spreading of diseases along river networks
DESCRIPTION
Enrico Bertuzzo covered instead the new topic of water borne diseases and their spreading along rivers. The way Enrico and coworkers analysed the problem, certainly inherited many notions and ideas sprout the early studies on river networks structure by Andrea (I had a part in it), but also on recent and domain specific achievements and findings. In the presentation he cited just one paper, but the research outcomes on the topic are certainly copious and exciting.TRANSCRIPT
Rivers, rainfall and cholera.
A new challenge for hydrologists
Enrico Bertuzzo, Senior Scientist, ECHO lab, EPFL
Interdisciplinary Workshop
on Frontiers in Hydrology and Hydrogeoscience
humanbacteria in the
environment
ingestion of
contaminated water
fecal contamination
ecological dynamics
• 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?)
the model
Continuous Compartmental
Spatially Explicit Epidemic Model
S susceptible
I infected
R recovered
B bacteria concentration in the
environment
S susceptible
I infected
R recovered
B bacteria concentration in the
environment
Pij hydrologic transport network
Continuous Compartmental
Spatially Explicit Epidemic Model
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
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
Haiti cholera epidemic
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)
Digital Terrain Model
SRTM3
network and watershed
delineation
definition of the graph
hydrologic transport
Digital Terrain Model
SRTM3
network and watershed
delineation
LandScan Project
1 km resolution population
distribution: downscaling of
census data through remote
sensing
Road Network
source: openstreetmap.org
distances between
communities
human-mediated
transport network
Road Network
source: openstreetmap.org
distances between
communities
Rinaldo et al. PNAS 2012
prediction Dec 2010Bertuzzo et al., GRL, 2011
prediction Nov 2011Rinaldo et al., PNAS, 2012
prediction Jan 2013Bertuzzo et al., in press SERRA
Stability analysis
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
spatially explicit model
Stability conditions
eigenvectorcases
leading eigenvalue
Intervention strategies
Intervention strategies
300’000 vaccines
3’000’000 vaccines
sanitation 40%
sanitation 40%
Epidemic or endemic?
probability of extinction
thanks for the attention