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research article

Generalized reproduction numbers and the prediction of patterns in waterborne disease

Gatto, M.
•
Mari, L.  
•
Bertuzzo, E.  
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2012
Proceedings Of The National Academy Of Sciences Of The United States Of America (PNAS)

Understanding, predicting, and controlling outbreaks of waterborne diseases are crucial goals of public health policies, but pose challenging problems because infection patterns are influenced by spatial structure and temporal asynchrony. Although explicit spatial modeling is made possible by widespread data mapping of hydrology, transportation infrastructure, population distribution, and sanitation, the precise condition under which a waterborne disease epidemic can start in a spatially explicit setting is still lacking. Here we show that the requirement that all the local reproduction numbers R-0 be larger than unity is neither necessary nor sufficient for outbreaks to occur when local settlements are connected by networks of primary and secondary infection mechanisms. To determine onset conditions, we derive general analytical expressions for a reproduction matrix G(0), explicitly accounting for spatial distributions of human settlements and pathogen transmission via hydrological and human mobility networks. At disease onset, a generalized reproduction number Lambda(0) (the dominant eigenvalue of G(0)) must be larger than unity. We also show that geographical outbreak patterns in complex environments are linked to the dominant eigenvector and to spectral properties of G(0). Tests against data and computations for the 2010 Haiti and 2000 KwaZulu-Natal cholera outbreaks, as well as against computations for metapopulation networks, demonstrate that eigenvectors of G(0) provide a synthetic and effective tool for predicting the disease course in space and time. Networked connectivity models, describing the interplay between hydrology, epidemiology, and social behavior sustaining human mobility, thus prove to be key tools for emergency management of waterborne infections.

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Type
research article
DOI
10.1073/pnas.1217567109
Web of Science ID

WOS:000312313900045

Author(s)
Gatto, M.
Mari, L.  
Bertuzzo, E.  
Casagrandi, R.
Righetto, L.  
Rodriguez-Iturbe, I.
Rinaldo, A.  
Date Issued

2012

Publisher

Natl Acad Sciences

Published in
Proceedings Of The National Academy Of Sciences Of The United States Of America (PNAS)
Volume

109

Issue

48

Start page

19703

End page

19708

Subjects

ecohydrology

•

aquatic ecosystems

•

invasion

•

bifurcations

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
ECHO  
Available on Infoscience
January 16, 2013
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/87892
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