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Table 1 The interpersonal contact models used throughout the paper

From: Epidemic risk assessment from geographic population density

Model Contact probability \(p_{u,v}\)
Name Acronym  
Homogeneous mixing \(\text {HM}\) constant
Distance–based mixing \(\text {DM}\) \(\propto d_{u,v}^{-1}\)
Distance and fitness–based mixing \(\text {DFM}\) \(\propto d_{u,v}^{-1}f_uf_v\)
Distance and age–based mixing \(\text {DAM}\) \(\propto s_{g(u),g(v)}d_{u,v}^{-1}\)
Multi–layer mixing \(\text {MLM}\) \(=1\) if \((u,v)\in E_H\), \(=0.5\) if \((u,v)\in E_A\),
   \(\propto s_{g(u),g(v)}d_{u,v}^{-1}f_u,f_v\) otherwise
  1. \(p_{u,v}\) is the probability that u and v are connected at each step of the simulation
  2. \(f_u\) is the Lognormally distributed social fitness of u
  3. \(s_{g_u,g_v}\) is the data–driven age–based social mixing for u and v’s age groups \(g_u\) and \(g_v\)
  4. \(E_H\) and \(E_A\) are the edge sets of two static networks, respectively used to represent households and acquaintances (see Sect. 4 and Guarino et al. (2021) for more details)