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 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

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) How do changes in frequency and direction of travel among socially linked communities influence patterns of disease spread within and among those communities?

2) How do differences in rates of contact and other aspects of social structure within communities affect epidemic transmission within and among communities?

3) What is the effect of different types of settlement structures and economic relationships among communities on patterns of epidemic spread?

4) What was the impact of quarantine policies on the spread of the flu through the study communities?

5) 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 wholedistribute mortality widely among familieshave 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

familieseither severely or barely affect individual families

What the data show

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Suggestions for future topics of discussion

1) To what degree have the results from spatial models for human diseases added to the body of knowledge available using other methods and models?

2) Real data are messy and complex. How much of this complexity needs to be reproduced in a model?

3) 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) 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?

5) 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?

6) 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?