Estimating behavioural relaxation induced by COVID-19 vaccines in the first months of their rollout

Abstract

The initial rollout of COVID-19 vaccines has been challenged by logistical issues, limited availability of doses, scarce healthcare capacity, spotty acceptance, and the emergence of variants of concern. Non-pharmaceutical interventions (NPIs) have been critical to support these phases. However, vaccines may have prompted behavioural relaxation, potentially reducing NPIs adherence. Epidemic models have explored this phenomenon, but they have not been validated against data. Moreover, recent surveys provide conflicting results on the matter. The extent of behavioural relaxation induced by COVID-19 vaccines is still unclear. Here, we aim to study this phenomenon in four regions. We implement five realistic epidemic models which include age structure, multiple virus strains, NPIs, and vaccinations. One of the models acts as a baseline, while the others extend it including different behavioural relaxation mechanisms. First, we calibrate the baseline model and run counterfactual scenarios to quantify the impact of vaccinations and NPIs. Our results confirm the critical role of both in reducing infection and mortality rates. Second, using different metrics, we calibrate the behavioural models and compare them to each other and to the baseline. Including behavioural relaxation leads to a better fit of weekly deaths in three regions. However, the improvements are limited to a [Formula: see text] reduction in weighted mean absolute percentage errors and these gains are generally offset by models' increased complexity. Overall, we do not find clear signs of behavioural relaxation induced by COVID-19 vaccines on weekly deaths. Furthermore, our results suggest that if this phenomenon occurred, it generally involved only a minority of the population. Our work contributes to the retrospective validation of epidemic models developed amid the COVID-19 Pandemic and underscores the issue of non-identifiability of complex social mechanisms.

Fig 1. Weekly deaths, vaccinations, contacts reduction, and calibration of baseline model.

The x-axis indicates the year and week. A) Fraction of daily newly vaccinated individuals across all age groups (shaded areas) and within the 70 +  age-group (solid lines) in the four regions from up to down: British Columbia, Lombardy, London, and São Paulo. B) Contact levels during the Pandemic with respect to a pre-pandemic baseline. C) Reported data describing weekly deaths per 100,000 (dots) and the results from the calibrated baseline model (solid lines representing the medians, shaded areas the $90\%$ confidence intervals). The grey vertical lines mark the start of vaccinations in different regions.

Fig 2. Impact of vaccines and non-pharmaceutical interventions on COVID-19 deaths (baseline model).

A) Relative deaths difference (RDD) for vaccines. B) RDD for NPIs. The boxplots in both panels show the results considering 1000 stochastic trajectories in each region. The horizontal line within each box marks the median value, while the top and bottom edges correspond to the $90\%$ CI. The whiskers extend to the maximum and minimum values. These estimates are obtained considering the baseline model.

Fig 3. Comparison of baseline and behavioural models.

Calibrated weekly deaths trajectories (i.e., weekly deaths per 100,000) for the baseline and four behavioural models across the four regions. Solid lines indicate the medians, while the shaded areas the $90\%$ confidence intervals. Reported weekly deaths are denoted by blue dots.

Fig 4. The impact of behavioural relaxation on COVID-19 deaths (behavioural models).

We plot the RDD (i.e., relative deaths difference) for behavioural mechanisms in the four models and regions. Each boxplot is built considering 1000 stochastic simulations. The horizontal line within each box marks the median value, while the top and bottom edges correspond to the $50\%$ CI. The whiskers extend to the maximum and minimum values after removing the outliers that beyond 1.5 times the interquartile range.

Fig 5. Epidemic compartment structure.

All compartments connected by solid lines constitute the baseline model. This model includes susceptible (S), latent (L), infected (I), recovered (R), and dead (D, ${\mathit{\text{D}}}^{\mathit{\text{o}}}$) compartments. The top row represents non-vaccinated compartments, whereas the bottom row represents vaccinated compartments. Individuals in the S compartment get vaccinated according to real vaccine rates ($\nu$) and then transition to the ${\mathit{\text{S}}}^{\mathit{\text{V}}}$ compartment. To account for the emergence of a second variant, we double the compartments creating $L^{\prime }$, $I^{\prime }$, $R^{\prime }$, $D^{\prime }$, and $D^{o^{\prime }}$. This is done also for the vaccinated compartments that become $L^{V^{\prime }}$, $I^{V^{\prime }}$, $R^{V^{\prime }}$, $D^{V^{\prime }}$, $D^{V{o}^{\prime }}$. Behavioural models include susceptible non-compliant compartments (S_NC, $S_{NC}^V$) connected by dotted lines, where individuals have r times higher probability of getting infected with respect to susceptible compliant individuals (S and ${\mathit{\text{S}}}^{\mathit{\text{V}}}$). In the constant rate model and the time-varying rate model, we include S_NC and $S_{NC}^V$, whereas in the vaccinated-only versions, we include only $S_{NC}^V$