The discounted reproductive number for epidemiology
The basic reproductive number, $\Ro$, and the effective reproductivenumber, $R$, are commonly used in mathematicalepidemiology as summary statistics for the size andcontrollability of epidemics.However, these commonly usedreproductive numbers can be misleading when appliedto predict pathogen evoluti...
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AIMS Press
2009-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.377 |
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| author | Timothy C. Reluga Jan Medlock Alison Galvani |
| author_facet | Timothy C. Reluga Jan Medlock Alison Galvani |
| author_sort | Timothy C. Reluga |
| collection | DOAJ |
| description | The basic reproductive number, $\Ro$, and the effective reproductivenumber, $R$, are commonly used in mathematicalepidemiology as summary statistics for the size andcontrollability of epidemics.However, these commonly usedreproductive numbers can be misleading when appliedto predict pathogen evolution because they do notincorporate the impact of the timing of events in the life-historycycle of the pathogen.To study evolution problems where the host population size ischanging, measures like the ultimate proliferation rate must be used.A third measure of reproductive success, which combines properties ofboth the basic reproductive number and the ultimate proliferationrate, is the discounted reproductive number$\mathcal{R}_d$. The discountedreproductive number is a measure of reproductive success that is anindividual's expected lifetime offspring production discounted by thebackground population growth rate. Here, we drawattention to the discounted reproductive number by providing anexplicit definition and a systematic application framework. Wedescribe how the discounted reproductive number overcomes thelimitations of both the standard reproductive numbers andproliferation rates, and show that $\mathcal{R}_d$ is closely connected toFisher's reproductive values for different life-history stages. |
| format | Article |
| id | doaj-art-93f095a9285b43058ceb1985b5bbb8a4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-93f095a9285b43058ceb1985b5bbb8a42025-01-24T01:59:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-02-016237739310.3934/mbe.2009.6.377The discounted reproductive number for epidemiologyTimothy C. Reluga0Jan Medlock1Alison Galvani2Department of Mathematics, Pennsylvania State University, State College, PA 16802Department of Mathematics, Pennsylvania State University, State College, PA 16802Department of Mathematics, Pennsylvania State University, State College, PA 16802The basic reproductive number, $\Ro$, and the effective reproductivenumber, $R$, are commonly used in mathematicalepidemiology as summary statistics for the size andcontrollability of epidemics.However, these commonly usedreproductive numbers can be misleading when appliedto predict pathogen evolution because they do notincorporate the impact of the timing of events in the life-historycycle of the pathogen.To study evolution problems where the host population size ischanging, measures like the ultimate proliferation rate must be used.A third measure of reproductive success, which combines properties ofboth the basic reproductive number and the ultimate proliferationrate, is the discounted reproductive number$\mathcal{R}_d$. The discountedreproductive number is a measure of reproductive success that is anindividual's expected lifetime offspring production discounted by thebackground population growth rate. Here, we drawattention to the discounted reproductive number by providing anexplicit definition and a systematic application framework. Wedescribe how the discounted reproductive number overcomes thelimitations of both the standard reproductive numbers andproliferation rates, and show that $\mathcal{R}_d$ is closely connected toFisher's reproductive values for different life-history stages.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.377gametheory.ultimate proliferation ratereproductive number |
| spellingShingle | Timothy C. Reluga Jan Medlock Alison Galvani The discounted reproductive number for epidemiology Mathematical Biosciences and Engineering gametheory. ultimate proliferation rate reproductive number |
| title | The discounted reproductive number for epidemiology |
| title_full | The discounted reproductive number for epidemiology |
| title_fullStr | The discounted reproductive number for epidemiology |
| title_full_unstemmed | The discounted reproductive number for epidemiology |
| title_short | The discounted reproductive number for epidemiology |
| title_sort | discounted reproductive number for epidemiology |
| topic | gametheory. ultimate proliferation rate reproductive number |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.377 |
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