-
Abstract
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.
Mathematics Subject Classification: Primary: 92D15, 92D25; Secondary: 91A22, 91A40.
\begin{equation} \\ \end{equation}
-
Access History
-