Why Canadian fur trappers should stay in

bed when they have the flu: modeling the

geographic spread of infectious diseases

Lisa SattenspielDepartment of Anthropology

University of Missouri-Columbia

Major approaches to modeling the transmission of infectious

diseases• Deterministic compartmental models (systems of

differential equations)

• Statistical approaches (e.g., regression analysis, time series analysis, generalized linear models, spatial statistics)

• Stochastic compartmental models (e.g. chain binomial model)

• Individual-based mathematical models

• Computer-based models– Microsimulations

– Agent-based models

a mobility process

the distribution of destinations

the rate of leaving a community

the rate of return

Community 1

Community 2

Community 3

+a disease process

Susceptible

Infectious

Recoveredinfection

recovery

The chance of infection is a function of both contact (a social process) and transmission (a biological process)

General structure of a deterministic epidemic model with three linked

communities

Community composition as a result of the mobility process

B B C C A A AB B B

C C C CB C C A A C C

A A B B C AB A C

mobility process

Transmission of infection occurs only between an infectious person and a susceptible person who happen to be in the same region at time t. The risk of infection is a function not only of the personal characteristics of the susceptible and infectious individuals, but also of the place where theycome into contact with one another.

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dS ik

dt= iikS ii −ikS ik − κkβijk

S ik I jk

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dI ii

dt= ik I ik − i I ii + κiβij i

S ii I j i

N i*

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dt= iik I ii −ik I ik + κkβijk

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dRii

dt= ikRik − iRii

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dRik

dt= iikRii −ikRik +γI ik

The Keewatin District

The environment at and near Norway House

Mortality before, during, and after the flu epidemic

Anglican burials at Norway House, 1909 to 1929

0

10

20

30

40

50

1909 1914 1919 1924 1929

year

burials

Mortality among communities within Manitoba

0

50

100

150

200

250

300

Norway House Fisher River Berens River Fort Alexander Oxford House God's Lake

Deaths per 1000

Distribution of deaths by family

Norway House 1919237 families

0

20

40

60

80

100

120

140

160

180

0 1 2 3+

number of deaths

number of families

Observed

Expected

G-value = 17.33, p < 0.05, df = 2

significantly fewer observed

Families with three to five deaths

Norway House 1919

0

1

2

3

4

5

6

Salmon Robin Robin Marten Moose Fisher Muskrat

family

number of individuals

Alive 1918

Dead 1919

Initial questions

a) How do changes in the rates and patterns of mobility affect epidemic spread?

b) How do changes in rates of contact within communities affect epidemic spread?

0

20

40

60

80

100

120

140

160

180

0 50 100 150 200 250 300

day

cases

NH—w≠

NH—s≠

OH—w≠

OH—s≠

GL—w≠

GL—s≠

Changes in rates and patterns of mobility do not significantly affect the size of epidemic peaks although they do affect the

timing of epidemic spread

Changing social organization by varying the contact rate within communities DOES lead to significant changes in the

size and timing of epidemic peaks

0

20

40

60

80

100

120

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180

200

0 50 100 150 200 250 300

Day

Number of cases

NH, both equal

and unequal

contact

OH, equal

contact

GL, equal

contact

OH, unequal

contactGL, unequal

contact

Some of the questions addressed in the project

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?

Solution: Develop an individual-based epidemic model that can deal with the

variability of individual behaviors and the stochasticity that results when

populations are small

BUT the real study populations are so small that the deterministic models presented so far are not

really the best ones to use.

Seasonal differences in social organization in the northern

fur trade

• Social group size and composition• Dispersal on the land• Resource availability • Modes of travel• Travel routes• Numbers traveling• Time to complete a journey

Stage 1

Develop a single-post agent-based model that captures significant

aspects of the community structure at the main post, Norway House

Comparison of a Summer & Winter Epidemic at Infectious Periods of 5 & 7

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140 160 180 200

Infectious Period (Days)

Number of People Infected

Winter - 5 Winter - 7 Summer - 5 Summer - 7

Summer Epidemics: short duration, high peak, peak quickly

Winter Epidemics: long duration, low peak, peak slowly

0

50

100

150

0 100 200 300

day

cases

NH—w≠

NH—s≠

OH—w≠

OH—s≠

GL—w≠

GL—s≠

Changes in rates and patterns of mobility do not significantly affect the size of epidemic peaks

Stage 2

Extend the Stage 1 model to three posts so that results can be compared directly to those from the deterministic model

An Epidemic at all Three Communities

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450

0 20 40 60 80 100 120 140 160 180 200

Day

Number

NHInfected

OHInfected

GLInfected

NHDead

OHDead

GLDead

NHOHGL Model NHODE Model

Predicted Number Infected at NH

717 190

Predicted Number Infected at OH

7 7

Predicted Number Infected at GL

0 7

Predicted Extent of Epidemic Spread

Rarely reaches OH, never reaches GL

Epidemic routinely reaches both OH and GL

Shape of the Epidemic Curve an initial case building up to a rather short and

defined epidemic peak.

an initial case building up to a rather

short and defined epidemic peak.

Timing of the epidemic peaks First at NH First at NH

Predicted Impact of Seasonality

Summer epidemic has earlier and more

severe peak

Summer epidemic has earlier and more severe

peak

Result of the Introduction of the flu at OH or GL instead of NH

Epidemic fails to spread; nearly all epidemic totals are

impacted

Epidemic spreads more readily; timing of the epidemic is affected but not the severity

Parameters that influence the timing of the epidemic

mobility, travel patterns, contact

rates, and population parameters

Mobility, travel patterns, and contact

rates

Parameters that Influence the spread of the epidemic

mobility, travel patterns, contact

rates, and population parameters

Mobility and travel patterns

Parameters that Influence Epidemic severity

mobility, travel patterns, contact

rates, and population parameters

Contact rates

Major potential contributions of mathematical models to human disease

research• Focus research efforts on factors most likely

to have a significant impact on patterns of epidemic spread.– Simulation results illuminated relative roles of

population mobility and social contact within communities on infectious disease spread and shifted focus to factors influencing social contact.

• Identify critical areas with insufficient data.– Results stimulated new archival searches to find data on

settlement structure and seasonal activities.

• Help to understand conditions under which infectious diseases emerge and spread across a landscape.– Simulations showed, for example, that patterns of

mobility influence the timing of epidemic peaks and the patterns of an epidemic’s spread across space.

Major potential contributions of mathematical models to human disease

research (cont.)• May help to identify potential hot spots for the

evolution of new diseases.– Simulations indicated the importance of communities

taking a central role in a region, suggesting that these communities are potential hot spots in their regions.

• Allow for “experimentation” on human populations that would be impossible or unethical in the real world.– Infectious disease simulations follow the progress of

potential epidemics within communities. Well-structured models that are grounded in high quality data provide valuable inferences with which to predict the impact of future epidemics within communities.

• Can be used to evaluate the efficacy of potential control strategies before attempting costly and/or risky field trials.– Simulations pointed out the difficulty of achieving

success with quarantine measures alone.

Acknowledgements

Collaborators and colleagues: McMaster University — Ann Herring, Dick PrestonUniversity of Manitoba — Rob HoppaUniversity of Missouri — Carrie Ahillen, Connie Carpenter, Nate Green, Suman Kanuganti, Melissa Stoops, Emily Williams

Funding:The National Science FoundationThe Canadian Social Sciences and Humanities Research Council

Special thanks to the Norway House First Cree Nation who generously gave permission to work with their historical documents. Leonard McKay, in particular, was a constant source of encouragement and assistance.