Quantifying Inaccuracies in Modeling COVID-19 Pandemic within a Continuous Time Picture

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 <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20188755v1_inline1.gif"/> </alternatives> </inline-formula> obtained within the continuous time representation is systematically shifted backwards in time with respect to the position <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20188755v1_inline2.gif"/> </alternatives> </inline-formula> predicted within the discrete time representation. Rather counterintuitively, the magnitude of this temporal shift <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20188755v1_inline3.gif"/> </alternatives> </inline-formula> 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.