Literature DB >> 845513

On periodic solutions of a delay integral equation modelling epidemics.

H L Smith.   

Abstract

A delay-integral equation, proposed by Cooke and Kaplan in [1] as a model of epidemics, is studied. The focus of this work is on the qualitative behavor of solutions as a certain parameter is allowed to vary. It is shown that if a certain threshold is not exceeded then solutions tend to zero exponentially while if this threshold is exceeded, periodic solutions exist. Many features or the numerical studies in [1] are explained.

Mesh:

Year:  1977        PMID: 845513     DOI: 10.1007/BF00276353

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


  3 in total

1.  Recurrent outbreaks of measles, chickenpox and mumps. II. Systematic differences in contact rates and stochastic effects.

Authors:  J A Yorke; W P London
Journal:  Am J Epidemiol       Date:  1973-12       Impact factor: 4.897

2.  Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates.

Authors:  W P London; J A Yorke
Journal:  Am J Epidemiol       Date:  1973-12       Impact factor: 4.897

3.  Asymptotic behavior in a deterministic epidemic model.

Authors:  H W Hethcote
Journal:  Bull Math Biol       Date:  1973 Nov-Dec       Impact factor: 1.758

  3 in total
  4 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

2.  Persistence in seasonally forced epidemiological models.

Authors:  Carlota Rebelo; Alessandro Margheri; Nicolas Bacaër
Journal:  J Math Biol       Date:  2011-06-08       Impact factor: 2.259

3.  Global asymptotic stability of a periodic solution to an epidemic model.

Authors:  R Volz
Journal:  J Math Biol       Date:  1982       Impact factor: 2.259

4.  Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior.

Authors:  S Amin Moosavi; Afshin Montakhab; Alireza Valizadeh
Journal:  Sci Rep       Date:  2017-08-02       Impact factor: 4.379

  4 in total

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