### Abstract

We consider models for the transmission of infectious diseases with an arbitrary infective period distribution in which there may be both disease fatalities and recoveries. The possibility of disease deaths complicates the analysis because the total population size can not be asymptotically constant. If the birth rate is constant there is always a unique asymptotically stable equilibrium. However, if the birth rate depends on susceptible population size, the endemic equilibrium may be unstable for some infective period distributions and the stability may depend on the fraction of infectives who recover from the disease.

Original language | English (US) |
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Pages (from-to) | 377-387 |

Number of pages | 11 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms |

Volume | 10 |

Issue number | 1-3 |

State | Published - Feb 1 2003 |

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### Keywords

- Arbitrary infective period distributions
- Disease mortality
- Epidemic model
- Instability

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics