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Generalized reproduction numbers and the prediction of patterns in waterborne disease.

ABSTRACT: 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 R0 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 G0, explicitly accounting for spatial distributions of human settlements and pathogen transmission via hydrological and human mobility networks. At disease onset, a generalized reproduction number ?0 (the dominant eigenvalue of G0) 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 G0. 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 G0 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.

SUBMITTER: Gatto M

PROVIDER: S-EPMC3511721 | biostudies-literature | 2012 Nov

REPOSITORIES: biostudies-literature

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Generalized reproduction numbers and the prediction of patterns in waterborne disease.

Gatto Marino M Mari Lorenzo L Bertuzzo Enrico E Casagrandi Renato R Righetto Lorenzo L Rodriguez-Iturbe Ignacio I Rinaldo Andrea A

Proceedings of the National Academy of Sciences of the United States of America 20121112 48

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 explici ...[more]

PMID: 23150538

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Project description:An SEQIJR model of epidemic disease transmission which includes immunization and a varying population size is studied. The model includes immunization of susceptible people (S), quarantine (Q) of exposed people (E), isolation (J) of infectious people (I), a recovered population (R), and variation in population size due to natural births and deaths and deaths of infected people. It is shown analytically that the model has a disease-free equilibrium state which always exists and an endemic equilibrium state which exists if and only if the disease-free state is unstable. A simple formula is obtained for a generalized reproduction number Rg where, for any given initial population, Rg<1 means that the initial population is locally asymptotically stable and Rg>1 means that the initial population is unstable. As special cases, simple formulas are given for the basic reproduction number R0 , a disease-free reproduction number Rdf , and an endemic reproduction number Ren . Formulas are derived for the sensitivity indices for variations in model parameters of the disease-free reproduction number Rdf and for the infected populations in the endemic equilibrium state. A simple formula in terms of the basic reproduction number R0 is derived for the critical immunization level required to prevent the spread of disease in an initially disease-free population. Numerical simulations are carried out using the Matlab program for parameters corresponding to the outbreaks of severe acute respiratory syndrome (SARS) in Beijing, Hong Kong, Canada and Singapore in 2002 and 2003. From the sensitivity analyses for these four regions, the parameters are identified that are the most important for preventing the spread of disease in a disease-free population or for reducing infection in an infected population. The results support the importance of isolating infectious individuals in an epidemic and in maintaining a critical level of immunity in a population to prevent a disease from occurring.

Dataset Information

Generalized reproduction numbers and the prediction of patterns in waterborne disease.

Publications

Generalized reproduction numbers and the prediction of patterns in waterborne disease.

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