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 most recent evolution of the pandemic COVID-19 disease in Western Europe indicates that this region is, together with the United States, the new centre of the pandemic spread (e.g. (1) and other reports issued by the World Health Organization). Italy and Spain are confronted with large outbreaks of SARS-CoV-2 infection. In France, the rate of new infections daily increases and measures have already been taken to increase the intensive care capacity of the main hospitals of the country. Also, in order to face with the strong heterogeneity of case number among the different regions in France, medevacs (either by air or railway) have been undertaken to optimally redistribute the most critical patients in the country's intensive care facilities. In this context, the situation of remote French territories like Guadeloupe is particularly critical since, although possible, medevacs should be anticipated with a longer delay because of the distance and the duration of the travels. Numerical models of the spread of epidemic diseases may be of some help to anticipate the evolution of the situation in a near-future of several weeks and, eventually, may reveal a likely disruption of the local intensive care capacity. In short, mathematical models may be ranked in two main categories, namely semi-analytical models and numerical stochastic and Monte Carlo models (see (2) for a review). In the former category, the spread of the disease is modelled by a set of coupled differential equations that account for the most important characteristics of the disease. This approach is largely followed (3) (4) (5) . The second category of models is, in some sense, more straightforward and relies on network models to explicitly considers the individuals constituting the population. Such an approach offers a great versatility to tackle with complicated features, like social interaction matrices, that are difficult to introduce in semi-analytical models. The main drawback of numerical stochastic models is their computer-intensive demand that, for large populations, necessitates the use of multi-scale or coarsegrained algorithms. Thanks to the moderate size of the population of Guadeloupe, no such difficulties are encountered and a straightforward approach is possible.