A new metaheuristic optimization algorithm based on COVID-19: mathematical model and application to pandemic control

Abstract This paper introduces the COVID-19 optimization algorithm (COA), a novel metaheuristic inspired by the dynamical processes of the SARS-CoV-2 pandemic, including viral transmission, quarantine measures, recovery, and mutation. COA models the search for optimal solutions through a state-transition framework in which candidate solutions evolve as susceptible, infected, quarantined, or recovered, enabling a unique and adaptive balance between exploration and exploitation. To demonstrate its practical utility, COA is coupled with a Bernoulli operational matrix collocation method to solve a complex optimal control problem (OCP) designed to mitigate the dual burden of COVID-19 and associated heart attack risks. The proposed OCP incorporates a novel compartmental model that tracks susceptible, exposed, infected, vaccinated, recovered, deceased, and a dedicated heart attack patient class while simultaneously optimizing four time-dependent control strategies: vaccination, preventive measures, antiviral treatment, and cardiovascular care. The objective is to minimize the total number of infected individuals, heart attack cases, mortality, and associated intervention costs. Prior to applying control, the uncontrolled model is rigorously analyzed: the existence and uniqueness of non-negative, bounded solutions are proven; the basic reproduction number $$\mathcal {R}_0$$ is derived; and the local and global stability of the equilibria are established. The model parameters are estimated by fitting the system to real epidemiological data from Wuhan, China, ensuring biological credibility. Computational results demonstrate that the proposed COA-based discretization metaheuristic approach effectively identifies optimal control profiles, significantly outperforming baseline scenarios. By integrating a biologically inspired optimization algorithm with a comprehensive epidemiological model and solid mathematical foundation, this work provides a robust, gradient-free framework for public health decision-making, offering actionable insights for managing infectious diseases alongside chronic comorbidities.