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Table 1 Common Symbols

From: Toward epidemic thresholds on temporal networks: a review and open questions

SymbolDefinition and Description
A,B,…matrices (bold upper case)
Ithe n×n identity matrix
ρ[ A]spectral radius (largest eigenvalue) of the matrix A
<·>statistical expectation
kidegree of the node i of the network
kthe degree distribution of the network
<k>,<k2>first and second moments of the degree distribution of the network
S(t),I(t),R(t)number of susceptible (S), infected (I), and recovered/removed (R) individuals in the population at time t
βinfection rate: probability of transmission of a pathogen from an infected individual to a susceptible individual per effective contact (e.g. contact per unit time in continuous-time models, or per time step in discrete-time models)
μrecovery rate: probability that an infected individual will recover per unit time (in continuous-time models) or per time step (in discrete-time models)
λtransmissibility: the infection rate rescaled by μ−1 so that λ=β/μ
λc,βc, etc.critical transmissibility, critical infection rate, etc., that define the epidemic threshold
ωrewiring rate or mixing rate
aactivity rate distribution for activity-driven networks
mnumber of connections to other nodes formed by an active node at each time step, for activity-driven networks