A primer on stable parameter estimation and forecasting in epidemiology by a problem-oriented regularized least squares algorithm

Smirnova, Alexandra; Chowell, Gerardo

(1.2) which simplifies its theoretical and numerical study. However, the statistical analysis of the fitting accuracy for the original and generalized Richards models indicates that the generalized Richards model outperforms its original version for epidemics characterized by an early sub-exponential growth phase . For such outbreaks, the value of parameter p in (1.1) is less than 1 (0 < p < 1), and the reduction in the residual sum of squares appears to be statistically significant. Several mechanisms could give rise to initial sub-exponential growth in case incidence including (Chowell, Viboud, Hyman, & Simonsen, 2015; Viboud, Simonsen, & Chowell, 2015) : (i) spatially clustered contact structures (e.g., high clustering levels) (Chowell et al., 2015; Szendroi & Csanyi, 2004) ; (ii) early onset of population behavioral changes and control interventions (Chowell et al., 2015; Szendroi & Csanyi, 2004) ; and (iii) substantial heterogeneity in susceptibility and infectivity of the host population that introduces high local variability in the local reproduction number that fluctuates around the epidemic threshold at 1.0. The two limiting cases of the generalized Richards model are those in which p ¼ 0 (constant incidence growth) or p ¼ 1 (exponential growth) (Viboud et al., 2015) . Fig. 2 illustrates representative epidemic profiles, dC dt , that the generalized Richards model supports, as the deceleration of growth parameter, p, is varied. Overall, as parameter p increases, the epidemic profile shows faster growth that converges to exponential rate as p/1 while keeping the epidemic size, K, fixed. On the other hand, parameter a modulates the epidemic turning point (Fig. 2) , which occurs earlier as this parameter increases.