The SARS-CoV-2 seroprevalence is the key factor for deconfinement in France.

A new virus, SARS-CoV-2, has spread world-wide since December 2019, probably affecting millions of people and killing thousands. Failure to anticipate the spread of the virus now seriously threatens many health systems. We have designed a model for predicting the evolution of the SARS-CoV-2 epidemic in France, which is based on seroprevalence and makes it possible to anticipate the deconfinement strategy.

Dear Editor,

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) emerged in Wuhan, China in December 2019 and spread largely by sustained human-to-human transmission.. The WHO declared the resulting disease a pandemic.. The virus, which causes severe respiratory illness in susceptible individuals, has spread so rapidly that it threatens to saturate health services, particularly their intensive care capacity. While this presently concerns mainly Italy, Spain, and France, other countries, such as the United States, may well succumb as it is difficult to predict how the infection will spread in the general population. A calibrated response to the epidemic must take into account the number of cases, including infected asymptomatic individuals, most of whom are not detected due to a lack of testing. The existing models for SARS-CoV-2 are based on published positive cases and do not take into account either people's age or any evolutive diffusion coefficient.

Our statistical model for predicting the spread of SARS-CoV-2 in France is based on a diffusion and transmission coefficient that varies with an individual's age, the likelihood of contagion, and two administration parameters (confinement and quarantine). We use models to measure how the dynamics of the SARS-CoV-2 infection is affected by these different factors and how to adapt the deconfinement strategy.

Consider the variables (S, P, Q, I). We define A as the age class variable:

On day n, for a given age class A,  S is the number of healthy people, is the number of undetected contagious carriers infected for i days (1 ≤ i ≤ N). Similarly, is the number of detected contagious carriers infected for i days (1 ≤ i ≤ N) on day n. D is the mortality rate per target age group. We assume that there is the same risk of virus-caused death at any stage of the infection. I is the number of people who are immunized or have died for a given age class A.

We define N as the number of days a person is contagious and α as the percentage of the population tested on day n. R 0 is the number of healthy people who a contagious person contacts and infects. We assume that the contagion coefficient varies over time and peaks when the virus load is maximal: 7 days after the start of infection. N is the total population at the start of the epidemic phase, c is the multiplier for the pace of the epidemic throughout the confinement (0 ≤ c ≤ 1), and q is the same multiplier during the quarantine period (0 ≤ q ≤ 1). c and q are equal to 1 when there is no confinement or quarantine phase.

And

N is given by:

On the transition from day n to day , we have:

(no quarantine the first day, you need the test results)

The model is a discretized version of a Susceptible Infectious and Recovered (SIR)-type model

We have chosen .

We estimated the initial model settings using data published by Johns Hopkins University for France and data collected by the Toulouse Virology Laboratory.

Without containment the prevalence of infection is 8.3% on March 17 and 97.5% on May 11 (Fig. 1 a). Containment began on March 17 in France and is scheduled to end on May 11. Fig. 1b, c, d, e showed predictions of new cases per day depending on the SARS-CoV-2 seroprevalence before and after the containment phase. Fig. 1b indicates that the seroprevalence before March 17 was 8.3%, and 17.5% after containment. There was an infection rebound on May 29. However, if the seroprevalence at the beginning of containment was 15.44% (Fig. 1c), the seroprevalence on May 11 would be 29.1% and there was an infection rebound. If 31.95% of the population contracted SARS-CoV-2 before March 17 (Fig. 1d), then 49% would be infected, immunized or dead on May 11 and the rebound would be smaller. Lastly, when the seroprevalence before containment was 40.05% (Fig. 1e) there was almost no rebound. The seroprevalence on May 11 was 56.7%. This is why we conclude that the seroprevalence after the containment phase should be between 49% and 56% in order to avoid a rebound.

Fig. 1

Dynamics of SARS-CoV-2 infection per day from January 22, 2020 to March 30, 2021 according to the seroprevalence before and after containment. a: no containment, b: seroprevalence before 8.3% and after 17.5%, c: seroprevalence before 15.4% and after 29.1%, d: seroprevalence before 31.9% and after 49%, e: seroprevalence before 40% and after 56.7%.

In Fig. 2 a we assumed that the containment did not end completely on May 11, but was abolished gradually from May 11 to June 30, to be totally relaxed from July, 1. We considered that this progressive phase consisted of a relaxation of 50% of the restrictive containment measures. Seroprevalence on June 30 was 31.7% and leaded to a rebound at the end of July. The ideal situation is that shown in Fig. 2b, with a progressive deconfinement phase lasting longer, from May 11 to October 25, at which time seroprevalence reached 51.2%. Relaxation of all restrictions after this date did not lead to a rebound.

Fig. 2

Progressive deconfinement strategies and their impact on infection rebound. a: complete removal of containment on June 30, b: complete removal of containment on October 25.

Our data indicate that seroprevalence must reach approximately 50% after total deconfinement on May 11 or a gradual exit phase over several months starting on May 11 if an infection rebound is to be avoided (Fig. 1d, e and Fig. 2b). While the seroprevalence in France before the confinement phase was not measured (March 17) it is probably possible to determine the proportion of the population who came into contact with the virus at the end of the confinement phase. This should provide a basis for estimating the size of any infection rebound. It remains highly unlikely that the case shown in Fig. 1e, with about 50% of seroprevalence, will apply. It will therefore be a question of adapting the deconfinement strategy to reach 50% seroprevalence gradually and so avoid a rebound. This may require wearing masks for several months while waiting for vaccine.

The predictive power of the model may be hampered by the way in which casualties are measured, as can the strategy used to detect the number of positive cases. Postprocessing the data to handle such biases will be the topic of future reports.