Figure 2

(a) An example of the 2-Mode-SIS model on a heterogeneous contact network: on some day t, there are two patients (\(P_1\), \(P_2\)), two HCWs (\(H_1\), \(H_2\)), and two locations (\(L_1\), \(L_2\)) in the network, and dash lines represent edges in the heterogeneous contact network (e.g., \(P_1\) was in \(L_1\) on day t as well as in contact with \(P_2\) and \(H_1\) on day t). For every node i, their pathogen load is represented as \({\varvec{l}}_t(i)\) by 2-Mode-SIS model, and these loads can spread via contacts. For patients \(P_1\), \(P_2\), their infection states can transfer between S (\({\varvec{x}}_t(i) = 0\)) and I (\({\varvec{x}}_t(i) = 1\)). See more details in the paper and Supplementary Information. (b) Our spectral characterization \(\rho ({\varvec{S}})\) captures a critical “tipping point”: When \(\rho ({\varvec{S}})>1\), the fraction of infected patients will be close to 1. When \(\rho ({\varvec{S}})<1\), almost none of the patients will be infected (i.e., the epidemic dies out).