# Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention

@article{Ketcheson2020OptimalCO, title={Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention}, author={David I. Ketcheson}, journal={Journal of Mathematical Biology}, year={2020}, volume={83} }

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…

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## References

SHOWING 1-10 OF 43 REFERENCES

Stability analysis and optimal control of an SIR epidemic model with vaccination

- MathematicsBiosyst.
- 2011

Optimal control in epidemiology

- Medicine
- 2017

This paper reviews the available literature on mathematical models that use optimal control theory to deduce the optimal strategies aimed at curtailing the spread of an infectious disease.

Intervention to maximise the probability of epidemic fade-out.

- MathematicsMathematical biosciences
- 2017

Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates

- MathematicsAppl. Math. Comput.
- 2014

Optimal and sub-optimal quarantine and isolation control in SARS epidemics

- EngineeringMathematical and Computer Modelling
- 2008

A contribution to the mathematical theory of epidemics

- Medicine, Mathematics
- 1927

The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.

The Mathematics of Infectious Diseases

- MathematicsSIAM Rev.
- 2000

Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.

Optimal isolation control strategies and cost-effectiveness analysis of a two-strain avian influenza model

- BiologyBiosyst.
- 2013

Optimal control of the chemotherapy of HIV

- MedicineJournal of mathematical biology
- 1997

Using an existing ordinary differential equation model, chemotherapy is introduced in an early treatment setting through a dynamic treatment and then solved for an optimal chemotherapy strategy based on a combination of maximizing benefit based on T cell counts and minimizing the systemic cost of chemotherapy.