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Continuous-Time Age-Structured Models in Population Dynamics and Epidemiology

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Mathematical Epidemiology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 1945))

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.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Alabama in Huntsville, 301, Sparkman Dr., Huntsville, AL, 35899, USA

    Jia Li

  2. Department of Mathematics, University of British Columbia, 1984, Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

    Fred Brauer

Authors
  1. Jia Li
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  2. Fred Brauer
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada

    Fred Brauer

  2. Department of Mathematics and Statistics, University of Victoria, 3060 STN CSC, Victoria, B.C. V8W 3R4, Canada

    Pauline van den Driessche

  3. Center for Disease Modeling Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

    Jianhong Wu

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Li, J., Brauer, F. (2008). Continuous-Time Age-Structured Models in Population Dynamics and Epidemiology. In: Brauer, F., van den Driessche, P., Wu, J. (eds) Mathematical Epidemiology. Lecture Notes in Mathematics, vol 1945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78911-6_9

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