Fitting and Selection of Within-Host Models for SARS-CoV-2 Infection
The main question in model selection for longitudinal RT-qPCR data is whether improvements in fit justify the additional parameters of more complex within-host models. We compared a target-cell-limited model (TIV), an eclipse-phase extension (TEIV), and a fractional-order TIV using infection waves reconstructed from SARS-CoV-2 cycle-threshold (Ct) measurements in a National Basketball Association cohort. Each trajectory was fitted on the Ct scale by maximizing a right-censored Gaussian likelihood using hybrid global-local optimization. Model selection was based primarily on the small-sample corrected Akaike information criterion (AICc), computed from the censored likelihood; while robustness to the choice of information criterion was assessed using the Akaike information criterion (AIC) and Bayesian information criterion (BIC). Among 868 evaluable trajectories, the unpenalized likelihood ranking identified TEIV as the clear best-fitting model in 34.0% of cases, fr-TIV in 30.2%, and TIV in 3.3%; the remaining 32.5% were effectively tied. After accounting for model complexity, AICc clearly favored TIV in 97.8% of trajectories and fr-TIV in 0.5%, while 1.7% were effectively tied; TEIV was not a clear winner in any of the trajectories. Thus, for these short, sparsely sampled Ct-only trajectories, TIV provided the best-supported parsimonious effective description. This does not imply that eclipse-phase or memory-like dynamics are biologically absent, but rather that the simpler TIV model is favoured by standard information criteria for the limited information contained in these data.