A bioeconomic model was developed to support the long-term lockdown lift strategy for Toulouse, a French city with 475,000 inhabitants. The model consists of an epidemiologic compartmental model that mimics epidemic dynamics and an economic optimization model that accounts for both monetary impact (local gross domestic product (GDP) and medical care costs) and medical staff and citizen welfare. The bio-economic approach considers both demographic and socio-professional profiles of the inhabitants and is focused on the trade-offs between economic impact limitations and the welfare of different groups of citizens.
2.1 Epidemiologic compartmental model
We built a deterministic discrete age-structured model, considering the demographic and age profile share of the population (younger than 18 years old, adults and seniors) based on the work performed by Di Domenico et al. (29). The compartmental model is described in Figure 1. In brief, individuals are divided into susceptible, exposed, infectious, hospitalized, in intensive care units (ICUs), recovered, and deceased. A prodromic phase is considered before the appearance of symptoms. During this phase, individuals have a smaller transmission rate (Tr) with respect to symptomatic individuals. During the second step of the infectious phase, individuals may remain asymptomatic (Ia) or develop different degrees of severity of symptoms. Individuals may remain paucisymptomatic (Ips) or face mild (Ims) or severe (Iss) symptoms. Asymptomatic individuals (including children) have a smaller transmission rate (Tr) than symptomatic individuals. Children are assumed to become either asymptomatic or paucisymptomatic only and are considered to be as susceptible as adults. The recovery stage has been divided into recovery from an epidemiologic point of view (REp), meaning staying at home after the disease, and from an economic point of view (REc), meaning returning to work (with the same current rules at this time). After infection, a small part of the population (Ps = 10%) is considered to be susceptible again.
Three main populations were considered for the epidemiologic approach (young, adults and seniors), and the model was refined by adding the socio-professional characteristics of the adults to account for differential lockdown exit strategies on this subpopulation (Table 1). The categories “medical” and “essential” workers were created, representing 30% of the whole active population. Students and unemployed subpopulations were also created since their movement and contacts were expected to differ from other adult populations during the lockdown and lockdown lift (25, 26). Four other socio-professional categories were created (25) based on i) the impossibility of having at least partial remote work (denoted Fixed) and a simplification of the official socio-professional classification: lower supervisory and technical occupations (denoted Lower), intermediate occupations (denoted Intermediate),, and higher managerial, administrative and professional occupations (denoted Higher). Small employers and individual entrepreneurs were not a specific category since they fall into either the fixed or the intermediary category. Similarly, lower managerial, administrative and professional occupations were not distinguished from other lower occupation profiles and were included in the Lower category.
The biological model is based on the principle that contacts within and between the subpopulations are modulated during the lockdown and thereafter depend on the lockdown lift scenarios. The likelihood of becoming Exposed (Figure 1) consequently depends on the contact matrix and the transmission rate (i.e., probability of becoming Exposed if in contact with an Infectious person). The number of simulated contacts during lockdown and for each lockdown scenario were defined in relation to the percentage or activity released, as indicated in Equation 1:
ContactsPopi*Popi’,Lj: contract matrix for the scenario L j and the populations i and i’
CoefContact : ponderation of the initial contract matrix due to change in behaviour with time
ContactPopi*Popi’,Init : initial contract matrix for the populations i and i’
ActReleasePopi,Lj: percentage of activity released for scenario Lj and population i
2.2 Lockdown and lockdown lift scenarios
In the lockdown scenario (L0, Table 1), all subpopulations are locked (3% of released activity in terms of contacts) except medical and essential workers. This represents the policy implemented in France in phase 1, from March 18th to May 11th, 2020 (27). Schools were closed, and 70% of non-essential workers worked remotely.
In phase 2, starting May 11th, three sets of monitored lockdown lift strategies (L1-L5, L5-L10 and L11–15) were simulated (Table 1) and applied. For all scenarios, medical and essential workers remained unlocked. In scenarios L1 to L5, all non-active subpopulations remained locked, and the 4 populations with economic activities experienced partial or total lockdown lift. Scenarios L6 to L10 were defined similarly to L1 to L5 with all schools open and partial unlocking of unemployed and seniors. L11 to L15 represent the same situation as L6 to L10 with containment of contacts within categories (wc) or partial (half) containment of contacts within categories (hwc).. This means that lockdown lift is adjusted to allow activities for specific days of the week depending on the subpopulation, leading to strictly limited inter-sub-population contacts. A mixed strategy was adopted with half within category contacts, limiting half of the contact between subpopulations thanks to a population-week regulation system (precise rules defining the combinations of exit authorizations depending on socio-professional category). In addition to the monitored scenarios L0-L15, a total lockdown exit at the start of phase 2 (scenario L99) was considered.
To better match the observed measures in the field, the monitored lockdown lift of phase 2 was combined with various options. The lockdown lift was implemented abruptly on May 11th (O1) or progressively at 4 or 8 weeks (O2 and O3). Because scenarios L1 to L15 cannot be applied indefinitely due to their economic and societal impacts, a third phase was created, and 2 other options were defined (based on O3 rules) to capture the long-term dynamics. Option O34 planned a total lockdown 2 weeks after the end of hospital saturation or after the peak of hospitalization if no saturation occurred. The total lockdown exit was definitive for O34 and was transitory for O35 (mixed strategy of lockdown lift and re-lockdown). The starting date of phase 3 consequently depends on the lockdown lift scenario.
