### Abstract

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 language | English |
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Journal | Mathematics and Computers in Simulation |

DOIs | |

Publication status | Accepted/In press - 2019 Jan 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Mathematics and Computers in Simulation*. https://doi.org/10.1016/j.matcom.2019.08.002

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**Optimal control problem of an SIR reaction–diffusion model with inequality constraints.** / Jang, Junyoung; Kwon, Hee Dae; Lee, Jeehyun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimal control problem of an SIR reaction–diffusion model with inequality constraints

AU - Jang, Junyoung

AU - Kwon, Hee Dae

AU - Lee, Jeehyun

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85070522216&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070522216&partnerID=8YFLogxK

U2 - 10.1016/j.matcom.2019.08.002

DO - 10.1016/j.matcom.2019.08.002

M3 - Article

AN - SCOPUS:85070522216

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

ER -