Optimal control problem of an SIR reaction–diffusion model with inequality constraints

Junyoung Jang, Hee Dae Kwon, Jeehyun Lee

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


This paper studies an optimal control problem of a susceptible–infected–recovered (SIR) reaction–diffusion model to derive an efficient vaccination strategy for influenza outbreaks. The control problem reflects realistic restrictions associated with limited total vaccination coverage and the maximum daily vaccine administration using state variable inequality constraints. We prove the existence of the optimal control solution and also investigate an optimality system by introducing a penalty function to deal with the constrained optimal control problem. A gradient-based algorithm is discussed to solve the optimality system. The spatial SIR model is solved by using the finite difference method (FDM) in time and the finite element method (FEM) in space. The results of numerical simulations show that the optimal vaccine strategy varies regionally according to the spreading rate of the disease.

Original languageEnglish
Pages (from-to)136-151
Number of pages16
JournalMathematics and Computers in Simulation
Publication statusPublished - 2020 May

Bibliographical note

Publisher Copyright:
© 2019 International Association for Mathematics and Computers in Simulation (IMACS)

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


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