Prediction of the time evolution of the COVID-19 disease in Guadeloupe with a stochastic evolutionary model

MERIEM ALLALI; PATRICK PORTECOP; MICHEL CARLES; DOMINIQUE GIBERT

We now turn to the case of the ΣN s curve (green circles in Fig. 6A ) which is particularly important because it generally corresponds to the available data. Contrarily to the instantaneous quantities N I and N s which give the number of either "I" or "s" patient at a given time, ΣN s is a cumulative quantity which gives the total number of patients who passed by stage "s" anytime before present. We emphasise that this quantity is NOT the integral of N s and, as a consequence, the slopes of the linear segments present in the ΣN s curve are not simply related to those of the N s curve. Indeed, a careful examination of the ΣN s reveals that the segments are not strictly linear. At the beginning of the process, we have ΣN s = N s until the end of the time periods where first "s" patients begin to switch either to the state "R" or "c". At that time, the two curves begin to diverge. The slopes of the linear segments in ΣN s are always slightly larger than the slopes of N s and the formula 2 and 3 are no more exact for the ΣN s case. Indeed, the R 0 values derived for ΣN s in the example (upper right part of Fig. 6 ) are significantly biased, and to obtain reliable R 0 estimates, it is necessary to use data at the very end of the process, in the narrow time-window comprised between the end of the onset period and the beginning of the switching from "s" to "c". The size of the confidence intervals appears constant in the semi-logarithmic plots (Fig. 6A ). This is typical of a multiplicative noise where the amplitude of the statistical fluctuations is proportional to the data amplitude as can be checked in Figure 6B ,D.