Modeling the affect of nationwide and regional lockdowns on the 2020 spring wave of COVID-19 in France

Transmission mannequin

We used a deterministic, age-structured, compartmental epidemic mannequin primarily based on demographic and age profile of the inhabitants of the 13 administrative areas of metropolitan France (Supplementary Determine S11). We thought of that people have been vulnerable (S), after which probably uncovered to the virus however not infectious (E). As noticed in scientific follow, we set kids and adolescents to be much less vulnerable to an infection than different age teams²². Uncovered people keep of their compartment for a median of two.72 days²³ earlier than transferring to both asymptomatic (A_s) or pre-symptomatic (I_ps) compartment in accordance with noticed threat of being asymptomatic²². We thought of that asymptomatic people have been 45% much less infectious than pre-symptomatic people have been²⁴ and we assumed they stayed within the compartment for a median of 10.91 days earlier than transferring to the eliminated compartment (R) of sufferers which might be cured or lifeless from COVID-19. Pre-symptomatic people will change into contaminated symptomatic (I_s) after a median period of two.38 days. This alternative of parameters gave a imply incubation interval of 5.1 days¹, inside round 2 days of pre-symptomatic transmissions. Then they change into after a median of 5 days (assumption) both hospitalized (I_h) or stay inside the group (I_nh) in accordance with age-dependent hospitalization dangers^25,26 adjusted to use solely to scientific circumstances²². We assumed that hospitalized people have been no extra infectious due to their hospitalization whereas non-hospitalized retains spreading the illness with the identical depth as symptomatic people. We assumed the common period in I_nh compartment was 3.53 days to match the whole period within the asymptomatic compartment. Lastly, each hospitalized and non-hospitalized people moved to the eliminated compartment. Equations of the mannequin are supplied as supplementary materials.

To match the epidemic dynamics and reproduce the Erlang distributions of durations in every compartment of the transmission mannequin, we subdivided every compartments having a task within the an infection course of into sub-compartments. This subdivision had no affect on the imply period spent in every compartment. A sensitivity evaluation testing a number of mixtures revealed that 10 sub-compartments in every compartment permitted to strategy the noticed dynamics of the epidemic (Supplementary Determine S12).

Mannequin parametrization

The inhabitants was divided into 17 age teams: 16 age-band of 5 years from 0 to 80 years, and a final group for folks aged 80 years and older. The inhabitants construction of every area was inferred from hospital catchment areas from 2016 and 2017 census knowledge supplied by the French Nationwide Institute of Statistics and Financial Research (Insee)^27,28. To simulate age and location-dependent mixing, we used inter-individual contacts matrices for the French inhabitants estimated by Prem et al.²⁹.

We retrieved publicly accessible epidemiological regional knowledge associated to the COVID-19 epidemic in metropolitan France gathered by the French Nationwide Public Well being Company (SpF-‘Santé publique France’)⁷ each day variety of hospital admissions (basic and intensive care unit (ICU) wards), each day variety of ICU admissions, each day variety of occupied ICU beds, and each day variety of deaths in hospitals (deaths in nursing properties and at residence weren’t thought of). All these epidemiological knowledge have been corrected for reporting delays following the identical process as Salje et al.⁴. We additionally obtained knowledge on the utmost ICU beds capability per French area from the ‘Course de la Recherche, des Études, de l’Évaluation et des Statistiques’ (Drees) relating to the scenario through the March 2020 lockdown (private communication) (Supplementary Desk S3).

Estimation of hospital-related outcomes

Primarily based on the estimated variety of new contaminated hospitalized circumstances per day supplied by our epidemiological mannequin, we inferred outcomes associated to hospital necessities, particularly ICU admissions, ICU occupied beds, and deaths.

We divided the hospital settings in two elements: basic ward and ICU ward (Supplementary Determine S13). The epidemiological transmission mannequin estimated the each day variety of new hospitalized circumstances resulting from COVID-19 an infection, whatever the ward (i.e. ICU and basic wards). As soon as admitted to hospital, contaminated circumstances might both stay within the basic ward till the tip of their keep or go into ICU, in the event that they turned extreme circumstances. We assumed that circumstances admitted in ICU entered ICU ward the identical day as they have been admitted in hospital (pre-ICU size of keep equal to 0 day). As soon as in ICU, circumstances might both die or keep in ICU till their discharge to basic ward. Instances generally ward might both die or keep generally ward till their discharge to residence.

