Fig 1.
Schematic overview of model types.
Fig 2.
(a) Transitioning system of the network model with subject-level infectiousness (λi for subject i). The transition rates refer to exponentially distributed residence times. The expected residence time in each disease stage is the inverse of the sum of the outgoing transitions (e.g. for I1 it is 1/(β1 + μ2) = 6 (days)). Likewise, the probability to go to I2 is 0.2.). (b) Corresponding ODE model with infection rate γ, where γ encodes connectivity and infectiousness.
Table 1.
Model parameters.
Fig 3.
Computation of R0 for fixed λ.
Right: The probability that an I1 − S edge transmits the infection, pI, is the sum of : probably that the infection is transmitted while the infected node is in I1;
: probability that I1 transitions to I2 (before transmitting the infection) and transmits while in I2; and
: probability that the infection happens in I3 (and not earlier). For individually varying λi, R0 ≈ kmean E[pI] is based on an integral over ν. Left: Representation of pI as a reachability probability (from Start to Goal) in a CTMC.
Fig 4.
Schematic visualizations of random graph models with 80 nodes and kmean = 8.
Fig 5.
Overview of how population heterogeneity shapes an epidemic.
f.l.t.r.: ODE model, a complete graph, a power-law network, and a power-law network with exponentially distributed infectiousness. The mean fraction of the population in each compartment at each point in time is shown. Shaded areas indicate standard deviations, not confidence intervals.
Fig 6.
Fraction of nodes in I1 (y-axis) over time Left: Fixed infection rate λ.
Right: Node-based infection rate λi drawn from an exponential distribution. Note the large difference between the two evolutions on the Watts–Strogatz (WS) networks.
Fig 7.
Experiment 1: Epidemic dynamics of different network types.
Row 1: Evolution in terms of mean fractions (and standard deviation) in each compartment over time. Row 2: Effective reproduction number Rt (the empirical R0 is shown as a black triangle) and coefficient of variation of the offspring distribution (with 95% CI, note a significant amount of noise in the power-law case). Row 3: Top-k plots: The fraction of new infections that can be attributed to a particular fraction of infected nodes. Row 4: Characterization of the offspring distribution in terms of the fraction of nodes that cause a specific number of secondary infections.
Fig 8.
Experiment 2: Epidemic dynamics with individual infectiousness λi.
Row 1: Evolution in terms of mean fractions in each compartment over time Row 2: Effective reproduction number Rt and coefficient of variance of the offspring distribution. Row 3: Top-k plots: what fraction of new infection can be attributed to which fraction of infected nodes. Row 4: Characterization of the offspring distribution in terms of what fraction of nodes have how many offspring (infect how many neighbors).