Catalyzing Inquiry at the Interface of Computing and Biology

192 CATALYZING INQUIRY

agent and an individual (e.g., an insect that bites an individual) or between individuals (e.g., an indi-
vidual who sneezes in a room filled with people) that leads to the transmission of disease. The dynamics
of infectious diseases depend on many things, such as the likelihood of transmission between carrier
agent and infected individual given that contact has been made, the geographical distribution of carrier
agents and individuals, and the susceptibility of individuals to the disease.
A central problem in epidemiology is how the dynamics of disease play out across geographical
space.^108 Problems of spatial heterogeneity play out at many different levels of aggregation: individu-
als, families, work groups and firms, neighborhood, and cities. Box 5.20 provides an example taken
from the study of measles.
At the same time, spatial heterogeneity is not the only inhomogeneity of interest. For example, the
epidemiology of sexually transmitted diseases (STDs) cannot be separated from a consideration of their
dynamics in different social groups. For example, patterns of STDs in prostitutes and intravenous drug

Box 5.20

Spatial Heterogeneity in Epidemiology: An Example

One of the best illustrations of [the significance of spatial heterogeneity] is provided by the highly dynamic spa-

tiotemporal epidemic pattern of measles. An important set of analyses of simple, homogeneous models predicted the

possibility of chaotic dynamics; however, the resulting large-amplitude [predicted] epidemics generate unrealistical-

ly low persistence of infection in small communities. Adding successive layers of social and geographical space—

and moving from deterministic to stochastic models—improves spatial realism and may reduce the propensity for

chaos.

The major computational challenge in these highly nonlinear stochastic systems is to represent hierarchical spatial

complexity and especially its impact on vaccination strategies. Depending on the problem, all scales—from the

individual level to big cities—may be important, both in terms of social space [family and school infection dynamics]

and in terms of geographic spread and coherency.

... [A] central question is: How spatially aggregated and parsimonious a model can provide useful results in a given
context? This is particularly important in comparisons between directly transmitted human infections—where long-
range movements may bring infection dynamics comparatively close to mean field behavior (in which every individ-
ual is assumed to have equal contact with every other individual, thus experiencing the mean or average field)—and
the equivalent infections in natural populations, where more restricted movements and host population dynamics
add extra complexities.

It is risky to model at a given level of detail without having data at the relevant spatial grain. Notifiable infectious

diseases are unusually well [documented], with large and often as yet uncomputerized spatiotemporal data sets.

These data provide a huge potential testbed for developing methods for characterizing spatiotemporal dynamics in

nonlinear, nonstationary stochastic systems. An encouraging development is that the current, generally nonparamet-

ric, approaches to characterizing chaos and other nonlinear behaviors are increasingly incorporating lessons from

mechanistic epidemiological models.

SOURCE: Reprinted by permission from S.A. Levin, B. Grenfell, A. Hastings, and A.S. Perelson, “Mathematical and Computational

Challenges in Population Biology and Ecosystems Science,” Science 275(5298):334-343, 1997. Copyright 1997 AAAS. (References omitted.)

(^108) K. Dietz, “The Estimation of the Basic Reproduction Number for Infectious Diseases,” Statistical Methods in Medical Research
2(1):23-41, 1993; A.D. Cliff and P. Haggett, Atlas of Disease Distributions: Analytic Approaches to Epidemiologic Data, Blackwell LTD,
Oxford, UK, 1988; D. Mollison and S.A. Levin, “Spatial Dynamics of Parasitism,” pp. 384-398 in Ecology of Infectious Diseases in
Natural Populations, B.T. Greenfell and A.P. Dobson, eds., Cambridge University, Cambridge, UK, 1995.