URL
https://arxiv.org/abs/2008.06375
Type d’article
Preprint
Thème
Stratégies de contrôle
Que retenir de cet article, en 1-2 phrases ?
This paper provides a mathematical analysis of the effect of social distancing by considering the case of a social network where links are rewired depending on the states of the agents (susceptible/infected). In the simplest framework studied by the authors, it is possible to prove that there is a discontinuous transition at a critical value of the infection rate.
Objectifs de l’étude / Questions abordées
The mathematical analysis of the limiting final fraction of infected individuals in an SI and an SIR models defined on a social network with rewiring resulting from social distancing between susceptible and infected individuals.
Méthode
The authors reduce the considered probabilistic model to a deterministic one, through a large population limit allowing to obtain central limit type theorems.
Résultats principaux
Evidence of a discontinuous transition in the infection rate, with final fraction of infected individual jumping from 0 to 1 at the transition if the rewiring is only to uninfected individuals. Full results are given for the SI model and partial results for the SIR model.
Commentaire / brève évaluation, limites, ouvertures possibles
The paper remains strictly on the mathematical side. There is no discussion of the authors' expectations for more realistic models and real life situations.