Biomedical Engineering Reference
In-Depth Information
nant host survival. Note that the mean trajectory that is typically modeled does
not correspond to any of the regimes actually observed. Figure 7D shows "knife-
edge" dynamics emerging in the same system when sick individuals randomly
withdraw from 50% of their potential contacts (instead of selectively avoiding
those most socially distant, as in 7C). Host/pathogen equilibrium is virtually
impossible to attain under these circumstances, and one population or the other
rapidly becomes extinct. However, given the dynamic instability of the system,
it is difficult to forecast which population will go extinct first on the basis of the
epidemic's early behavior. As a result, Figure 7E shows how conventional linear
statistical analyses fail to accurately forecast observed disease trajectories due to
their highly unsmooth derivatives (dashed lines represent a 95% prediction in-
terval based on ARIMA 1,1,0 time-series analysis of the first 30 mortality preva-
lence observations). Figure 7F gives a phase space for the epidemic (number of
infected hosts at time
t
vs.
t
- 1), which shows kinetics that are neither classi-
cally chaotic (smooth-curved) or randomly stochastic (scattered), but migrate
noisily around the autoregressive major diagonal. In all of the models in Figure
7, contacts are realized at an average rate of 1 per unit time with a probability
inversely proportional to the square of the social distance (summing to 100% per
unit time), and infected agents can transmit disease for 1 time unit before the
appearance of illness and 3 units thereafter. Potential network reactions to dis-
ease (7C-7F) include sick individuals withdrawing contact with partners more
than 2 units of social space distant (i.e., outside their own block of 3) and
healthy individuals avoiding overtly sick individuals with a success rate of 50%.
Hosts begin with a resistance of .2 (probability of infection, given exposure),
which drops to .05 for those with no social contact in the previous time epoch.
From a public-health perspective, Figure 7E is the key result, showing that ini-
tially smooth disease trajectories provide a poor basis for predicting the subse-
quent spread of disease in the face of realistic network structures and link
dynamics. Sparsity-driven discretization drives this unpredictability by generat-
ing frequent opportunities for the bifurcation of disease trajectories, as observed
in Figures 2H, 2J, 3C, 4D, 5B, 6B, and 6E. Even epidemics that have thoroughly
"burnt into" a population can suddenly sinter out or explode because they are
maintained in a perpetual state of knife-edge criticality by reactive network
dynamics (e.g., Figure 7D).
3.4. Evolutionary Consequences
In the context of such highly leveraged systems, weak interventions can
have powerful effects (13). The strength of an intervention is often analyzed in
terms of its individual impact, but the key to protecting a network lies in an in-
tervention's breadth and consistency. Perfect protection of an individual has little
epidemiologic impact if disease can reach the same destination through another
