# Epidemic model on a network: analysis and applications to COVID-19

## TL;DR

This paper analyzes a network-based epidemic model with applications to COVID-19, introducing strategies for vaccination and containment, and providing insights into effective interventions and deconfinement scenarios.

## Contribution

It presents a novel epidemic model on networks with a new vaccination strategy based on node degree and applies it to COVID-19 data.

## Key findings

- Vaccinating high-degree nodes is most effective.
- The model can evaluate deconfinement and second wave scenarios.
- Few parameters allow fitting to COVID-19 data.

## Abstract

We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic criterion and examine different vaccination/containment strategies: we prove that it is most effective to vaccinate a node of highest degree. The model is also useful to evaluate deconfinement scenarios and prevent a so-called second wave. The model has few parameters enabling fitting to the data and the essential ingredient of importation of infected; these features are particularly important for the current COVID-19 epidemic.