A practical generation interval-based approach to inferring the strength of epidemics from their speed

Sang Woo Park; David Champredon; Joshua S. Weitz; Jonathan Dushoff

where ρ =Ḡ/C = rḠmeasures how fast the epidemic is growing (on the time scale of the mean generation interval) -or, equivalently, the length of the mean generation interval (in units of the characteristic time of exponential growth). The longer the generation interval is compared to C, the higher the estimate of R (see Fig. 1 ). We then explore the behaviour of the gammaapproximated speed-strength relationship R gamma defined above (equivalent to the Tsallis "q-exponential", with q = 1 − κ [43] ): its shape determines how the estimate of R changes with the estimate of normalized generation length ρ. For small ρ, R gamma always looks like 1 + ρ, regardless of the shape parameter 1/κ, which determines the curvature: if 1/κ = 1, we get a straight 7 . CC-BY 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/312397 doi: bioRxiv preprint line, for 1/κ = 2 the curve is quadratic, and so on (see Fig. 2 ). For large values of 1/κ, R gamma converges toward exp(ρ).