Application of Carleman approximants for the estimation of epidemic parameters from incidence data time-series

We have analyzed the possibility of estimating epidemiological parameters from daily infection incidence data. In particular, we have focused on the determination of the instantaneous reproduction number, the contagion period and the duration of the infectious period using only the reported incidence time-series information. We have developed a data-driven method based on the instantaneous mapping of the infection incidence data on the simplest (two parameter) SIR model, along the progression of an epidemy. The mapping is carried out via Carleman linearization of the non-linear model equations. We concluded that the daily infection incidence series on its own does not carry enough information to provide estimates for the above time scales and hence additional measurements and/or hypotheses must be considered. In contrast, the prevalence time-series does allow for accurate estimates. For the case in which the characteristic infectious period is available, a new algebraic formula for the instantaneous reproduction number has been derived.