Covid-19 predictions using a Gauss model, based on data from April 2

Janik Schuttler; Reinhard Schlickeiser; Frank Schlickeiser; Martin Kroger

The key of these behavior lies in the sigmoidal nature of saturating processes. Intuitively, we know that the cumulative number of cases for a wave of any pandemic must start from a constant (often 0), then increase exponentially and eventually saturate at a higher constant level. Functions that capture such a behavior, i.e. a smooth change from a lower constant to a higher constant over a finite duration, are called sigmoidal. The derivative of sigmoidal functions have a bell-shaped form, similar to a Gaussian function, but may be asymmetric in general. We here model the daily fatalities d, formally the derivative of the cumulative fatalities D. Since we expect cumulative cases D to be sigmoidal, from common-sense reasoning as argued above, this fixes the derivative, the daily fatalities d, to a bell-shaped form. Even though all pandemics thus give rise to bell-shaped d by this argument, the curve's parameters might differ, influenced mostly by policy, health system and culture. The predictive power of our model rests on the assumption that these influences are encoded already into the early data of casualties, combined with the assumption that the principal shape of all pandemics is fixed. This is of course an unjustified assumption or, if at all, justified only in a statistical sense when considering large number of trials. Why do we choose a symmetric bell-shaped form, the Gaussian function? We recognize that other models, such as Poisson functions that fade out slower after their maximum, might be more realistic. However, a symmetric function is the simplest model among all bell-shaped functions and works well enough to convey the idea of such models. Second, the times of greatest interest to policy makers are until the bell-curve's peak since once passed the health system should be able to cope.