Global Stability and Optimal Control for a COVID-19 Model with Vaccination and Isolation Delays

Haitao Song, Ruifeng Wang, Shengqiang Liu, Zhen Jin, Daihai He

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)


COVID-19 pandemic remains serious around the world and causes huge deaths and economic losses. To investigate the effect of vaccination and isolation delays on the transmission of COVID-19, we propose a mathematical model of COVID-19 transmission with vaccination and isolation delays. The basic reproduction number is computed, and the global dynamics of the model are proved. When R0<1, the disease-free equilibrium is globally asymptotically stable. The unique endemic equilibrium is globally asymptotically stable if R0>1. Based on the public information, parameter values are estimated, and sensitivity analysis is carried out by the partial rank correlation coefficients (PRCCs) and the extended version of the Fourier amplitude sensitivity test (eFAST). Our results suggest that the isolation rates of asymptomatic and symptomatic infectious individuals have a significant impact on the transmission of COVID-19. When the COVID-19 is epidemic, the optimal control strategies of our model with vaccination and isolation delays are analyzed. Under the limited resource with constant and time-varying isolation rates, we find that the optimal isolation rates may minimize the cumulative number of infected individuals and the cost of disease control, and effectively contain the transmission of COVID-19. Our study may help public health to prevent and control the COVID-19 spread.

Original languageEnglish
Article number106011
Pages (from-to)1-13
Number of pages13
JournalResults in Physics
Publication statusPublished - Nov 2022


  • COVID-19
  • Isolation delays
  • Mathematical model
  • Optimal control
  • Threshold dynamics
  • Vaccination

ASJC Scopus subject areas

  • General Physics and Astronomy


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