We used age-dependent ICU admission dangers for hospitalized sufferers estimated by Salje et al.⁴ We additionally used age-specific lengths of keep in ICU to estimate the variety of occupied ICU beds³⁰. We estimated the variety of deaths utilizing hospital and ICU loss of life dangers estimated by the Drees on all of the hospitalized circumstances of the primary wave of epidemic in France (March-June 2020)³⁰. Deaths have been delayed in time utilizing the time from hospital or ICU admission to loss of life³⁰. Lengths of keep generally ward earlier than discharge, lengths of keep generally ward earlier than loss of life and post-ICU lengths of keep generally ward weren’t used as we didn’t estimated the whole variety of hospital beds wanted. This had no affect on the outcomes supplied by the mannequin.

We additionally estimated the variety of life years and quality-adjusted life years (QALY) misplaced for every loss of life utilizing life tables supplied by INSEE for 2012–2016³¹ and utility measures of every age-group in France³².

Statistical framework

We estimated region-specific mannequin parameters by most chance in a two-step course of utilizing the bbmle R bundle³³. First, on the interval stretching from March 14 to Could 10, 2020, similar to the evolution of the epidemic till the tip of the nationwide lockdown, we estimated the worth of the transmission parameter β, governing the worth of R₀, the preliminary state in every compartment per age group on March 1, 2020 and the consequences of the nationwide lockdown. The latter was estimated by means of a transmission discount parameter, hereafter referred to as ({c}_{beta }), and multiplied the transmission parameter (and thus contact matrices) to breed the a number of mitigation measures carried out and their penalties on the regional propagation. We collectively estimated these parameters by becoming the each day de-seasonalized time sequence of hospital admissions (hereafter denoted Hosp) utilizing the chance ({L}_{beta }) outlined in Eq. (1).

the place NBin(.|X) is a unfavorable binomial distribution of imply X and overdispersion ({X}^{delta }), (delta) being a parameter particular to every area to be estimated. Confidence intervals of those two parameters have been estimated utilizing chance profiling strategies³³.

In a second step, we collectively estimated three regional coefficients adjusting age-specific dangers of ICU admissions, threat of deaths and lengths of keep in ICU (together with ICU stays resulting in loss of life). They have been estimated by concurrently becoming the time sequence of ICU admissions (hereafter denoted ICU), deaths (each smoothed utilizing 7-day centered transferring common) and occupied ICU beds (hereafter denoted BedICU) from March 14 to Could 10, 2020 utilizing the chance ({L}_{ICU-deaths}) outlined in Eq. (2).

the place NBin(.|X) is a unfavorable binomial distribution of imply X and overdispersion ({X}^{delta }), (delta) being a parameter estimated for every area.

Evaluation of nationwide and regional lockdowns

For every area, we estimated the copy quantity earlier than the lockdown (R_prelockdown), and after its implementation (R_lockdown). Then, as a way to simulate a regional lockdown, we used the R_prelockdown as much as the beginning date of the measure; and the R_lockdown estimated within the area after that date. We assumed that the transmission fee remained fixed till July 1. We additionally assumed that the epidemic dynamic was pushed by native behaviour inside areas and that interactions between areas had no affect on native copy numbers.

We simulated nationwide lockdowns beginning on all dates from March 10 to March 31, thus exploring different dates of begin past the precise date of March 17. We then simulated asynchronous regional lockdowns, through which every area may very well be locked down independently of different areas, on completely different dates. We thought of the next epidemic thresholds as beginning dates of regional lockdowns: both (1) the date on which the estimated incidence of hospital admissions within the area reached the extent of essentially the most affected area through the first wave (i.e. Grand-Est, right here referred to as GES threshold), or (2) the final date on which a lockdown would permit the area to remain under its ICU capability restrict (right here referred to as ICU capability threshold).

Outcomes

For every simulation, we computed on the nationwide and regional ranges the cumulative numbers of hospital and ICU admissions, most occupied ICU beds, deaths, life years and quality-adjusted life years (QALY) misplaced between March 1 and July 1 and computed the relative change in comparison with the outcomes obtained when the actual lockdown date was used. The transmission mannequin was carried out in C++. Information assortment, knowledge administration, simulations, outcomes evaluation and reporting have been carried out utilizing R³⁴.

State of affairs with a slower epidemic development

To raised perceive how the copy quantity have an effect on the estimated affect of the lockdown, we analysed eventualities the place R_prelockdown is within the vary 1.1–1.5. This corresponds to the copy numbers noticed in France at first of 2021. On this evaluation, we saved the beforehand estimated R_lockdown for every area through the lockdown.