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 Tc1/2 obtained within the continuous time representation is systematically shifted backwards in time with respect to the position Td1/2 predicted within the discrete time representation. Rather counterintuitively, the magnitude of this temporal shift τ ≡ Tc1/2 − Td1/2 < 0 is basically insensitive to changes in infection rate κ. For a broad range of κ values deduced from COVID-19 data at extreme situations (exponential growth in time and complete lockdown), we found a rather robust estimate τ ≈ -2.65 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.
A Continuous Time Representation of smFRET for the Extraction of Rapid Kinetics
