Optimal control and global dynamics of a fractional-order infectious disease model incorporating vaccination and generalized incidence rate

Abstract To investigate the transmission dynamics of infectious diseases driven by highly contagious pathogens, we propose a fractional-order model for infectious disease spread. The model encapsulates the isolation and vaccination measures by delineating the dynamics of isolated and vaccinated populations. The dynamic properties of the model are examined through the establishment of the basic reproduction number R0. By considering the value of R0 as a critical threshold, we analyze the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium within the proposed model. Ultimately, vaccination and isolation measures serve to diminish the number of effective contacts between infected and susceptible individuals, thereby leading to a reduction in the infection rate. Consequently, the control parameters are carefully chosen to modulate the infection rate, leading to the formulation of a corresponding fractional optimal control problem (FOCP). Utilize diverse datasets pertaining to the Corona Virus Disease 2019 (COVID-19) to identify the model parameters. The effectiveness of the proposed model in delineating the transmission dynamics of infectious diseases is corroborated through a comprehensive data fitting analysis. Concurrently, utilizing COVID-19 data, the associated theoretical results are numerically validated. Moreover, the FOCP is numerically addressed under various control strategies, offering theoretical insights for the control and prevention of infectious disease transmission.