An SIS Epidemic Model with Variable Population Size and a Delay

Overview

Journal J Math Biol

Date 1995 Jan 1

PMID 8576654

Citations 14

Authors

H W Hethcote

P van den Driessche

Affiliations

Soon will be listed here.

Abstract

The SIS epidemiological model has births, natural deaths, disease-related deaths and a delay corresponding to the infectious period. The thresholds for persistence, equilibria and stability are determined. The persistence of the disease combined with the disease-related deaths can cause the population size to decrease to zero, to remain finite, or to grow exponentially with a smaller growth rate constant. For some parameter values, the endemic infective-fraction equilibrium is asymptotically stable, but for other parameter values, it is unstable and a surrounding periodic solution appears by Hopf bifurcation.

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References

Greenhalgh D . Some results for an SEIR epidemic model with density dependence in the death rate. IMA J Math Appl Med Biol. 1992; 9(2):67-106. DOI: 10.1093/imammb/9.2.67. View

Bremermann H, Thieme H . A competitive exclusion principle for pathogen virulence. J Math Biol. 1989; 27(2):179-90. DOI: 10.1007/BF00276102. View

Greenhalgh D . Vaccination in density-dependent epidemic models. Bull Math Biol. 1992; 54(5):733-58. DOI: 10.1007/BF02459928. View

Busenberg S, van den Driessche P . Analysis of a disease transmission model in a population with varying size. J Math Biol. 1990; 28(3):257-70. DOI: 10.1007/BF00178776. View

Lin X . Qualitative analysis of an HIV transmission model. Math Biosci. 1991; 104(1):111-34. DOI: 10.1016/0025-5564(91)90033-f. View

Lin X . On the uniqueness of endemic equilibria of an HIV/AIDS transmission model for a heterogeneous population. J Math Biol. 1991; 29(8):779-90. DOI: 10.1007/BF00160192. View

Busenberg S, Cooke K . The effect of integral conditions in certain equations modelling epidemics and population growth. J Math Biol. 1980; 10(1):13-32. DOI: 10.1007/BF00276393. View

Pugliese A . Population models for diseases with no recovery. J Math Biol. 1990; 28(1):65-82. DOI: 10.1007/BF00171519. View

Derrick W, van den Driessche P . A disease transmission model in a nonconstant population. J Math Biol. 1993; 31(5):495-512. DOI: 10.1007/BF00173889. View

10.

Hethcote H . Dynamic models of infectious diseases as regulators of population sizes. J Math Biol. 1992; 30(7):693-716. DOI: 10.1007/BF00173264. View

11.

Anderson R, Jackson H, May R, Smith A . Population dynamics of fox rabies in Europe. Nature. 1981; 289(5800):765-71. DOI: 10.1038/289765a0. View

12.

Greenhalgh D . An epidemic model with a density-dependent death rate. IMA J Math Appl Med Biol. 1990; 7(1):1-26. DOI: 10.1093/imammb/7.1.1. View

13.

Gao L, Hethcote H . Four SEI endemic models with periodicity and separatrices. Math Biosci. 1995; 128(1-2):157-84. DOI: 10.1016/0025-5564(94)00071-7. View

14.

Hethcote H, van den Driessche P . Some epidemiological models with nonlinear incidence. J Math Biol. 1991; 29(3):271-87. DOI: 10.1007/BF00160539. View

15.

Castillo-Chavez C, Cooke K, Huang W, Levin S . On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). Part 1: Single population models. J Math Biol. 1989; 27(4):373-98. DOI: 10.1007/BF00290636. View

16.

Greenhalgh D . Some threshold and stability results for epidemic models with a density-dependent death rate. Theor Popul Biol. 1992; 42(2):130-51. DOI: 10.1016/0040-5809(92)90009-i. View

17.

Zhou J, Hethcote H . Population size dependent incidence in models for diseases without immunity. J Math Biol. 1994; 32(8):809-34. DOI: 10.1007/BF00168799. View

18.

Anderson R, Medley G, May R, Johnson A . A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS. IMA J Math Appl Med Biol. 1986; 3(4):229-63. DOI: 10.1093/imammb/3.4.229. View

19.

Anderson R, May R . Population biology of infectious diseases: Part I. Nature. 1979; 280(5721):361-7. DOI: 10.1038/280361a0. View

20.

Lin X, Hethcote H, van den Driessche P . An epidemiological model for HIV/AIDS with proportional recruitment. Math Biosci. 1993; 118(2):181-95. DOI: 10.1016/0025-5564(93)90051-b. View