  Typically, mathematical simulation studies on COVID-19 pandemic forecasting
are based on deterministic differential equations which assume that both the
number ($n$) of individuals in various epidemiological classes and the time
($t$) on which they depend are quantities that vary continuous. This picture
contrasts with the discrete representation of $n$ and $t$ underlying the real
epidemiological data reported in terms daily numbers of infection cases, for
which a description based on finite difference equations would be more
adequate. Adopting a logistic growth framework, in this paper we present a
quantitative analysis of the errors introduced by the continuous time
description. This analysis reveals that, although the height of the
epidemiological curve maximum is essentially unaffected, the position
$T_{1/2}^{c}$ obtained within the continuous time representation is
systematically shifted backwards in time with respect to the position
$T_{1/2}^{d}$ predicted within the discrete time representation. Rather
counterintuitively, the magnitude of this temporal shift $\tau \equiv
T_{1/2}^{c} - T_{1/2}^{d} < 0$ is basically insensitive to changes in infection
rate $\kappa$. For a broad range of $\kappa$ values deduced from COVID-19 data
at extreme situations (exponential growth in time and complete lockdown), we
found a rather robust estimate $\tau \simeq -2.65\,\mbox{day}^{-1}$. Being
obtained without any particular assumption, the present mathematical results
apply to logistic growth in general without any limitation to a specific real
system.
