TY - JOUR
T1 - Optimal Control Problem of an SIR Model with Random Inputs Based on a Generalized Polynomial Chaos Approach
AU - Hwang , Yoon-Gu
AU - Kwon , Hee-Dae
AU - Lee , Jeehyun
JO - International Journal of Numerical Analysis and Modeling
VL - 2-3
SP - 255
EP - 274
PY - 2022
DA - 2022/04
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/20480.html
KW - Optimal control problem, random differential equation, generalized polynomial chaos.
AB - <p style="text-align: justify;">This paper studies the optimal control problem of a susceptible-infectious-recovered
(SIR) epidemic model with random inputs. We prove the existence and uniqueness of a solution
to the SIR random differential equation (RDE) model and investigate the numerical solution to
the model by using a generalized polynomial chaos (gPC) approach. We formulate the optimal
control problem of the SIR RDE model and consider the gPC Galerkin method to convert the
problem into an optimal control problem with high-dimensional ordinary differential equations.
Numerical simulations show that to effectively control an epidemic, vaccination should be given
at the highest rate in the first few days, and after that, vaccination should be stopped completely.
In addition, we observe that the optimal control function and the corresponding states are very
robust to the uncertainty of random inputs.</p>