TY - JOUR
T1 - Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention
AU - Ketcheson, David I.
N1 - KAUST Repository Item: Exported on 2021-06-29
Acknowledgements: The author was supported by funding from King Abdullah University of Science & Technology (KAUST).
PY - 2021/6/26
Y1 - 2021/6/26
N2 - We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The control is allowed to be applied only over a finite time interval, while the objective is to minimize the total number of individuals infected in the long-time limit, subject to some cost function for the control. We first consider the no-cost scenario and analytically determine the optimal control and solution. We then study solutions when a cost of intervention is included, as well as a cost associated with overwhelming the available medical resources. Examples are studied through the numerical solution of the associated Hamilton-Jacobi-Bellman equation. Finally, we provide some examples related directly to the current pandemic.
AB - We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The control is allowed to be applied only over a finite time interval, while the objective is to minimize the total number of individuals infected in the long-time limit, subject to some cost function for the control. We first consider the no-cost scenario and analytically determine the optimal control and solution. We then study solutions when a cost of intervention is included, as well as a cost associated with overwhelming the available medical resources. Examples are studied through the numerical solution of the associated Hamilton-Jacobi-Bellman equation. Finally, we provide some examples related directly to the current pandemic.
UR - http://hdl.handle.net/10754/663431
UR - https://link.springer.com/10.1007/s00285-021-01628-9
U2 - 10.1007/s00285-021-01628-9
DO - 10.1007/s00285-021-01628-9
M3 - Article
C2 - 34176029
VL - 83
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
SN - 0303-6812
IS - 1
ER -