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Social interactions and the prophylaxis of SI epidemics on networks ☆

Authors
  • Bouveret, Géraldine1
  • Mandel, Antoine2
  • 1 Nanyang Technological University, School of Physical and Mathematical Sciences, 21 Nanyang Link, 637371, Singapore
  • 2 Paris School of Economics-Université Paris 1 Panthéon-Sorbonne, Centre d’Économie de la Sorbonne, 106 Boulevard de l’hôpital, 75013, Paris, France
Type
Published Article
Journal
Journal of Mathematical Economics
Publisher
Elsevier B.V.
Publication Date
Feb 05, 2021
Volume
93
Pages
102486–102486
Identifiers
DOI: 10.1016/j.jmateco.2021.102486
PMID: 33583996
PMCID: PMC7863793
Source
PubMed Central
Keywords
Disciplines
  • Article
License
Unknown

Abstract

We investigate the containment of epidemic spreading in networks from a normative point of view. We consider a susceptible/infected model in which agents can invest in order to reduce the contagiousness of network links. In this setting, we study the relationships between social efficiency, individual behaviours and network structure. First, we characterise individual and socially efficient behaviour using the notions of communicability and exponential centrality. Second we show, by computing the Price of Anarchy, that the level of inefficiency can scale up linearly with the number of agents. Third, we prove that policies of uniform reduction of interactions satisfy some optimality conditions in a vast range of networks. In setting where no central authority can enforce such stringent policies, we consider as a type of second-best policy the implementation of cooperation frameworks that allow agents to subsidise prophylactic investments in the global rather than in the local network. We then characterise the scope for Pareto improvement opened by such policies through a notion of Price of Autarky, measuring the ratio between social welfare at a global and a local equilibrium. Overall, our results show that individual behaviours can be extremely inefficient in the face of epidemic propagation but that policy can take advantage of the network structure to design welfare improving containment policies.

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