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.

Automated summary

As the COVID-19 mutates, the infection rate is increasing rapidly and the vaccine is ineffective against the mutated strain. This paper proposes a SEIR-type fractional model with reinfection and vaccine inefficacy, which successfully captures the dynamics of the mutated COVID-19 pandemic. The model's existence, uniqueness, boundedness, and nonnegativeness are derived, and the local and global stability based on the basic reproduction number R0 are analyzed. Sensitivity analysis evaluates the impact of each parameter on R0 and ranks key epidemiological parameters. Additionally, necessary conditions for implementing fractional optimal control and corresponding optimal solutions for mitigating COVID-19 transmission are obtained.