Discrete epidemic models

Mathematical Biosciences and Engineering : MBE
Fred BrauerCarlos Castillo-Chavez

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 mar...Continue Reading

Citations

Aug 4, 2012·Journal of American College Health : J of ACH·Karen Palin, Meredith L Greer
Jan 9, 2010·Theoretical Biology & Medical Modelling·Hiroshi NishiuraCarlos Castillo-Chavez
Mar 3, 2011·Mathematical Biosciences and Engineering : MBE·Julien ArinoPing Yan
Mar 3, 2011·Mathematical Biosciences and Engineering : MBE·Olivia ProsperCarlos Castillo-Chavez
Mar 3, 2011·Mathematical Biosciences and Engineering : MBE·Sunmi LeeCarlos Castillo-Chavez
Nov 20, 2013·Mathematical Biosciences and Engineering : MBE·Fred BrauerP van den Driessche
Nov 20, 2013·Mathematical Biosciences and Engineering : MBE·Gerardo ChowellBaojun Song
Sep 15, 2015·Journal of Biological Dynamics·Christopher M Kribs, Christopher Mitchell
Mar 5, 2011·BMC Public Health·Fred Brauer
Mar 3, 2011·Mathematical Biosciences and Engineering : MBE·Paula A González-ParraCarlos Castillo-Chavez
Apr 18, 2020·Journal of Biological Dynamics·P van den Driessche, Abdul-Aziz Yakubu
Oct 31, 2018·Journal of Biological Dynamics·P van den Driessche, Abdul-Aziz Yakubu
Jun 26, 2013·Bulletin of Mathematical Biology·Nancy Hernandez-CeronCarlos Castillo-Chavez
May 8, 2018·Journal of Biological Dynamics·Jummy Funke David
Jan 1, 2017·International Journal of Dynamics and Control·Omar ZakaryIlias Elmouki
Apr 14, 2018·Bulletin of Mathematical Biology·P van den Driessche, Abdul-Aziz Yakubu
Oct 23, 2015·Bulletin of Mathematical Biology·Derdei BicharaCharles Perrings
Jan 1, 2016·Advances in Difference Equations·Xiaolin FanZhidong Teng
Apr 5, 2021·Journal of Mathematical Biology·A Gómez-CorralM T Rodríguez-Bernal
Sep 26, 2021·Proceedings of the National Academy of Sciences of the United States of America·Odo DiekmannMartin C J Bootsma

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