Biomedical Engineering Reference
In-Depth Information
small number of stochastic events, it is difficult to accurately predict the course
of an epidemic from its early trajectory. Repeated simulations show wildly dif-
ferent kinetics in panels 2H-2L. Under the homogeneous mixing assumption,
epidemiologic kinetics seem highly predictable (2G), but more realistic network
structures reveal much greater variability. Often, it is not even possible to pre-
dict whether the host population or the pathogen will perish first (2H, 2J,
and 2K).
3.2. Dynamic Network Structures
In addition to structural heterogeneity, social contact networks also show
temporal heterogeneity in realized linkages. Two basic processes drive these
dynamics. First, the development of biological immunity or death removes indi-
viduals from the system of transmitters following a certain period of infectious-
ness. Second, the social interactions that transmit disease are intrinsically
dynamic in their own right. We each know hundreds of people, but on any given
day we interact with only a small number of them. The links we do realize are
clustered in both time and social space because we typically interact with a
small and stable social core (e.g., family members and immediate coworkers).
The vast majority of potential links are realized only rarely. This "small-world"
temporal structure implies a functional decrease in network connectivity per unit
time, but it is not equivalent to removing low-frequency links because the net-
work retains a capacity for occasional far leaps in disease distribution. Tempo-
rally sparse social contact is modeled by generating a fixed set of possible
contacts for each individual and realizing a constant number of contacts per unit
time according to a specified probability model (Figure 3).
Temporal link dynamics can profoundly impact the propagation of disease
even through highly vulnerable social structures such as the small-world net-
work (all links realized in Figure 3A vs. a random 50% in 3B; note differential
frequency of host population extinction). Compared to a uniform probability of
realizing any possible contact (3B), increased probability of realizing more
proximal links results in considerably enhanced survival despite the fact that the
total number of realized links remains constant (3C). These examples come from
epidemics initiated by 3 infected individuals in the midst of a 200-host popula-
tion with a small-world contact distribution ranging from 1 to 5 possible con-
tacts per individual (496 total links), and an infectious duration of 1 time unit. In
Figure 3B, each link is realized with a probability of 50% per unit time for all
individuals. In Figure 3C the probability of realizing each link is an average of
50% that varies between 0 and 1 depending on the squared social distance be-
tween source and target. In addition to slowing the mean disease penetrance
trajectory, sociospatial link heterogeneity also greatly increases variability in
outcomes.
