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

The technical details of the model are explained in the appendix Stochastic Monte Carlo model, and we here recall its main characteristics. A flowchart of the model is shown in Figure 1 . As stated above, all individuals forming the population are considered as nodes in a fully connected network where everyone is able to meat anyone. By using social contact matrices, this full connection could be modified to account for demographic and social heterogeneity. Also, we have not considered the age-dependence of the COVID-19 effects. Each individual of the network may, temporarily or definitely, be in the following state ( Fig. 1) : non-infected, infected with minor symptoms ("infectious"), infected with severe symptoms ("severe"), infected critical ("critical"), dead or recovered. In the vocabulary of epidemic modelling, non-infected correspond to the so-called "Susceptibles" and minor infected are "Infectious". In our model, both the severe and critical infected are not considered as infectious because they are isolated in hospital facilities and unable to significantly contaminate others. Although this is statistically justified in our model, actually this assumption is contradicted by the sad death of several French medics. According to the classical nomenclature, our model is a SIscRd model where the lowercase "sc" indicate the transient and non-contaminating nature of these states. To the best of our knowledge at the time of writing this paper, it does not seem that recovered "R" patients are able to again become infectious "I" (6). The deceased "d" patients may remain infectious several days (7) and we assume that they are safely isolated to prevent any contamination. 1 . Flowchart of the stochastic modelling procedure. In the general case, a susceptible non-infected person S1 becomes infected. This new infected I may contaminate a number R0 of other susceptibles (here S2 and S3) during his infected period T I (red line) which may run beyond the recovery period ∆T I (in yellow). During the sub-period δTs (shaded rectangle), the infectious "I" may switch to state "severe" with a probability ps. If the patient remains in state "I" until the end of the recovery period ∆T I , he becomes definitively recovered "R". Instead, if the patient switches to state "s", he may either recover at the end of the recovery period ∆Ts or switch with a probability pc to state critical "c" during the switching period δTc. The same procedure applies to state critical "c".