Literature DB >> 19048254

A graph-theoretic method for the basic reproduction number in continuous time epidemiological models.

Tomás de-Camino-Beck1, Mark A Lewis, P van den Driessche.   

Abstract

In epidemiological models of infectious diseases the basic reproduction number 'R(0) is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for 'R(0) can be obtained from the digraphs in the reduction process.

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Year:  2008        PMID： 19048254     DOI： 10.1007/s00285-008-0240-9

Source DB:  PubMed          Journal:  J Math Biol        ISSN： 0303-6812            Impact factor:   2.259


  14 in total

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2.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.

Authors:  P van den Driessche; James Watmough
Journal:  Math Biosci       Date:  2002 Nov-Dec       Impact factor: 2.144

3.  A brief history of R0 and a recipe for its calculation.

Authors:  J A P Heesterbeek
Journal:  Acta Biotheor       Date:  2002       Impact factor: 1.774

4.  A comparison of continuous and discrete-time West Nile virus models.

Authors:  Mark A Lewis; Joanna Rencławowicz; P van den Driessche; Marjorie Wonham
Journal:  Bull Math Biol       Date:  2006-04-05       Impact factor: 1.758

5.  A new method for calculating net reproductive rate from graph reduction with applications to the control of invasive species.

Authors:  T de-Camino-Beck; M A Lewis
Journal:  Bull Math Biol       Date:  2007-02-15       Impact factor: 1.758

6.  The pluses and minuses of R0.

Authors:  M G Roberts
Journal:  J R Soc Interface       Date:  2007-10-22       Impact factor: 4.118

7.  On net reproductive rate and the timing of reproductive output.

Authors:  T de-Camino-Beck; M A Lewis
Journal:  Am Nat       Date:  2008-07       Impact factor: 3.926

8.  Modeling spatial spread of west nile virus and impact of directional dispersal of birds.

Authors:  Rongsong Liu; Jiangping Shuai; Jianhong Wu; Huaiping Zhu
Journal:  Math Biosci Eng       Date:  2006-01       Impact factor: 2.080

9.  An epidemiological model for West Nile virus: invasion analysis and control applications.

Authors:  Marjorie J Wonham; Tomás de-Camino-Beck; Mark A Lewis
Journal:  Proc Biol Sci       Date:  2004-03-07       Impact factor: 5.349

10.  Transmissibility of 1918 pandemic influenza.

Authors:  Christina E Mills; James M Robins; Marc Lipsitch
Journal:  Nature       Date:  2004-12-16       Impact factor: 49.962
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  5 in total

Review 1.  Next-generation tools for evolutionary invasion analyses.

Authors:  Amy Hurford; Daniel Cownden; Troy Day
Journal:  J R Soc Interface       Date:  2009-12-02       Impact factor: 4.118

2.  A discrete-time epidemic model for the analysis of transmission of COVID19 based upon data of epidemiological parameters.

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Journal:  Eur Phys J Spec Top       Date:  2022-03-16       Impact factor: 2.707

Review 3.  The failure of R0.

Authors:  Jing Li; Daniel Blakeley; Robert J Smith
Journal:  Comput Math Methods Med       Date:  2011-08-16       Impact factor: 2.238

Review 4.  A Survey on Mathematical, Machine Learning and Deep Learning Models for COVID-19 Transmission and Diagnosis.

Authors:  Christopher Clement John; VijayaKumar Ponnusamy; Sriharipriya Krishnan Chandrasekaran; Nandakumar R
Journal:  IEEE Rev Biomed Eng       Date:  2022-01-20

Review 5.  Reproduction numbers of infectious disease models.

Authors:  Pauline van den Driessche
Journal:  Infect Dis Model       Date:  2017-06-29
  5 in total

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