Literature DB >> 9120378

Melnikov analysis of chaos in a simple epidemiological model.

P Glendinning1, L P Perry.   

Abstract

Melnikov's method is applied to an SIR model of epidemic dynamics with a periodically modulated nonlinear incidence rate. This analysis establishes mathematically, for the first time, the existence of chaotic motion in these models. A related technique also makes it possible to prove that homoclinic bifurcations occurs in the model.

Mesh：

Year:  1997        PMID： 9120378     DOI： 10.1007/s002850050056

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


  10 in total

1.  Resonance of the epidemic threshold in a periodic environment.

Authors:  Nicolas Bacaër; Xamxinur Abdurahman
Journal:  J Math Biol       Date:  2008-05-07       Impact factor: 2.259

Review 2.  Persistence, chaos and synchrony in ecology and epidemiology.

Authors:  D J Earn; P Rohani; B T Grenfell
Journal:  Proc Biol Sci       Date:  1998-01-07       Impact factor: 5.349

3.  Invariant predictions of epidemic patterns from radically different forms of seasonal forcing.

Authors:  Irena Papst; David J D Earn
Journal:  J R Soc Interface       Date:  2019-07-31       Impact factor: 4.118

4.  Chaotic dynamics in the seasonally forced SIR epidemic model.

Authors:  Pablo G Barrientos; J Ángel Rodríguez; Alfonso Ruiz-Herrera
Journal:  J Math Biol       Date:  2017-04-22       Impact factor: 2.259

5.  Do fatal infectious diseases eradicate host species?

Authors:  Alex P Farrell; James P Collins; Amy L Greer; Horst R Thieme
Journal:  J Math Biol       Date:  2018-05-21       Impact factor: 2.259

6.  First principles modeling of nonlinear incidence rates in seasonal epidemics.

Authors:  José M Ponciano; Marcos A Capistrán
Journal:  PLoS Comput Biol       Date:  2011-02-17       Impact factor: 4.475

7.  Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model.

Authors:  Jorge Duarte; Cristina Januário; Nuno Martins; Svitlana Rogovchenko; Yuriy Rogovchenko
Journal:  J Math Biol       Date:  2019-02-26       Impact factor: 2.164

8.  Chaos in a seasonally perturbed SIR model: avian influenza in a seabird colony as a paradigm.

Authors:  Suzanne M O'Regan; Thomas C Kelly; Andrei Korobeinikov; Michael J A O'Callaghan; Alexei V Pokrovskii; Dmitrii Rachinskii
Journal:  J Math Biol       Date:  2012-05-31       Impact factor: 2.259

9.  Projected geographic disparities in healthcare worker absenteeism from COVID-19 school closures and the economic feasibility of child care subsidies: a simulation study.

Authors:  Elizabeth T Chin; Benjamin Q Huynh; Nathan C Lo; Trevor Hastie; Sanjay Basu
Journal:  medRxiv       Date:  2020-04-16

10.  Analysis and control of an SEIR epidemic system with nonlinear transmission rate.

Authors:  Na Yi; Qingling Zhang; Kun Mao; Dongmei Yang; Qin Li
Journal:  Math Comput Model       Date:  2009-08-28
  10 in total

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