Abstract

The mathematical theory of single outbreak epidemic models really began with the work of Kermack and Mackendrick about 8 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 2003 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.

Original languageEnglish (US)
Pages (from-to)1-15
Number of pages15
JournalMathematical Biosciences and Engineering
Volume7
Issue number1
DOIs
StatePublished - Jan 2010

Fingerprint

Epidemic Model
Discrete Model
Disease Outbreaks
Expand
Severe Acute Respiratory Syndrome
Unit of time
Continuous-time Model
Discrete-time Model
Influenza
Infectious Diseases
Public Health
Public health
Immediately
Inclusion
Entire
Pandemics
emerging diseases
Human Influenza
pandemic
influenza

Keywords

  • Continuous time epidemic models
  • Discrete epidemic models
  • Epidemic
  • Final size
  • Single outbreak

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Computational Mathematics
  • Agricultural and Biological Sciences(all)
  • Medicine(all)

Cite this

Discrete epidemic models. / Brauer, Fred; Feng, Zhilan; Castillo-Chavez, Carlos.

In: Mathematical Biosciences and Engineering, Vol. 7, No. 1, 01.2010, p. 1-15.

Research output: Contribution to journalArticle

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