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Mathematical Biosciences and Engineering
Article . 2010 . Peer-reviewed
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Mathematical Biosciences and Engineering
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Discrete epidemic models

Authors: Fred Brauer; Zhilan Feng; Carlos Castillo-Chávez;

Discrete epidemic models

Abstract

The mathematical theory of single outbreak epidemic models really began with the work of Kermack and Mackendrick about decades ago. This gave a simple answer to the long-standing question of why epidemics woould appear suddenly and then disappear just as suddenly without having infected an entire population. Therefore it seemed natural to expect that theoreticians would immediately proceed to expand this mathematical framework both because the need to handle recurrent single infectious disease outbreaks has always been a priority for public health officials and because theoreticians often try to push the limits of exiting theories. However, the expansion of the theory via the inclusion of refined epidemiological classifications or through the incorporation of categories that are essential for the evaluation of intervention strategies, in the context of ongoing epidemic outbreaks, did not materialize. It was the global threat posed by SARS in that caused theoreticians to expand the Kermack-McKendrick single-outbreak framework. Most recently, efforts to connect theoretical work to data have exploded as attempts to deal with the threat of emergent and re-emergent diseases including the most recent H1N1 influenza pandemic, have marched to the forefront of our global priorities. Since data are collected and/or reported over discrete units of time, developing single outbreak models that fit collected data naturally is relevant. In this note, we introduce a discrete-epidemic framework and highlight, through our analyses, the similarities between single-outbreak comparable classical continuous-time epidemic models and the discrete-time models introduced in this note. The emphasis is on comparisons driven by expressions for the final epidemic size.

Keywords

final size, single outbreak, Severe Acute Respiratory Syndrome, Communicable Diseases, Models, Biological, epidemic, discrete epidemic models, Disease Outbreaks, Influenza A Virus, H1N1 Subtype, Severe acute respiratory syndrome-related coronavirus, Influenza, Human, QA1-939, Disease Progression, Humans, continuous time epidemic models., Public Health, TP248.13-248.65, Mathematics, Biotechnology

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
68
Top 10%
Top 10%
Top 10%
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