Speed and strength of an epidemic intervention

Jonathan Dushoff; Sang Woo Park

Though there is a clear intuition for why both strengths increase as early transmission goes down, the speed paradigm provides insight into why these two increases are so close to parallel. The estimated epidemic speed depends only on the observed growth rate -it does not change if we change our assumption about the proportion of early transmission. For the test-and-treat intervention, the effective epidemic speed also stays relatively constant (Fig. 4D) , in part because we have (plausibly) assumed that hazard stays relatively constant for a few key months, and in part because the backward generation-interval distributions for different scenarios are relatively similar. The intervention speed increases slightly as proportion of early transmission increases because the subpopulation that the intervention fails to reach become relatively more important if late transmission is more important. Thus, the speed paradigm provides an intuitive underpinning for the originally surprising result of Eaton and Hallett (2014) : the effectiveness of test-and-treat interventions should not depend much on the proportion of early transmission. 7 . CC-BY-ND 4.0 International license author/funder. It is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.03.02.974048 doi: bioRxiv preprint C q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q (12)) assuming 23% early transmission. (D) The estimated amount of early transmission has little effect on the effective speed of intervention, and none on the speed of the epidemic estimated from incidence data. Circles indicate the baseline scenario. Test-and-treat intervention is modeled phenomenologically: L test (τ ) = exp ( τ 0 h test (σ)dσ) and h test (τ ) = h max (1 − exp(−Kf (τ ))), where f (τ ) is a gamma probability density function with a mean of 1 year and a shape parameter of 2, K = 4/ max(f (τ )), and h max = 2 year −1 .