The discounted reproductive number for epidemiology - Timothy C. Reluga; Jan Medlock; Alison Galvani (Mathematical Biosciences and Engineering)
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.