Optimal control and bifurcation analysis of a delayed fractional-order SIRS model with general incidence rate and delayed control

Abstract

A fractional-order generalized SIRS model considering incubation period is established in this paper for the transmission of emerging pathogens. The corresponding Hopf bifurcation is discussed by selecting time delay as the bifurcation parameter. In order to control the occurrence of Hopf bifurcation and achieve better dynamic behaviors, a delayed feedback control is adopted to the model. Further, the delayed fractional-order optimal control problem (DFOCP) is proposed and discussed. The parameters of the proposed model are identified through the measurement data of coronavirus disease 2019 (COVID-19). Based on the results of parameter identification, the corresponding DFOCP with delayed control is numerically solved.

Keywords

• optimal control
• bifurcation analysis
• fractional-order epidemic model
• time delay
• COVID-19 pandemic