During confinement, the reproduction number was estimated at 0.53 [0.49, 0.58] (95% confidence interval) using the next-generation matrix method whereas before confinement it was estimated at 3 [2.8, 3.2] (previous work).
Under the assumption of an opening of nursery and elementary schools on May 11, the model projects on August 1 a number of confirmed cases 2 to 3.2 times higher than that predicted in the case of continued closure of schools . The epidemic would however remain under control, with a maximum occupancy of 65 [54.76] % of intensive care units. The epidemic situation would remain under control with an additional opening of colleges and high schools on June 8.
On all the previous scenarios and for all the infectivity parameters of children, the maximum increase in cases would be 4.5 to 5.5 times greater at the beginning of the summer compared to the reference scenario, resulting in a maximum occupancy of intensive care units of 77 [62 - 87]% to 138 [118 - 159]% depending on the infectivity of the children.
For a reopening of all schools on May 11, the model projects a second wave similar to the first. However, this situation could be controlled via a reception protocol limited to 50% of students. The maximum occupancy of the intensive care services would then be 61 [50 - 69]%.
For each of the scenarios, the impact of the reopening would only be visible after a certain delay. On all the scenarios allowing the control of the epidemic, the maximum of predicted cases per day is 1000. Finally, it is important to note that results are strongly dependent on the rate of isolation of the contaminated cases. Sensitivity studies show that this parameter reduced to 25% instead of 50% gives rise to a second wave for all scenarios, even the reference one.
This study combines several strengths, addressing questions still relevant today regarding the impact of reopening schools and age-related differences in susceptibility and infectivity. Using contact matrices, the authors model and compare several protocols for reopening schools. These projections are made under several assumptions of children's infectivity. Finally, the model integrates the stages of hospitalization, making it possible to predict the impact of various potential government interventions on the occupation of hospital services.
Regarding the choice of parameter values, the sources of the literature are all specified but the learning or calibration methods of certain parameters are not detailed. Additionally, code for model calibration and simulations is not shared.
The results are amply detailed and illustrated. Some sensitivity studies are done, concerning the number of reproductions and the percentage of tests and isolation of cases.
- Model: A stochastic compartmental model was used to simulate the spread of the virus. This was a SEIRD model incorporating additional compartments for hospitalizations and intensive care admissions. Two stages were also distinguished within infected individuals: a first prodromal phase followed by a phase of development of the disease which can be broken down into different possible profiles (asymptomatic, paucisymptomatic, mild symptoms, severe symptoms).
- Calibration of the model parameters: The parameters related to hospitalization were learned or calibrated on hospital data from the APHP before confinement and over the period from April 8 to 28. The durations within the compartments relating to hospitalization were modeled by gamma or exponential laws. Other parameters were issued from the literature or from the Italian Higher Institute of Health.
- Segmentation by age and modeling of the different strategies: The model was segmented by age groups: 0 to 11 years (kindergarten and elementary), 11 to 19 years (middle and high school), 19 to 65 (working population) and 65 years and over (seniors). The contact rates between different age groups depending on the meeting place (home, work, school, etc.) were given by contact matrices estimated in France in 2012 (Béraud et al, 2015). The different scenarios can be directly modeled by modifying contact rates according to age group and meeting place.
Four types of scenarios were tested:
- reference scenario (containment, testing and isolation measures for cases, maintaining the closure of schools)
- reopening of nursery and elementary schools on May 11
- reopening of nursery and elementary schools on May 11 and reopening of middle and high schools on June 9
- reopening of all schools on May 11
For each of the school reopening scenarios, four protocols were tested (complete and immediate, complete and progressive, partial and immediate, partial and progressive).
From the literature, several hypotheses were made concerning the relative susceptibility and infectivity of children and adolescents compared to adults.
Children were considered to be as susceptible to the virus as adults. However, they can only be asymptomatic or pauci-symptomatic.
Adolescents had a reduced infectivity equivalent to that of adults in the absence of symptoms.
For children, several values of relative infectivity were tested, making it possible to explore the hypothesis according to which they are a weaker source of infection. The model was simulated over 250 stochastic iterations for each scenario.
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