# Barrier Gesture Relaxation during Vaccination Campaign in France: Modelling Impact of Waning Immunity

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model

_{im}, E

^{k}

_{jm}, I

_{jm}, and V

^{l}

_{im}to denote the number of susceptible, exposed, infectious, and vaccinated individuals in each age group m (1 ≤ m ≤ 16), where i (1 ≤ i ≤ 4) denotes immune status, j (2 ≤ j ≤ 4) denotes symptom severity, k (1 ≤ k ≤ 3) represents stages in the exposed class, and l (1 ≤ l ≤ 2) denotes the number of vaccine doses that individuals have received.

_{1}), somewhat immune (S

_{2}), moderately immune (S

_{3}), and fully resistant to infection (S

_{4})); three infectious states with mild (I

_{2}), moderate (I

_{3}), and severe (I

_{4}) symptoms (i.e., infections requiring at least one medical consultation); and three infected but not-yet-infectious states (E

^{k}

_{j}, j = 2,3,4, k = 1,2,3). It is assumed that individuals of higher immune status are less susceptible to infection than those of lower status. Co-morbidity statuses by age [35] determine the probability of mild, moderate, and severe symptoms for each age group. Immunity develops after infection. It is assumed that people with mild, moderate, and severe symptoms move to immune classes S

_{2}, S

_{3,}and S

_{4}, respectively, upon recovery (i.e., the severity of symptoms is proportional to neutralizing immunity development [14,36,37,38]). Vaccination is implemented into the model using a two-dose structure, where compartments V

^{1}

_{i}and V

^{2}

_{i}denote those with one and two doses, respectively, where i is the level of susceptibility. It is assumed that two doses of the vaccine, or one dose of the vaccine administered to individuals in immune states S

_{3}and S

_{4}, provide the same level of immunity or protection from infection as S

_{4}; i.e., full resistance to infection. Additionally, it is assumed that one dose of the vaccine given to individuals in S

_{1}and S

_{2}provides protection similar to states S

_{2}and S

_{3}, respectively, where protective efficacies against infection and/or severe disease decrease with a lower level of immunity. Finally, it is assumed that the immunity gained from infection or vaccination wanes over time (Figure 1, black lines).

#### 2.2. Parameters

_{2}) or moderately immune (S

_{3}) corresponds respectively to 1/3 and 2/3 of that of an individual fully susceptible (S

_{1}). Infectivity (β) is assumed to vary by the severity of the disease and is chosen to produce a basic reproduction number, R0, equal to 2.9 [4] using the Next Generation Matrix method [48]. By immunity status, we assume that the infectivity of individuals with mild (I

_{2}) or severe (I

_{4}) infections is 0.5 and 0.1 times the infectivity of moderate infections (I

_{3}). Indeed, people with milder symptoms are expected to have lower infectivity [39]. Simultaneously, more severe disease outcomes are expected to induce behavioral changes that lower infectivity, such as limiting mobility,. Infectivity is considered in the calculation of the infection force λ, which takes into account the average number of contacts between age classes and the proportion of the population infected and infectious (Appendix A—Model equations). Susceptible individuals S

_{i}, upon infection, move to the mild, moderate, and severe symptom classes with probabilities p

^{j}

_{im}for each age group m and each immune status i. These probabilities are determined by the prevalence of zero, one, and two or more co-morbidities that increase the risk of severe COVID-19 disease within each age group, informed by [35]. p

^{j}

_{1m}is directly derived from these prevalences, whereas p

^{j}

_{2m}and p

^{j}

_{3m}are modified in order to assume that people in the S

_{2}and S

_{3}compartments are, respectively, 70% protected and fully protected against moving to the severe disease class I

_{4}(Table S2). The incubation period lasts on average 4.5 days. Therefore, it is assumed that the progression rates through the pre-infectious period κ is equal to 1/1.5. The contagious period is estimated to last 7 to 8 days [41,49,50] and depends on symptom severity, with milder disease associated with shorter infectious periods [51,52]. Thus, we assumed that the recovery rate is respectively equal to 1/5, 1/10, and 1/15 for mild (I

_{2}), moderate (I

_{3}), and severe infections (I

_{4}). Given the short period considered, we assume the absence of natality, mortality, and aging. Finally, we assume that immunity lasts on average 3 years between successive stages, which means that it takes 9 years to pass from a fully resistant to a fully susceptible compartment. For vaccinated classes, we assume that immunity in V

^{1}

_{1}wanes to S

_{1}, V

^{1}

_{2}wanes to S

_{2}, and that of all other vaccinated classes wanes to S

_{3}.

