Literature DB >> 7328366

Stability analysis for models of diseases without immunity.

H W Hethcote, H W Stech, P van den Driessche.   

Abstract

A cyclic, constant parameter epidemiological model is described for a closed population divided into susceptible, exposed and infectious classes. Distributed delays are introduced and the model is formulated as two coupled Volterra integral equations. The delays do not change the general nature of thresholds or asymptotic stability; in all cases considered the disease either dies out, or approaches an endemic steady state.

Mesh:

Year:  1981        PMID: 7328366     DOI: 10.1007/bf00275213

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


  7 in total

1.  On a transcendental equation in the stability analysis of a population growth model.

Authors:  H O Walther
Journal:  J Math Biol       Date:  1976-06-30       Impact factor: 2.259

2.  Spatial heterogeneity and the stability of predator-prey systems.

Authors:  A Hastings
Journal:  Theor Popul Biol       Date:  1977-08       Impact factor: 1.570

3.  Population biology of infectious diseases: Part I.

Authors:  R M Anderson; R M May
Journal:  Nature       Date:  1979-08-02       Impact factor: 49.962

4.  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

5.  Integral equation models for endemic infectious diseases.

Authors:  H W Hethcote; D W Tudor
Journal:  J Math Biol       Date:  1980-03       Impact factor: 2.259

6.  The effect of integral conditions in certain equations modelling epidemics and population growth.

Authors:  S Busenberg; K L Cooke
Journal:  J Math Biol       Date:  1980-08       Impact factor: 2.259

7.  Population biology of infectious diseases: Part II.

Authors:  R M May; R M Anderson
Journal:  Nature       Date:  1979-08-09       Impact factor: 49.962

  7 in total
  8 in total

1.  Some epidemiological models with nonlinear incidence.

Authors:  H W Hethcote; P van den Driessche
Journal:  J Math Biol       Date:  1991       Impact factor: 2.259

2.  Models for the spread of universally fatal diseases.

Authors:  F Brauer
Journal:  J Math Biol       Date:  1990       Impact factor: 2.259

3.  An epidemiological model with a delay and a nonlinear incidence rate.

Authors:  H W Hethcote; M A Lewis; P van den Driessche
Journal:  J Math Biol       Date:  1989       Impact factor: 2.259

4.  Dynamical behavior of epidemiological models with nonlinear incidence rates.

Authors:  W M Liu; H W Hethcote; S A Levin
Journal:  J Math Biol       Date:  1987       Impact factor: 2.259

5.  An SIS epidemic model with variable population size and a delay.

Authors:  H W Hethcote; P van den Driessche
Journal:  J Math Biol       Date:  1995       Impact factor: 2.259

6.  Prelude to Hopf bifurcation in an epidemic model: analysis of a characteristic equation associated with a nonlinear Volterra integral equation.

Authors:  O Diekmann; R Montijn
Journal:  J Math Biol       Date:  1982       Impact factor: 2.259

7.  The evolutionary effect of endemic infectious disease: continuous models for an invariant pathogen.

Authors:  J T Kemper
Journal:  J Math Biol       Date:  1982       Impact factor: 2.259

8.  The Hybrid Incidence Susceptible-Transmissible-Removed Model for Pandemics : Scaling Time to Predict an Epidemic's Population Density Dependent Temporal Propagation.

Authors:  Ryan Lester Benjamin
Journal:  Acta Biotheor       Date:  2022-01-29       Impact factor: 1.185

  8 in total

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