Speed and strength of an epidemic intervention

Abstract

An epidemic can be characterized by its speed (i.e., the exponential growth rate r) and strength (i.e., the reproductive number R). Disease modelers have historically placed much more emphasis on strength, in part because the effectiveness of an intervention strategy is typically evaluated on this scale. Here, we develop a mathematical framework for this classic, strength-based paradigm and show that there is a corresponding speed-based paradigm which can provide complementary insights. In particular, we note that r = 0 is a threshold for disease spread, just like R = 1, and show that we can measure the speed and strength of an intervention on the same scale as the speed and strength of an epidemic, respectively. We argue that, just as the strength-based paradigm provides the clearest insight into certain questions, the speed-based paradigm provides the clearest view in other cases. As an example, we show that evaluating the prospects of "test-and-treat" interventions against the human immunodeficiency virus (HIV) can be done more clearly on the speed than strength scale, given uncertainty in the proportion of HIV spread that happens early in the course of infection. We suggest that disease modelers should avoid over-emphasizing the reproductive number at the expense of the exponential growth rate, but instead look at these as complementary measures.

Challenges in control of COVID-19: short doubling time and long delay to effect of interventions

“…However, scientific results should not be summarized solely as R 0 estimates, and policy decisions should not rely exclusively on R 0 as a measure of epidemic spread. First, R 0 lacks temporal information related to the speed of epidemic growth, and hence the optimal timing of interventions [ 11 , 27 ]. Second, estimates of R 0 can vary considerably—and in particular do so for COVID-19—not only as a reflection of genuine differences in geography and settings [ 11 ], but also because of how they are calculated: R 0 is typically indirectly derived through mathematical models, with values varying depending on model structure and estimates of, or assumptions on, parameter values (e.g.…”

Challenges in control of COVID-19: short doubling times and long delay to effect of interventions

“…Nevertheless, over-reliance on R 0 should be avoided. First, R 0 lacks temporal information related to the speed of epidemic growth, and hence the optimal timing of interventions (20, 21). Second, estimates of R 0 can vary considerably – and in particular do so for COVID-19 – as a reflection of both genuine differences in geography and settings, but also how it is calculated: R 0 is typically indirectly derived through mathematical models, with values varying depending on model structure and estimates of (or assumptions on) parameter values, even when the same data are used for model fits.…”

Are epidemic growth rates more informative than reproduction numbers?

“…is the author/funder, who has (which was not certified by peer review) copyright holder for this preprint The this version posted April 20, 2021. ; https://doi.org/10.1101/2021.04.15.21255565 doi: medRxiv preprint of its apparent independence from modelling assumptions and its explicit consideration of the epidemic speed (i.e. it more naturally includes temporal information) (Pellis et al, 2020;Dushoff and Park, 2021).…”