Epidemic Spreading and Equilibrium Social Distancing in Heterogeneous Networks

Hamed Amini () and Andreea Minca ()
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Hamed Amini: Georgia State University
Andreea Minca: Cornell University

Dynamic Games and Applications, 2022, vol. 12, issue 1, No 12, 258-287

Abstract: Abstract We study a multi-type SIR epidemic process within a heterogeneous population that interacts through a network. We base social contact on a random graph with given vertex degrees, and we give limit theorems on the fraction of infected individuals. For given social distancing individual strategies, we establish the epidemic reproduction number $$\mathfrak {R}_0$$ R 0 , which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper, we study the equilibrium of the social distancing game. Individuals choose their social distancing level according to an anticipated global infection rate, which must equal the actual infection rate following their choices. We give conditions for the existence and uniqueness of an equilibrium. In the case of random regular graphs, we show that voluntary social distancing will always be socially sub-optimal.

Keywords: Epidemic risks; Multi-type SIR; Social distancing game; Heterogeneous networks; Random graphs with given vertex degrees (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13235-021-00411-1

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