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 .
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. 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 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 , in which individuals choose their social distancing level according to an anticipated global infection rate, which then must equal the actual infection rate following their choices. We give conditions for the existence and uniqueness of equilibrium. For the case of random regular graphs, we show that voluntary social distancing will always be socially sub-optimal .
R
SIRD
multi-type SIR
D
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.
R
\mathfrak{R
R
R
and
, in which individuals choose their social distancing level according to an anticipated global infection rate, which then must equal the actual infection rate following their choices. We give conditions for the existence and uniqueness of equilibrium. For the case of random regular graphs,
D
. Our numerical study using Covid-19 data serves to quantify the absolute and relative utility gaps across age cohorts