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

Abstract

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 , locally stability and globally stability are analyzed. The sensitivity analysis evaluate the influence of each parameter on the 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.

Controllability of Fractional Complex Networks

“…Note that for any x 0 and x t f in R N , the adequacy and necessity condition with an external controller vector u(t) satisfying (13)…”

“…Due to its memory and hereditary properties, fractional calculus has garnered considerable attention across various scientific fields and is widely adopted in science and engineering [13][14][15][16][17][18][19][20]. Fractional operators have been integrated into traditional complex networks, significantly improving model accuracy.…”

Positive Solutions and Their Existence of a Nonlinear Hadamard Fractional-Order Differential Equation with a Singular Source Item Using Spectral Analysis

“…Wu et al [2] used a new nonlinear fractional-order damaged pattern with viscosity, elasticity and plasticity for rock and soil materials to characterize three-stage creep behaviors, and their pattern fully calculated and predicted the deformation with hysteresis derived from the rapid creep in tunnel engineering. Ma et al [3] developed a fractional-order model termed as SEIR type and subsequently the beingness, uniqueness, boundness of such a fractional-order system were determined. The research conclusions indicated that it is difficult for humans to avoid coexistence with the spread of the COVID-19 epidemic.…”