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

A common characteristic to all 3 models presented above, is the need of a quite large number Z I = 80 of initial infectious persons coupled with a large R 0 4 at the beginning of the epidemic spread. This large Z I could be explained either by the importation of a large number of infected persons or the presence of several super contaminators able to contaminate tens of persons during meetings in a short period of time (see (13, 14) for the effects of mass gathering). Let us remark that large R 0 are reported by others; for instance, Tang et al. report values as high as 6.47 for data from China. These authors mention that this high R 0 corresponds to data collected during a period of intensive social contacts (i.e. before the Chinese New Year). Mizumoto and Chowell report R 0 values as high as 10 for the case of Diamond Princess, and for the same data Rocklöv et al. find a maximum R 0 = 14.8 and a 8-fold reduction to R 0 = 1.78 during isolation and quarantine. Another characteristic of the model is the need to significantly reduce R 0 to fit the decelerating curvature of the ΣN I data curve (e.g. Fig. 2A ). This reduction is delayed by about 3 days with respect to the beginning of the containment and confirms an overall good respect of the social distancing rules by the population of Guadeloupe. Several French national media published articles stating that Guadeloupe was relativity spared from the disease (18) . Such a claim could have triggered a common sense reflex of protection applied through social distancing and usage of rules of hygiene. To fit the most recent ΣN I data, a low R 0 = 0.35 must be applied. If true, this would indicate that people of Guadeloupe continued to improve their social behaviour during the 3 weeks after the beginning of the containment. The models allows to get an estimate of the number of instantaneous infectious N I and cumulative recovered patients ΣN R . In absence of systematic detection of COVID-19 among the population, no N I data are available and the N I curve is actually indirectly constrained by the fit to the ΣN s and N c data and by the switching probabilities p s and p c . However, the values given to these probabilities fall in ranges widely recognised by the medical community and we may safely consider them sufficiently reliable to give credit to the modelled N I and ΣN R curves. A simple assessment may be done by dividing ΣN d by the observed number of deceased patients. On day 28 (April 7), this ratio equals 0.7%, a value slightly lower than the generally recognised ratio of 1 − 2% (19) . For the models discussed above, several thousands of persons have been infected and a large fraction of them have recovered and are supposed protected against another infection. However, these supposedly protected persons represent a relatively small part of the total population and the number of susceptible persons remains sufficiently large to ensure a restart of a second epidemic spread of the disease. This is shown in Figure 5 which represents a long-term simulation with model 1 as in Figure 2 but with an abrupt resetting of R 0 = 4.0 at day 70 (mid-May), about 2 months after the beginning of the containment. This corresponds to a situation of uncontrolled end of containment. Because of the existence of only several infectious cases, the spread of the virus proceed at a low-level during approximately 3 weeks (i.e. until day 90) before exponentially exploding again into a second epidemic crisis. These