Mathematical Analysis of a Fractional SEIQHRV COVID-19 Model with Optimal Control and Public Health Interventions

This paper develops a seven-compartment fractional-order SEIQHRV model for COVID-19 transmission, with susceptible, exposed, infected, quarantined, hospitalized, recovered, and vaccinated classes and Caputo derivatives capturing memory effects. Three controls representing vaccination, quarantine-isolation, and clinical treatment are incorporated. Well-posedness, positivity, and boundedness are proved; the reproduction number, its sensitivity indices, a controlled threshold, and the endemic equilibrium are derived explicitly; and existence of optimal controls and the fractional Pontryagin Maximum Principle with exact costate equations are established. Simulations by a forward-backward sweep with an Adams-type scheme, verified by convergence and gradient tests, show that combined control is most effective, that vaccination and quarantine are complementary, and that smaller fractional orders yield flatter but more persistent epidemics.