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

In this section we present several simulations to illustrate the effects of the key parameters of the model. This will help the reader to understand where information able to put constrains on the parameters can be obtained from the data processed in section Bootstrapping method of data analysis. In order to quantify the random fluctuations due to the stochastic nature of the model, each simulation is performed 20 times to compute the median and the confidence intervals of the results. The first simulation corresponds to a duration of 80 days with a basic reproduction number R 0 = 2.0 from day 1 to day 39, and R 0 = 1. Figure 6 shows the results of the simulation for the time variations of N I (Fig. 6B) , and of ΣN s and N s (Fig. 6C) . The three curves together with N c are represented in a common semi-logarithmic graph in Figure 6A . The Natural logarithm is used throughout the present paper. As a starting point for the discussion, it can first be observed that the time variations of N I and N s significantly depart from a pure exponential pattern, particularly because of the presence of smooth bumps in the curves around day 55. These bumps can be better understood in the semi-logarithmic plot of Figure 6A where the N I and N s curves appear partly linear in two segments. The same linear segments are also visible in the N c curve. The presence of linear segment in the curves indicates an exponential time variation. In the N I curve (orange symbols), a first linear segment goes from day 1 until day 39 with slope β = 0.108. A second linear segment with slope β = 0.035 starts at day 50. A curved segment locates in between the two linear segments, from day 40 to day 50. The slopes β of the linear segments are related to the basic reproductive number through,