Fractional mathematical analysis of COVID-19 variant waves with delayed state and control variables

Abstract

Following the emergence of the Omicron variant alongside the Delta variant of COVID-19 in November 2021, this study investigates their coexistence dynamics through the development of a potential novel model. Our research focuses on the fundamental properties of an epidemic model incorporating susceptible individuals $(S)$, infected with the Delta variant $(I_1)$, infected with the Omicron variant $(I_2)$, cured of the Delta compartments $(R_1)$ and cured of the Omicron compartments $(R_2)$, incorporating delays in state and control variables. Using a blocking and isolation program as the main control measure, our aim is to minimize the prevalence of infected individuals. Based on Pontryagin's maximum principle, the study establishes the existence of optimal control. The optimality system is efficiently handled by a discretization method using forward and backward difference approximations. Numerical results, derived from a comprehensive analysis of Delta and Omicron variants, confirm the effectiveness of the optimization strategy. This research offers valuable insights into the competitive dynamics between these variants, and introduces an innovative approach to control strategies in a context of evolving viral threats.