Figure 2 summarizes the 3 phases of the French situation and the corresponding simulated lockdown exit strategies.
2.3 Economic optimization model
Six economic scenarios (denoted E0 to E5) were considered (Table 2) for the 4 studied active populations locked down (Active_fixed, Active_lower, Active_intermediate and Active_higher). During lockdown, the percentage of productivity compared to the pre-lockdown period is considered to vary depending on the socio-professional category (E0). This decrease in productivity is an average for the whole lockdown period (phase 1) and the subpopulation and should not be compared to productivity of workers with partial home working before lockdown. During the monitored lockdown lift (phase 2), the percentage of productivity compared to the pre-lockdown period was considered to depend on the percentage of activity released, in accordance with the lockdown lift scenario for a given subpopulation, as indicated in Equation 2:
ProdPopi,Ek is the productivity permitted by the active population Pop i (Active_fixed, Active_lower, Active_intermediate and Active_higher) for the economic scenario Ek and the lockdown lift scenario Ll
ActEcoPopi,Ek is the percentage of economic activity for the economic scenario Ek
GDPPopi is the daily GDP for the population Popi
Equation 2 aims to reproduce the fact that partial lockdown may help to improve economic activity compared to strict lockdown and that very good performance can be achieved with partial lockdown for some socio-professional categories.
Optimization under constraint was performed on the minimal total cost for Cost Ek, Lj and hospitalization for the whole 300 or 600 d period. Economic risk was not accounted for. To combine the main key dimensions within the decision-making, the optimal solution that minimizes the overall economic impact for a given Tr was plotted considering 3 main constraints. Three levels of constraint were considered based on the quartile and median mortality rate observed between all the scenarios for a given option and a given Tr. The mortality criteria high, medium and low used for optimization correspond to no constraints on mortality, within the best half of the situation (lowest half mortality rate) and within the best quarter (lowest quartile mortality rate), respectively. The same type of rule was applied for the welfare criteria. The welfare criteria high, medium and low used for optimization correspond to within the best half or 75% of the number of person-days unlocked or no constraints on person-days unlocked, respectively. The criteria related to hospital saturation were defined by the duration of hospital saturation not to exceed or to the number of day-beds lacking for the whole period, with the criteria high meaning no constraints. The calculation of the total cost for each scenario and option allowed us to calculate the opportunity cost of choosing any combination of scenario and option compared to the scenario and option with the minimal cost for the whole period and given Tr.
2.4 Model parameterization
The number of contacts per person was defined within and between the 8 subpopulations, meaning de facto that contacts within and between the 3 epidemiologic populations (young, adults and seniors) were considered. Hospitalization and admission to the ICU for severe cases were identified from Toulouse hospital data (28) and adjusted for the analysed population. Hospitalization and ICU bed occupations were used to evaluate the capacity to welcome patients requiring these levels of care. The calibration of the compartmental model (Table 3) was performed similarly to Di Domenico et al. (29). At the beginning of the lockdown, other French areas were close to the hospital saturation level, and communication by the media raised peoples’ awareness of health risks. We consequently consider that people changed their behaviour dramatically for both the number of contacts during lockdown and Tr. As a consequence, the number of contacts within and between the subpopulations (Table 4) was based on previous publications (29, 30) and adjusted for the number of hospitalized and ICU patients during lockdown for the considered area. The simulated incidence of clinical cases was compared with the observed local incidence to appropriately adjust the number of contacts (Table 4). The value of Tr was likely to change with time during the studied period due to changes in rules, behaviours and protections availability, including masks. It was kept constant for a given simulation, and the values of 0.06, 0.10, 0.125, 0.20 and 0.25 were retained.
The assumptions on social distancing intervention made by (29) were kept. A 75% decrease in the number of contacts is expected if severe symptoms are observed in one individual. Five percent of adults stayed at home in the case of school closures, with the exception of the medical and essential activities subpopulations. Working from home was adopted by 6% of the active adult population before the lockdown. The isolation of positive cases when returning home was not considered as possible for phase 1, in accordance with the main observations during this phase. The number of beds available for hospitalization and ICU was 1,000 and 300, respectively (28). A higher number of patients hospitalized or in the ICU on a given day defined the saturation situation, which was associated with a three-fold higher mortality risk for people above the threshold. The price per day-bed was fixed to 500 € and 1,500 € for hospitalization and ICU, respectively (31).
The parameters of the six economic scenarios are reported in Table 2. The range of activity during lockdown compared to the pre-lockdown period was considered to vary between 0 (fixed) and 66%. This means, for instance, that the productivity of a home worker is 66% of his or her former productivity. A sensitivity analysis is permitted with scenarios E2 to E4, which attribute a fixed extra percentage of productivity, and in scenario E5 (limited productivity even if there is a high rate of lockdown lift).
Daily GDP was obtained as the yearly GDP per worker (€77,212 in 2018 for the Occitanie area (32)) and adjusted for each subpopulation due to variation in the official estimation of socioprofessional standard living incomes (26). The local standard living incomes were officially assessed as €18,870, €18,870, €24,520 and €33,090 for the socio-professional categories Active_low, Active_fixed, Active_intermediate and Active_high, respectively. The yearly GDP per worker for each socio-professional category was then divided by 200 days worked yearly (Table 2).