^{1}

_{i}given the desired coverage at the end of each month of the vaccination program. From January to June 2021, the monthly coverage is derived from the VAC-SI (Système d’Informations pour le suivi de la VACcination) database (Table S4). From July, we assume that 15 million doses (including first and second doses) will be administrated each month, which corresponds to the average distribution in the previous 3 months. Monthly coverage is scaled to a daily rate accounting for the portion of the population in the current vaccine-eligible age groups in each eligible compartment (S

_{1}, S

_{2}, S

_{3}, and S

_{4}). Individuals receive a second dose 28 days after the first one and acquire immunity immediately. The vaccine’s efficacy against all infections is assumed to be 50% after 1 dose and 80% after 2 doses. The vaccine’s efficacy against severe infections is assumed to be 70% after 1 dose. Given the model architecture, the efficacy against severe infections after 2 doses is equal to the efficacy against all infections after 2 doses.

#### 2.3. Contact Matrices and Public Health Mitigation Strategies

_{ma}, the governmental measures taken to mitigate the epidemic such as lockdowns, curfews, the closing of schools, businesses, bars, restaurants, or working from home. The schedule of these governmental measures is available at https://www.gouvernement.fr/info-coronavirus/les-actions-du-gouvernement [56]. Specific modifications to the contact matrices are provided in the Supplementary Material (Tables S5–S8).

#### 2.4. Calibration

_{4}) and 3/5 of the moderate cases (I

_{3}). The k-value is the only model parameter that is fit to COVID-19 data, and reflects the population compliance to barrier gestures. Given that climatic conditions are not implemented in the model, the k-value also captures part of the influence of the climate on the transmission [57]. This parameter lies between 0 and 1 (1 being pre-pandemic value; i.e., no barrier gesture application), and it linearly scales contact-rates from the contact matrices. Thus, the force of infection λ

_{im}depends on the k-value (Appendix A).

#### 2.5. Barrier Gesture Relaxation Scenarios

_{4}, i.e., infections requiring at least one medical consultation, and on the number of prevalent intensive care units’ (ICU) hospitalizations. Due to the fact that our model does not directly incorporate a hospitalized compartment, we extrapolated the predictive number of ICU hospitalizations by estimating the mean ratio between the past ICU hospitalizations from the SI-VIC database (Système d’Information pour le suivi des VICtimes d’attentats et de situations sanitaires exceptionnelles) and the past I

_{4}cases.

#### 2.6. Sensitivity Analyses

^{2}compartments, ultimately returning all 75+ individuals that were previously protected by vaccination back to the V

^{2}protective classes.

## 3. Results

#### 3.1. Calibration

#### 3.2. Impact of Barrier Gesture Relaxation, Main Analysis

_{4}incidence for each relaxation scenario are presented in Figure 4 from 1 July 2021. Regardless of the timing, the complete relaxation of barrier gestures (setting k-value to 1, pink curve) is followed by an epidemic resurgence whose peak systematically exceeds that of the 2nd and 3rd epidemic waves in France. However, even in the optimistic scenario of no relaxation (defined as a barrier gesture applying at an equivalent level to that of the same period in 2020), we do observe a significant rebound (black curve).

_{4}cases in the past history of the pandemic (Figure S7), which is on average 3.62%. Whatever the scenario (Figure 5), the complete relaxation of barrier gestures leads to a predicted increase of prevalent ICU hospitalizations, and the peak consistently exceeds French health care capacities (which is estimated at a maximum of about 5000 ICU beds at the national level [58]).

_{4}(Figure S8). While 90% of the 75+ have been vaccinated at least once by the end of June 2021 (Figure S6), about 25% of them are fully susceptible in September 2021 (Figure S9) due both to waning immunity and to the vaccine efficacy hypothesis. Nevertheless, in a sensitivity analysis assuming a 90% vaccine efficacy against infections after two doses, even though the predicted peak ICU hospitalizations following each relaxation scenario is on average 41.0% lower than in the main analysis, a complete relaxation of barrier gestures still overwhelms health care system (Table S10 and Figure S10).

