandemic. In this study, we present a compartmental mathematical model using ordinary differential equations to investigate the impact of four different SARS-CoV-2 variants on the transmission of SARS-CoV-2 across India. The proposed mathematical model incorporates the alpha variant, beta variant, gamma variant, and delta variant subpopulations apart from the typical susceptible, exposed, recovered, and dead subpopulations. As part of the India pandemic, we used the model to determine the basic reproduction number (R0) and the daily rates of infection, death, and recovery for each strain. Sensitivity analysis is employed to comprehend the influence of estimated parameter values on the number of infections that result in four variants. Then, using vaccine and therapy as the control variables, we define and analyse an optimum control problem. These optimal controls are described by the Pontryagin’s Minimal Principle. Results showed that the combination of vaccination and treatment strategies was most efficient in minimizing infection and enhancing recovery. The cost-effectiveness analysis is used to determine the best control strategy to minimize infected individuals.