Social interactions and the prophylaxis of SI epidemics on networks

Géraldine Bouveret () and Antoine Mandel
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Géraldine Bouveret: NTU - Nanayang Technological University

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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 to 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.

Keywords: Public Good; Epidemic Spreading; Price of Anarchy; Network (search for similar items in EconPapers)
Date: 2021-03
New Economics Papers: this item is included in nep-gth and nep-soc
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03165772v1
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Published in Journal of Mathematical Economics, 2021, 93, ⟨10.1016/j.jmateco.2021.102486⟩

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Journal Article: Social interactions and the prophylaxis of SI epidemics on networks (2021)
Working Paper: Social interactions and the prophylaxis of SI epidemics on networks (2021)
Working Paper: Social interactions and the prophylaxis of SI epidemics on networks (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-03165772

DOI: 10.1016/j.jmateco.2021.102486

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