#### 3.3. Impact of Immunity Duration Hypothesis

#### 3.4. Impact of Vaccine Hesitancy

#### 3.5. Booster Campaign

## 4. Discussion

_{4}, and by using reduced contact rates using the k-value, which can moderate these over- and under-estimations. Another limitation of our model is that it underestimates vaccine efficacy against severe infections after two doses, assuming that it is equal to vaccine efficacy against all infections (which is set to 80% in the main analysis). However, assuming an optimistic 90% vaccine efficacy after two doses against infections and severe cases leads to similar conclusions with no possibility to fully relax barrier gestures safely. In addition, it ignores the fact that both mRNA and vectored vaccines have been used in France, which may have different immunogenicity. Nevertheless, 90% of the administrated vaccines in France are mRNA vaccines, in great majority BNT162b2 [64], for which we calibrated the model. Thus, we believe it may not have a significant impact on our results. Also, we did not account for the increased risk of hospitalization related to the alpha variant compared to the historical strain [65] which could explain that our ICU hospitalizations/prevalent I

_{4}ratio tends to increase over the calibration period. This could lead to an underestimation of the ICU hospitalizations rebound. We also did not account for the age-related immune response heterogeneity to the SARS-CoV2 infection and vaccine, which will have to be considered in the future to investigate more accurately the impact of a booster vaccination campaign among the elderly. Finally, although it would require more data on the dynamic of the epidemic at a finer level and individual mobility data, the extension of this work from a national to a regional or local level, in the line of Viguerie et al. work [66], could be considered. This would be particularly interesting with respect to the questions of removing the barrier gestures locally when incidence is low, or vaccination uptake is high.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Variants of Concern Data for France Are Publicly Available on

## Conflicts of Interest

## Appendix A

_{im}. Infectious individuals of symptom severity j and age m are denoted by I

_{jm}. Infected but not-yet-infectious individuals of symptom severity j, age m and stage k are denoted by E

^{k}

_{jm}. Vaccinated individuals of initial immune status i, age m and dose l are denoted by V

^{l}

_{im}. Parameter descriptions are found in Table 1 in the main test. The system of ODEs for age group m is given by the following set of equations:

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**Figure 1.**Schematic of the age-structured SEIVS model for one age group, derived from Childs et al. [33]. Here, S

_{1}, S

_{2}, S

_{3}, and S

_{4}(blue shaded boxes) represent susceptible individuals who are fully susceptible, have some low and moderate immunity, and full immunity, respectively. I

_{2}, I

_{3}, and I

_{4}(yellow boxes) represent infected individuals with mild, moderate, and severe symptoms, respectively, who will develop some low, moderate, or full immunity once recovered (yellow lines), respectively. V

^{1}

_{i}and V

^{2}

_{i}represent vaccinated individuals from the S

_{i}classes (1 ≤ i ≤ 4) after 1 and 2 doses of vaccine, respectively. E

^{k}

_{j}(2 ≤ j ≤ 4) represent exposed individuals (infected but not-yet-infectious) with progressive stages k (1 ≤ k ≤ 3) that will experience mild I

_{2}, moderate I

_{3}, and severe I

_{4}symptoms. Susceptible and vaccinated individuals can be infected and move to the exposed classes (red lines). Immunity gained from infection and vaccination can wane (black lines). Susceptible and vaccinated classes in the same shade of blue have similar protection.

**Figure 2.**(

**a**) Main analysis k-value estimation (reflecting the population compliance to barrier gestures) in France from 13 May 2020 to 1 July 2021; (

**b**) Main analysis estimation of reduction in the average number of contacts consecutively to non-pharmaceutical interventions given the combined effect of the modifications in the contact matrices and the fitted k-value in France from 13 May 2020 to 1 July 2021.

**Figure 3.**Main analysis model fit. Daily incidence of severe (I

_{4}, solid line), moderate and severe (I

_{3}+ I

_{4}, dotted line), and all infections (I

_{2}+ I

_{3}+ I

_{4}, dashed line) from the model and reported COVID-19 cases from French surveillance database (red crosses show daily incidence data, red line shows smoothed incidence data) from May 2020 to 1 July 2021 (logarithmic scale).

**Figure 4.**Evolution of incident COVID-19 severe cases (I

_{4}) in France for each barrier gesture relaxation scenario in the main analysis (i.e., 9 years waning immunity assumption). Relaxation scenarios: k-value (barrier gesture compliance index) raised either to 0.7, 0.8, 0.9, or 1 in August, September, October, November, or December. The start of relaxation is indicated by the vertical dashed black line. No relaxation: k-value equal to previous year estimates at the same period (black line). Prediction starts from 1 July 2021 (vertical red line).

