Spreading of diseases along river networks
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Transcript of Spreading of diseases along river networks
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Rivers, rainfall and cholera.
A new challenge for hydrologists
Enrico Bertuzzo, Senior Scientist, ECHO lab, EPFL
Interdisciplinary Workshop
on Frontiers in Hydrology and Hydrogeoscience
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humanbacteria in the
environment
ingestion of
contaminated water
fecal contamination
ecological dynamics
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• Mortality rate less than 1% if properly treated
• Recovery time of about 5 days
• Immunity is acquired after infection; not permanent, lasts a few years (1–5?)
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the model
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Continuous Compartmental
Spatially Explicit Epidemic Model
S susceptible
I infected
R recovered
B bacteria concentration in the
environment
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S susceptible
I infected
R recovered
B bacteria concentration in the
environment
Pij hydrologic transport network
Continuous Compartmental
Spatially Explicit Epidemic Model
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Continuous Compartmental
Spatially Explicit Epidemic Model
S susceptible
I infected
R recovered
B bacteria concentration in the
environment
Pij hydrologic transport network
Qij human mobility transport
network
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Continuous Compartmental
Spatially Explicit Epidemic Model
S susceptible
I infected
R recovered
B bacteria concentration in the
environment
Pij hydrologic transport network
Qij human mobility transport
network
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Haiti cholera epidemic
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Haiti cholera epidemic. First case on October 2010
As of April 15 2014:
00’000 reported cases (7% of the population)
’552 deaths (1.2% of the total cases)
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Digital Terrain Model
SRTM3
network and watershed
delineation
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definition of the graph
hydrologic transport
Digital Terrain Model
SRTM3
network and watershed
delineation
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LandScan Project
1 km resolution population
distribution: downscaling of
census data through remote
sensing
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Road Network
source: openstreetmap.org
distances between
communities
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human-mediated
transport network
Road Network
source: openstreetmap.org
distances between
communities
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Rinaldo et al. PNAS 2012
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prediction Dec 2010Bertuzzo et al., GRL, 2011
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prediction Nov 2011Rinaldo et al., PNAS, 2012
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prediction Jan 2013Bertuzzo et al., in press SERRA
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Stability analysis
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unstable disease
free equilibrium
perturbation (I>0)
epidemic outbreak
10R
stable disease
free equilibrium
perturbation (I>0)
epidemic fades out
Basic reproduction number: number of secondary cases produced by a single
case over the course of the infectious period
10R
Stability conditionsspatially implicit model
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spatially explicit model
Stability conditions
eigenvectorcases
leading eigenvalue
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Intervention strategies
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Intervention strategies
300’000 vaccines
3’000’000 vaccines
sanitation 40%
sanitation 40%
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Epidemic or endemic?
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probability of extinction
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thanks for the attention