Continuous-time age-structured models in population dynamics and epidemiology

Jia Li, Fred Brauer

Research output: Chapter in Book/Report/Conference proceedingChapter

21 Citations (Scopus)

Abstract

We present continuous-time models for age-structured populations and disease transmission. We show how to use the method of characteristic lines to analyze the model dynamics and to write an age-structured population model as an integral equation model. We then extend to an agestructured SIR epidemic model. As an example we describe an age-structured model for AIDS, derive a formula for the reproductive number of infection, and show how important a role pair-formation plays in the modeling process. In particular, we outline the semi-group method used in an age-structured AIDS model with non-random mixing. We also discuss models for populations and disease spread with discrete age structure.

Original languageEnglish (US)
Title of host publicationMathematical Epidemiology
PublisherSpringer Verlag
Pages205-227
Number of pages23
ISBN (Print)9783540789109
DOIs
StatePublished - Jan 1 2008
Externally publishedYes

Publication series

NameLecture Notes in Mathematics
Volume1945
ISSN (Print)0075-8434

Fingerprint

Age-structured Model
Continuous-time Model
Epidemiology
Population Dynamics
Age-structured Population
Reproductive number
SIR Epidemic Model
Age Structure
Method of Characteristics
Process Modeling
Population Model
Infection
Integral Equations
Semigroup
Model
Line

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Li, J., & Brauer, F. (2008). Continuous-time age-structured models in population dynamics and epidemiology. In Mathematical Epidemiology (pp. 205-227). (Lecture Notes in Mathematics; Vol. 1945). Springer Verlag. https://doi.org/10.1007/978-3-540-78911-6_9

Continuous-time age-structured models in population dynamics and epidemiology. / Li, Jia; Brauer, Fred.

Mathematical Epidemiology. Springer Verlag, 2008. p. 205-227 (Lecture Notes in Mathematics; Vol. 1945).

Research output: Chapter in Book/Report/Conference proceedingChapter

Li, J & Brauer, F 2008, Continuous-time age-structured models in population dynamics and epidemiology. in Mathematical Epidemiology. Lecture Notes in Mathematics, vol. 1945, Springer Verlag, pp. 205-227. https://doi.org/10.1007/978-3-540-78911-6_9
Li J, Brauer F. Continuous-time age-structured models in population dynamics and epidemiology. In Mathematical Epidemiology. Springer Verlag. 2008. p. 205-227. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-540-78911-6_9
Li, Jia ; Brauer, Fred. / Continuous-time age-structured models in population dynamics and epidemiology. Mathematical Epidemiology. Springer Verlag, 2008. pp. 205-227 (Lecture Notes in Mathematics).
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