Biomedical Engineering Reference
In-Depth Information
Figure 2
.
Social structure and disease propagation
. Connectivity structures are plotted for a homo-
geneous randomly linked population (
A
) and several structured alternatives, including a reciprocal
binary system with defectors (
B
), a sparse random network (
C
), a small-world network of one-to-
many mappings (
D
), a block structure with random interconnections among blocks (
E
), and a con-
tinuous adjacency band (
F
). Points represent contacts with the potential to transmit disease from a
source (horizontal axis) to a target (vertical axis), and all targets are connected to at least one source.
Disease propagates through alternative contact structures at very different rates despite the fact that
the total number of links realized per unit time is equivalent (1 in G-L). In G-L thin lines represent
realized mortality trajectories for each system, and heavy lines show the average. Trajectories achiev-
ing a flat slope before 100% mortality have burned out (pathogen extinction), whereas those reaching
100% indicate host extinction.
to a stable dyad (2H) rather than a random partner (2G), population survival
rates increase substantially. However, such effects are not equivalent to reducing
the total number of potential contacts (2I) because the network retains the capac-
ity for occasionally generating far leaps in disease distribution. Even a small
number of highly connected individuals can undermine a population's protection
from disease, as in 2J's small-world network where possible contact numbers for
each individual follow a power-law distribution between 1 and 5. In contrast,
organization of social contacts into highly clustered blocks can profoundly re-
tard disease propagation even when total possible links are fivefold greater than
those of a randomly connected network (10 vs. 2 in 2K vs. 2G). Smooth adja-
cency networks with the same number of links show an intermediate phenotype
(2L), with disease decelerated relative to a random homogeneous system (2G)
but still marching inexorably through the population due to the absence of
clearly delineated subgroups that can bottle up and extinguish the infection.
Structured networks provide lots of opportunities to halt an epidemic, but how
quickly or even whether this happens depends critically on small random varia-
tions in realization of a few links between members of different subpopulations
(e.g., in Figure 2J,K). Because population-wide disease penetrance depends on a
