Models for the spread of universally fatal diseases

Research output: Contribution to journalArticle

68 Citations (Scopus)

Abstract

In the formulation of models of S-I-R type for the spread of communicable diseases it is necessary to distinguish between diseases with recovery with full immunity and diseases with permanent removal by death. We consider models which include nonlinear population dynamics with permanent removal. The principal result is that the stability of endemic equilibrium may depend on the population dynamics and on the distribution of infective periods; sustained oscillations are possible in some cases.

Original languageEnglish (US)
Pages (from-to)451-462
Number of pages12
JournalJournal of Mathematical Biology
Volume28
Issue number4
DOIs
StatePublished - Jan 1 1990
Externally publishedYes

Fingerprint

Population Dynamics
Population dynamics
population dynamics
Nonlinear Dynamics
infectious diseases
Communicable Diseases
oscillation
Immunity
Si
Endemic Equilibrium
immunity
death
Recovery
Model
Oscillation
Necessary
Formulation

Keywords

  • AIDS
  • Distributed delays
  • Epidemiology
  • Stability of endemic equilibrium

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Cite this

Models for the spread of universally fatal diseases. / Brauer, Fred.

In: Journal of Mathematical Biology, Vol. 28, No. 4, 01.01.1990, p. 451-462.

Research output: Contribution to journalArticle

@article{732ed99502c6491facfab6ca7d29bc1b,
title = "Models for the spread of universally fatal diseases",
abstract = "In the formulation of models of S-I-R type for the spread of communicable diseases it is necessary to distinguish between diseases with recovery with full immunity and diseases with permanent removal by death. We consider models which include nonlinear population dynamics with permanent removal. The principal result is that the stability of endemic equilibrium may depend on the population dynamics and on the distribution of infective periods; sustained oscillations are possible in some cases.",
keywords = "AIDS, Distributed delays, Epidemiology, Stability of endemic equilibrium",
author = "Fred Brauer",
year = "1990",
month = "1",
day = "1",
doi = "10.1007/BF00178328",
language = "English (US)",
volume = "28",
pages = "451--462",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Verlag",
number = "4",

}

TY - JOUR

T1 - Models for the spread of universally fatal diseases

AU - Brauer, Fred

PY - 1990/1/1

Y1 - 1990/1/1

N2 - In the formulation of models of S-I-R type for the spread of communicable diseases it is necessary to distinguish between diseases with recovery with full immunity and diseases with permanent removal by death. We consider models which include nonlinear population dynamics with permanent removal. The principal result is that the stability of endemic equilibrium may depend on the population dynamics and on the distribution of infective periods; sustained oscillations are possible in some cases.

AB - In the formulation of models of S-I-R type for the spread of communicable diseases it is necessary to distinguish between diseases with recovery with full immunity and diseases with permanent removal by death. We consider models which include nonlinear population dynamics with permanent removal. The principal result is that the stability of endemic equilibrium may depend on the population dynamics and on the distribution of infective periods; sustained oscillations are possible in some cases.

KW - AIDS

KW - Distributed delays

KW - Epidemiology

KW - Stability of endemic equilibrium

UR - http://www.scopus.com/inward/record.url?scp=0025041909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025041909&partnerID=8YFLogxK

U2 - 10.1007/BF00178328

DO - 10.1007/BF00178328

M3 - Article

C2 - 2384722

AN - SCOPUS:0025041909

VL - 28

SP - 451

EP - 462

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 4

ER -