Dynamics and combinational optimal control of the SEIQHR epidemic model

Abstract This paper proposes a SEIQHR compartmental model for infectious diseases, which further subdivides the population carrying the pathogen based on the severity of symptoms in individuals. Then we analyze the existence and stability of the equilibrium by calculating the basic reproduction number. Sensitivity analysis indicates that the outbreak of asymptomatic individuals is a key factor in the spread of an epidemic, making it crucial to screen and isolate this population. Further, taking into account quarantine and hospitalization as control measures, we propose an optimal strategy, which aims to minimize the costs associated with disease burden and the implementation of controls. Utilizing the Pontryagin’s Maximum Principle, the optimal control curves of the corresponding controls are obtained. Ultimately, numerical simulation demonstrate that quarantine can mitigate the epidemic peak and diminish the duration of disease prevalence. Hospitalization is beneficial for alleviating the pressure on medical resources within hospitals, which is more economically viable than quarantine. The combinational control strategy can aptly manage the epidemic while substantially reducing the control cost, which verifies the effectiveness of this comprehensive approach to epidemic control.