# Contact rate epidemic control of COVID-19: an equilibrium view

arXiv: https://arxiv.org/abs/2004.08221 · HTML: https://mlsanity.com/paper/2004.08221/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2020.

## Built on by (most cited first, 5 of 5)

- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [Developing, Evaluating and Scaling Learning Agents in Multi-Agent Environments](https://mlsanity.com/paper/2209.10958/) (2022)
- [Robust Pandemic Control Synthesis with Formal Specifications: A Case Study on COVID-19 Pandemic](https://mlsanity.com/paper/2103.14262/) (2021)
- [A novel approach for predicting epidemiological forecasting parameters based on real-time signals and Data Assimilation](https://mlsanity.com/paper/2307.01157/) (2023)
- [Recurrent Structural Policy Gradient for Partially Observable Mean Field Games](https://mlsanity.com/paper/2602.20141/) (2026)

## Abstract (arXiv)

We consider the control of the COVID-19 pandemic through a standard SIR compartmental model. This control is induced by the aggregation of individuals' decisions to limit their social interactions: when the epidemic is ongoing, an individual can diminish his/her contact rate in order to avoid getting infected, but this effort comes at a social cost. If each individual lowers his/her contact rate, the epidemic vanishes faster, but the effort cost may be high. A Mean Field Nash equilibrium at the population level is formed, resulting in a lower effective transmission rate of the virus. We prove theoretically that equilibrium exists and compute it numerically. However, this equilibrium selects a sub-optimal solution in comparison to the societal optimum (a centralized decision respected fully by all individuals), meaning that the cost of anarchy is strictly positive. We provide numerical examples and a sensitivity analysis, as well as an extension to a SEIR compartmental model to account for the relatively long latent phase of the COVID-19 disease. In all the scenarii considered, the divergence between the individual and societal strategies happens both before the peak of the epidemic, due to individuals' fears, and after, when a significant propagation is still underway.