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Optimistic scenarios, pessimistic scenarios, predictions: mathematical modeling is at the heart of the discussions of deconfinement in time of Covid-19. How are these models developed and used? To study the spread of Covid-19, several research teams have chosen to use so-called "compartmental" models. In these models, the population is divided into separate groups, called compartments. Depending on the purpose of the study, the nature and number of these compartments may change. The team of Marc Brisson, a full professor at Laval University and director of the Research Group in Mathematical Modeling and the Health Economics of Infectious Diseases, chose to divide the population into six large compartments. These respectively represent people susceptible to catching the disease, those exposed to it, those who are asymptomatic infectious, those who are symptomatic infectious, those who have recovered and finally those who have died.
The model describes the number of people who are moved from one compartment to another, using equations based on entry and exit rates, for example the death and recovery rates in the case of the "infectious" compartment. " Parameters, estimates of which can be found in the literature, describe these entry and exit rates. What makes the work of Marc Brisson and his team remarkable is that he did not limit himself to using a single estimate for each parameter, but rather chose to represent these by uniform distributions between the maximum values and minimum values. They were thus able to perform simulations on hundreds of millions of different combinations of possible values. The 500 combinations that best represent the current data for the Quebec population were selected and then made predictions. According to a May 28 report, 90% of the model's predictions show an increase in hospitalizations and deaths according to a scenario of weak adherence to distancing measures. Predictions are also divided in the case of a strong agreement between decrease and slow increase in hospitalizations and deaths. A mathematical model is always an imperfect representation of a complex phenomenon. These models do not hold the truth, but allow the testing of different scenarios that may possibly help contain the epidemic.