Fig. 2: Comparison of stochastic simulations and approximate lumping of the susceptible–infected–recovered (SIR) model of epidemics.
From: Micro-scale foundation with error quantification for the approximation of dynamics on networks
a Illustrates the evolution of the mean number of infected vertices from 3000 stochastic simulations (thick red line) and the approximate lumping (thick blue line) for the SIR model on the Haselmere 1m network. The red and blue shading illustrate the 90-percentile of the corresponding distributions. The light blue dash, yellow dot, and grey dash-dot lines indicate the mean number of infected vertices for homogeneous, heterogeneous and individual based mean-field approximations respectively. b Illustrates the probability distribution of the total number of infections computed from 100,000 stochastic simulations, each run until t = 1000 (grey shading). The corresponding probability distribution computed from the approximate lumping is illustrated in blue. c and d Illustrate the same as a and b, respectively, but for an Erdős–Rényi graph with N = 369 vertices and mean degree z = 20.
