Speed and strength of an epidemic intervention

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.