Discrete epidemic models with arbitrary stage distributions and applications to disease control
Identifieur interne : 001960 ( Main/Merge ); précédent : 001959; suivant : 001961Discrete epidemic models with arbitrary stage distributions and applications to disease control
Auteurs : Nancy Hernandez-Ceron [États-Unis] ; Zhilan Feng [États-Unis] ; Carlos Castillo-Chavez [États-Unis]Source :
- Bulletin of mathematical biology [ 0092-8240 ] ; 2013.
Abstract
W. O. Kermack and A. G. McKendrick introduced in their fundamental paper, A Contribution to the Mathematical Theory of Epidemics, published in 1927, a simple deterministic model that captured the qualitative dynamic behavior of single infectious disease outbreaks. A Kermack-McKendrick discrete-time general framework, motivated by the emergence of a multitude of models used to forecast the dynamics of SARS and influenza outbreaks, is introduced in this manuscript. Results that allow us to measure quantitatively the role of classical and general distributions on disease dynamics are presented. The case of the geometric distribution is used to evaluate the impact of waiting-time distributions on epidemiological processes or public health interventions. In short, the geometric distribution is used to set up the baseline or null epidemiological model used to test the relevance of realistic stage-period distribution on the dynamics of single epidemic outbreaks. A final size relationship involving the control reproduction number, a function of transmission parameters and the means of distributions used to model disease or intervention control measures, is computed. Model results and simulations highlight the inconsistencies in forecasting that emerge from the use of specific parametric distributions. Examples, using the geometric, Poisson and binomial distributions, are used to highlight the impact of the choices made in quantifying the risk posed by single outbreaks and the relative importance of various control measures.
Url:
DOI: 10.1007/s11538-013-9866-x
PubMed: 23797790
PubMed Central: 4002294
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<front><div type="abstract" xml:lang="en"><p id="P1">W. O. Kermack and A. G. McKendrick introduced in their fundamental paper,
A Contribution to the Mathematical Theory of Epidemics, published in 1927, a
simple deterministic model that captured the qualitative dynamic behavior of
single infectious disease outbreaks. A Kermack-McKendrick discrete-time general
framework, motivated by the emergence of a multitude of models used to forecast
the dynamics of SARS and influenza outbreaks, is introduced in this manuscript.
Results that allow us to measure quantitatively the role of classical and
general distributions on disease dynamics are presented. The case of the
geometric distribution is used to evaluate the impact of waiting-time
distributions on epidemiological processes or public health interventions. In
short, the geometric distribution is used to set up the baseline or null
epidemiological model used to test the relevance of realistic stage-period
distribution on the dynamics of single epidemic outbreaks. A final size
relationship involving the control reproduction number, a function of
transmission parameters and the means of distributions used to model disease or
intervention control measures, is computed. Model results and simulations
highlight the inconsistencies in forecasting that emerge from the use of
specific parametric distributions. Examples, using the geometric, Poisson and
binomial distributions, are used to highlight the impact of the choices made in
quantifying the risk posed by single outbreaks and the relative importance of
various control measures.</p>
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