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

Lorenzo Pellis; Francesca Scarabel; Helena B Stage; Christopher E Overton; Lauren H K Chappell; Katrina A Lythgoe; Elizabeth Fearon; Emma Bennett; Jacob Curran-Sebastian; Rajenki Das; Martyn Fyles; Hugo Lewkowicz; Xiaoxi Pang; Bindu Vekaria; Luke Webb; Thomas A House; Ian Hall

To allow, in semi-parametric manner, time variation in growth rates we adapt a generalised additive model (GAM) where I ∝ e s(t) for some smoother s(t). In particular, we use a quasi-Poisson family with canonical link and a thin-plate spline as implemented in the R package mgcv [45, 46 ] . The instantaneous local growth rate is then the time derivative of the smootherṡ(t) and an instantaneous doubling time calculated as t D = ln(2)/ṡ(t). Potential issues with the GAM approach include that extrapolation outside of the data range (and hence forecasting epidemic trend) is not sensible, and that there may be boundary effects from the choice of smoother. However, this approach has the major advantage that it allows for time-varying estimates of doubling time and thereby implicitly allows for missing explanatory information.