Mathematical Biosciences and Engineering, 2009, 6(2): 377-393. doi: 10.3934/mbe.2009.6.377.

Primary: 92D15, 92D25; Secondary: 91A22, 91A40.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

The discounted reproductive number for epidemiology

1. Department of Mathematics, Pennsylvania State University, State College, PA 16802
2. Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT 06520

The basic reproductive number, $\Ro$, and the effective reproductive number, $R$, are commonly used in mathematical epidemiology as summary statistics for the size and controllability of epidemics. However, these commonly used reproductive numbers can be misleading when applied to predict pathogen evolution because they do not incorporate the impact of the timing of events in the life-history cycle of the pathogen. To study evolution problems where the host population size is changing, measures like the ultimate proliferation rate must be used. A third measure of reproductive success, which combines properties of both the basic reproductive number and the ultimate proliferation rate, is the discounted reproductive number $\mathcal{R}_d$. The discounted reproductive number is a measure of reproductive success that is an individual's expected lifetime offspring production discounted by the background population growth rate. Here, we draw attention to the discounted reproductive number by providing an explicit definition and a systematic application framework. We describe how the discounted reproductive number overcomes the limitations of both the standard reproductive numbers and proliferation rates, and show that $\mathcal{R}_d$ is closely connected to Fisher's reproductive values for different life-history stages.
  Figure/Table
  Supplementary
  Article Metrics

Keywords game theory.; ultimate proliferation rate; reproductive number

Citation: Timothy C. Reluga, Jan Medlock, Alison Galvani. The discounted reproductive number for epidemiology. Mathematical Biosciences and Engineering, 2009, 6(2): 377-393. doi: 10.3934/mbe.2009.6.377

 

This article has been cited by

  • 1. Eberhard O. Voit, The fourteenth Bellman Prize, Mathematical Biosciences, 2014, 247, A1, 10.1016/j.mbs.2013.12.001
  • 2. Jing Li, Daniel Blakeley, Robert J. Smith, The Failure ofR0, Computational and Mathematical Methods in Medicine, 2011, 2011, 1, 10.1155/2011/527610
  • 3. Timothy C. Reluga, Allison K. Shaw, Optimal migratory behavior in spatially-explicit seasonal environments, Discrete and Continuous Dynamical Systems - Series B, 2014, 19, 10, 3359, 10.3934/dcdsb.2014.19.3359
  • 4. Timothy C. Reluga, Allison K. Shaw, Resource distribution drives the adoption of migratory, partially migratory, or residential strategies, Theoretical Ecology, 2015, 8, 4, 437, 10.1007/s12080-015-0263-y
  • 5. Timothy C. Reluga, Carl T. Bergstrom, Game Theory of Social Distancing in Response to an Epidemic, PLoS Computational Biology, 2010, 6, 5, e1000793, 10.1371/journal.pcbi.1000793
  • 6. Xiao-Tian Wang, , Encyclopedia of Evolutionary Psychological Science, 2016, Chapter 3585-1, 1, 10.1007/978-3-319-16999-6_3585-1

Reader Comments

your name: *   your email: *  

Copyright Info: 2009, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved