Download Why Canadian fur trappers should stay in bed when they have the flu

Why Canadian fur trappers should stay in bed when
they have the flu: modeling the geographic spread of
infectious diseases
Lisa Sattenspiel
Department 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
General structure of a deterministic epidemic model
with three linked communities
+
a disease process
Susceptible
Infectious
infection
Recovered
recovery
a mobility process
Community
1
Community
2
The chance of infection is a function
of both contact (a social process) and
transmission (a biological process)
Community
3
, the rate of leaving a community
, the distribution of destinations
, the rate of return
Community composition as a result of
the mobility process
AA B
B C A
B A C
mobility process
B BCC
A A A
B B B
C C C C
B C C A
A C C
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 they
come into contact with one another.
dSii
  ik Sik   i Sii    i iji
dt





k
dSik
dt
Sik I jk
N k*
j
  ik I ik   i I ii    i iji
dI ik
dt
dRii
dt
dRik
dt
N i*
j
  i ik Sii  ik Sik    k ijk
dt
dI ii
Sii I ji
k
Sii I ji
j
  i ik I ii  ik I ik    k ijk
j
  ik Rik   i Rii  I ii
k
  i ik Rii  ik Rik  I ik
N i*
 I ii
Sik I jk
N k*
 I 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
50
burials
40
30
20
10
0
1909
1914
1919
year
1924
1929
Mortality among communities within Manitoba
300
Deaths per 1000
250
200
150
100
50
0
Norway House
Fisher River
Berens River Fort Alexander Oxford House
God's Lake
Distribution of deaths by family
Norway House 1919
237 families
180
Observed
Expected
number of families
160
140
120
significantly fewer observed
100
80
60
40
20
0
0
1
2
3+
number of deaths
G-value = 17.33, p < 0.05, df = 2
Families with three to five deaths
Norway House 1919
6
number of individuals
5
4
Alive 1918
Dead 1919
3
2
1
0
Salmon
Robin
Robin
Marten
family
Moose
Fisher
Muskrat
Initial questions
a)
b)
How do changes in the rates and patterns of
mobility affect epidemic spread?
How do changes in rates of contact within
communities affect epidemic spread?
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
180
160
140
NH—w °
cases
120
NH—s°
100
OH—w °
80
OH—s°
GL—w °
60
GL—s°
40
20
0
0
50
100
150
day
200
250
300
Changing social organization by varying the contact rate within communities DOES lead to
significant changes in the size and timing of epidemic peaks
200
NH, both equal
and unequal
contact
180
Number of cases
160
140
120
100
OH, equal
contact
80
GL, equal
contact
60
40
OH, unequal
contact
20
GL, unequal
contact
0
0
50
100
150
Day
200
250
300
Some of the questions addressed in the
project
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?
BUT the real study populations are so small that the deterministic
models presented so far are not really the best ones to use.
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
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 agentbased model that captures
significant aspects of the
community structure at the main
post, Norway House
150
NH—w°
100
OH—w°
NH—s°
OH—s°
50
GL—w°
GL—s°
0
0
100
200
300
day
Comparison of a Summer & Winter Epidemic at Infectious Periods of 5 & 7
600
Summer Epidemics: short duration, high peak, peak quickly
500
Number of People Infected
cases
Changes in rates and patterns of mobility do not significantly
affect the size of epidemic peaks
400
300
Winter Epidemics: long duration, low peak, peak slowly
200
100
0
0
20
40
60
80
100
120
140
Infectious Period (Days)
Winter - 5
Winter - 7
Summer - 5
Summer - 7
160
180
200
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
450
NH
Infected
400
Number
350
300
OH
Infected
250
GL
Infected
NH
Dead
200
150
OH
Dead
100
GL
Dead
50
0
0
20
40
60
80
100
Day
120
140
160
180
200
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 Preston
University of Manitoba — Rob Hoppa
University of Missouri — Carrie Ahillen, Connie Carpenter, Nate Green,
Suman Kanuganti, Melissa Stoops, Emily Williams
Funding:
The National Science Foundation
The 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.