Pandemic Risks and Equilibrium Social Distancing in Heterogeneous Networks

Amini, Hamed; Minca, Andreea

We study a SIRD epidemic process among a heterogeneous population that interacts through a network. We give general upper bounds for the size of the epidemic starting from a (small) set of initially infected individuals. Moreover, we characterize the epidemic reproduction numbers in terms of the spectral properties of a relevant matrix based on the network adjacency matrix and the infection rates. We suggest that this can be used to identify sub-networks that have high reproduction numbers before the epidemic reaches and picks up in them. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected individuals. For a given social distancing individual strategies, we establish the epidemic reproduction number $\mathfrak{R}_0$ 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 and we show that voluntary social distancing will always be socially sub-optimal. Our numerical study using Covid-19 data serves to quantify the absolute and relative utility gaps across age cohorts.