Modeling the process of contact between subgroups in spatial epidemics

1
Modeling the process of contact between subgroups
in spatial epidemics

• Lisa Sattenspiel
• University of Missouri-Columbia

2
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

3
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

4
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

5
An application the spatial spread of influenza
6
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

7
Examples of influenza diffusion patterns
8
Examples of influenza diffusion patterns
9
Examples of influenza diffusion patterns
10
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

11
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

12
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

13
The Russian transportation network
14
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.

15
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

16
Types of results from applications of B-R-L
modelRussian 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

17
Types of results from applications of B-R-L model
Rvachev-Longini global simulations
18
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 lt 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

19
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 Hudsons 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

20
Some questions addressed in the simulations

• 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?

21
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

22
What the data show
23
Suggestions for future topics of discussion

• 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?

24
Suggestions for future topics of discussion

• 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 cant 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?