Optimal control analysis of a multigroup SEAIHRD model for COVID-19 epidemic

The COVID-19 pandemic has threatened public health and caused substantial economic loss to most countries worldwide. A multigroup susceptible–exposed–asymptomatic–infectious–hospitalized–recovered–dead (SEAIHRD) compartment model is first constructed to model the spread of the disease by dividing the population into three age groups: young (aged 0–19), prime (aged 20–64), and elderly (aged 65 and over). Then, we develop a free terminal time, partially fixed terminal state optimal control problem to minimize deaths and costs associated with hospitalization and the implementation of different control strategies. And the optimal strategies are derived under different assumptions about medical resources and vaccination. Specifically, we explore optimal control strategies for reaching herd immunity in the COVID-19 outbreak in a free terminal time situation to evaluate the effect of nonpharmaceutical interventions (NPIs) and vaccination as control measures. The transmission rate of SARS-CoV-2 is calibrated by using real data in the United States at the early stage of the epidemic. Through numerical simulation, we conclude that the outbreak of COVID-19 can be contained by implementing appropriate control of the prime age population and relatively strict control measures for young and elderly populations. Within a specific period, strict control measures should be implemented before the vaccine is marketed.