**Figure 5.**Peak of Intensive Care Units’ hospitalizations (ICU) predicted in France from July 2021 following each relaxation scenario, assuming that immunity wanes in 9 years. Relaxation scenarios: k-value (barrier gesture compliance index) raised either to 0.7, 0.8, 0.9, or 1 in August, September, October, November, or December.

**Figure 6.**Peak of Intensive Care Units’ hospitalizations (ICU) predicted in France from July 2021 following each relaxation scenario, assuming that immunity wanes in 3 years (

**a**), or assuming that immunity does not wane (

**b**). Relaxation scenarios: k-value (barrier gesture compliance index) raised either to 0.7, 0.8, 0.9 or 1 in August, September, October, November or December.

**Figure 7.**Peak of Intensive Care Units’ hospitalizations (ICU) predicted in France from July 2021 following each relaxation scenario assuming no vaccine hesitancy with a 9 years immunity duration assumption. Relaxation scenarios: k-value (barrier gesture compliance index) raised either to 0.7, 0.8, 0.9 or 1 in August, September, October, November or December.

Parameter | Definition | Value | References | ||
---|---|---|---|---|---|

Fixed Parameters | |||||

α_{i} | Susceptibility by immune status i | α_{1} | α_{2} | α_{3} | Hypothesis, taken from Childs et al. [33] |

1 | 0.66 | 0.33 | |||

β_{j} | Infectivity by infection severity j | β_{2} | β_{3} | β_{4} | [39] |

0.045 | 0.089 | 0.009 | |||

λ_{im} | Force of infection by immune status i and age m | Appendix A | Estimated | ||

c_{ma} | Contact-rates between individuals in age group m and age group a | Described in Section 2.3 | [40] | ||

R0 | Basic reproductive number | 2.9 | [4] | ||

p^{j}_{im} | Proportion of S going to I_{j} by age m and by immune status i | Table S2 | [35] | ||

A_{m} | Population size by age m | Table S1 | INSEE * | ||

γ_{j} | Recovery rate by infection severity j | γ_{2} | γ_{3} | γ_{4} | Hypothesis |

1/5 | 1/10 | 1/15 | |||

κ | Rate of progress through the exposed compartments | 1/1.5 | [41,42,43] | ||

Variable Parameters | |||||

σ^{1}_{im} | Vaccination rate by age m and by immune status i for first dose | Described in Section 2.2 paragraph 2 | VAC-SI ** | ||

σ^{2}_{im} | Vaccination rate by age m and by immune status i for second dose | 1/28 | |||

ω | Waning rate of immunity | Main analysis | Sensitivity analysis | [21,22] | |

1/1095 | 1/365 | 0 | |||

ρ | Vaccine efficacy against infections after 2 doses | Main analysis | Sensitivity analysis | [44,45,46,47] | |

0.8 | 0.9 | ||||

1 − ε | Vaccine efficacy against infections after 1 dose | Main analysis | Sensitivity analysis | [44,45,46,47] | |

0.5 | 0.7 | ||||

1 − q | Vaccine efficacy against severe cases after 1 dose | Main analysis | Sensitivity analysis | [44,45,46,47] | |

0.7 | 0.7 |

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**MDPI and ACS Style**

Vignals, C.; Dick, D.W.; Thiébaut, R.; Wittkop, L.; Prague, M.; Heffernan, J.M.
Barrier Gesture Relaxation during Vaccination Campaign in France: Modelling Impact of Waning Immunity. *COVID* **2021**, *1*, 472-488.
https://doi.org/10.3390/covid1020041

**AMA Style**

Vignals C, Dick DW, Thiébaut R, Wittkop L, Prague M, Heffernan JM.
Barrier Gesture Relaxation during Vaccination Campaign in France: Modelling Impact of Waning Immunity. *COVID*. 2021; 1(2):472-488.
https://doi.org/10.3390/covid1020041

**Chicago/Turabian Style**

Vignals, Carole, David W. Dick, Rodolphe Thiébaut, Linda Wittkop, Mélanie Prague, and Jane M. Heffernan.
2021. "Barrier Gesture Relaxation during Vaccination Campaign in France: Modelling Impact of Waning Immunity" *COVID* 1, no. 2: 472-488.
https://doi.org/10.3390/covid1020041