Modeling the process of contact between
subgroups in spatial epidemics
Lisa Sattenspiel
University of Missouri-Columbia
Goals of the presentation
• Stimulate discussion about the pros and cons of different
ways to formulate spatial models, especially in light of
existing and potential data sources
– Describe and critique use of spatial models to explain and predict
epidemics of influenza
– Discuss nature and limitations of data used in these studies
– Suggest areas for future discussion and study, especially in relation
to issues of data needs, availability, and quality
Some general modeling issues
• Simplicity vs. complexity
– Simple models may not represent reality adequately for
the questions at hand
– A model that is too detailed leads to less general results
that may not be applicable to situations other than the
one being modeled
• Population-based vs. individual-based
• Stochastic vs. deterministic
• Continuous time vs. discrete time
Considerations guiding decisions about the
type of model to use
• The questions to be asked of the model
• The amount of underlying information
known about the system being modeled
• The kinds of available data
• The undesirability of producing either an
unnecessarily complex or an excessively
simple and unrealistic model
An application: the spatial spread of influenza
Characteristics of influenza
• Transmitted readily
from one person to
another through
airborne spread and
direct droplet contact
• Rapid virus evolution
limits immunity
• Short incubation and
infectious periods
Examples of influenza diffusion patterns
Examples of influenza diffusion patterns
Examples of influenza diffusion patterns
Influenza models that have incorporated
actual data sets for parameter estimation
• Rvachev-Baroyan-Longini model (migration metapopulation
model)
– Flu in England and Wales (Spicer 1979)
– Russian and European flu epidemics (Baroyan, Rvachev, and
colleagues)
– French flu epidemics (Flahault and colleagues)
– Flu in Cuba (Aguirre and Gonzalez 1992)
• Sattenspiel and Dietz model (migration metapopulation
model)
– Flu in central Canadian fur trappers
• Elveback, Fox, Ewy, and colleagues (microsimulation model)
– Flu in northern US community
Rvachev-Baroyan-Longini (B-R-L)
model
• Discrete time SEIR model in a continuous
state space
• Incorporates a transportation network that
links cities to one another
• Has been applied to the spread of flu in
Russia, Bulgaria, France, Cuba, England
and Wales, and throughout Europe, as well
as worldwide
Data used in applications of B-R-L
model
• The original Russian simulations were not based
on actual transportation data, but instead assumed
that interaction between cities was proportional to
the product of their population size
• Later Russian and Bulgarian simulations used bus
and rail transportation
The Russian transportation network
Data used in applications of B-R-L model (cont.)
• Rvachev and Longini (1985) applied the model to global
patterns of spread using air transportation data. This
application has recently been updated by Rebecca Freeman
Grais in her 2002 PhD dissertation.
• Flahault and colleagues used rail transportation data in
France (Flahault, et al. 1988) and air transportation among
European cities (Flahault, et al. 1994)
• Spicer (1979) compared results from the B-R-L model to flu
data from England and Wales, but did not have English
transportation data. Aguirre and Gonzalez (1992) also
applied the B-R-L results to flu epidemics in Cuba.
Available transportation data usually give an
incomplete picture of real patterns
• Only one or at most two modes of transportation are
usually considered in any one application
• Transportation data are very difficult to find, and those
that are available are often so complex that they either
make simulations unwieldy (e.g., Portland data) or they
must be simplified in structure, introducing additional
assumptions into a model
• Data often indicate how many people started in one place
and ended in another, but provide little or no information
on changes in between
Types of results from applications of B-R-L model
Russian simulations
• Transportation data (or approximations of the
patterns) were used in the model to fit simulation
results to observed data from 128 cities during a
1965 flu epidemic
• The resulting model was then used to forecast
cases through the mid-1970s
• Model predicted peak day to within one week of
actual peak 80-96% of the time; predictions of
height of epidemic peaks were not as accurate
Types of results from applications of B-R-L model
Rvachev-Longini global simulations
Results from Flahault and colleagues’ applications
of the B-R-L model
• Simulations of a 1985 French epidemic
– Computed results did not fit observed data in each district, but general
trends often predicted
• An east-west high prevalence band was predicted and observed
• The epidemic was predicted to end in the northeast of the country, which was
also observed
• Predictions of peak times of epidemics were at or very near observed peak
times for 5 of 18 districts and were within two weeks for an additional 9
districts; predictions of the sizes of epidemic peaks deviated by < 25% for 11
of 18 districts
• Simulations of a flu epidemic in 9 European cities
– Results using air travel data suggest that the time lag for action is probably
less than one month after the first detection of an epidemic
The Sattenspiel-Dietz influenza model
• Incorporates an explicit mobility model that allows for
biased rates of travel throughout a region (i.e., travel in to a
community is not necessary equal to travel out)
• Disease transmission occurs among people who are present
within a community at any particular time
• Applied to the spread of the 1918-19 flu epidemic in three
central Canadian fur trapping communities
• Mobility data derived from Hudson’s Bay Company post
records listing daily visitors to each of the three posts,
often including where they came from and where they
were going next
Some questions addressed in the simulations
1)
2)
3)
4)
5)
How do changes in frequency and direction of travel among socially
linked communities influence patterns of disease spread within and
among those communities?
How do differences in rates of contact and other aspects of social
structure within communities affect epidemic transmission within and
among communities?
What is the effect of different types of settlement structures and
economic relationships among communities on patterns of epidemic
spread?
What was the impact of quarantine policies on the spread of the flu
through the study communities?
Do we see the same kinds of results with other diseases and in other
locations and time periods?
An example of the kinds of inferences derived
from the model simulations
• A summer epidemic should:
 be more severe within a community as a whole
 distribute mortality widely among families
 have a moderate effect on individual families
• A winter epidemic should:
 be less severe within a community as a whole
 focus mortality in a relatively small number of
families
 either severely or barely affect individual families
What the data show
6
number of individuals
5
4
3
2
1
0
Salmon
Robin
Robin
Marten
family
Moose
Fisher
Muskrat
Suggestions for future topics of discussion
1)
2)
3)
To what degree have the results from spatial models for
human diseases added to the body of knowledge
available using other methods and models?
Real data are messy and complex. How much of this
complexity needs to be reproduced in a model?
Is it possible to come up with guidelines to help
modelers decide on the appropriate level of complexity
and type of model to use for particular questions of
interest?
Suggestions for future topics of discussion
4)
5)
6)
Individual-based simulation models such as the EpiSims model are
clearly more realistic than population-based models. But how
generalizable are the results, are the necessary data likely to be
available for most locations, and what can you learn from such a
model that you can’t learn from simpler models?
What sources of data can be used to help determine patterns of
contact among human populations? And is it possible to develop
methods that use disease prevalence data to reconstruct contact
patterns?
How can modelers work with public health authorities to make sure
that the data needed to make useful predictions from spatial
epidemic models are collected on a regular basis?