Fractional modeling and optimal control strategies for mutated COVID-19 pandemic

As the COVID-19 continues to mutate, the number of infected people is increasing dramatically, and the vaccine is not enough to fight the mutated strain. In this paper, a SEIR-type fractional model with reinfection and vaccine inefficacy is proposed, which can successfully capture the mutated COVID-19 pandemic. The existence, uniqueness, boundedness, and nonnegativeness of the fractional model are derived. Based on the basic reproduction number R0$$ {R}_0 $$, locally stability and globally stability are analyzed. The sensitivity analysis evaluate the influence of each parameter on the R0$$ {R}_0 $$ and rank key epidemiological parameters. Finally, the necessary conditions for implementing fractional optimal control are obtained by Pontryagin's maximum principle, and the corresponding optimal solutions are derived for mitigation COVID-19 transmission. The numerical results show that humans will coexist with COVID-19 for a long time under the current control strategy. Furthermore, it is particularly important to develop new vaccines with higher protection rates.