# An eradication time problem for the SIR model

arXiv: https://arxiv.org/abs/2008.12744 · HTML: https://mlsanity.com/paper/2008.12744/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2020.

## Built on by (most cited first, 1 of 1)

- [Physics-Informed Neural Networks for Optimal Vaccination Plan in SIR Epidemic Models](https://mlsanity.com/paper/2502.19890/) (2025)

## Abstract (arXiv)

We consider a susceptible, infected, and recovered infectious disease model which incorporates a vaccination rate. In particular, we study the problem of choosing the vaccination rate in order to reduce the number of infected individuals to a given threshold as quickly as possible. This is naturally a problem of time-optimal control. We interpret the optimal time as a solution of two dynamic programming equations and give necessary and sufficient conditions for a vaccination rate to be optimal.