Robustness analysis for quantitative assessment of vaccination effects and SARS-CoV-2 lineages in Italy

Abstract

Background: In Italy, the beginning of 2021 was characterized by the emergence of new variants of SARS-CoV-2 and by the availability of effective vaccines that contributed to the mitigation of non-pharmaceutical interventions and to the avoidance of hospital collapse.

Methods: We analyzed the COVID-19 propagation in Italy starting from September 2021 with a Susceptible-Exposed-Infected-Recovered (SEIR) model that takes into account SARS-CoV-2 lineages, intervention measures and efficacious vaccines. The model was calibrated with the Bayesian method Conditional Robust Calibration (CRC) using COVID-19 data from September 2020 to May 2021. Here, we apply the Conditional Robustness Analysis (CRA) algorithm to the calibrated model in order to identify model parameters that most affect the epidemic diffusion in the long-term scenario. We focus our attention on vaccination and intervention parameters, which are the key parameters for long-term solutions for epidemic control.

Results: Our model successfully describes the presence of new variants and the impact of vaccinations and non-pharmaceutical interventions in the Italian scenario. The CRA analysis reveals that vaccine efficacy and waning immunity play a crucial role for pandemic control, together with asymptomatic transmission. Moreover, even though the presence of variants may impair vaccine effectiveness, virus transmission can be kept low with a constant vaccination rate and low restriction levels.

Conclusions: In the long term, a policy of booster vaccinations together with contact tracing and testing will be key strategies for the containment of SARS-CoV-2 spread.

Keywords: COVID-19; Conditional robustness analysis; Italy; ODE model.

Fig. 1

Flowchart of the computational workflow adopted to study the spread of COVID-19. The ODE model is calibrated against epidemiological data of COVID-19 through the Bayesian method CRC. Then, the CRA algorithm is applied in order to study the influence of infection and vaccination parameters on the hospitalization capacity. The main steps of the CRA are the following: (1) choice of an evaluation function representative of the property of interest, (2) perturbation of the parameter space with LHS, (3) model integration using the generated parameter vectors, (4) kernel density approach for estimating the conditional density of each model parameter. The final result is an index, called MIRI, which denotes the impact of the parameter on the chosen model observable

Fig. 2

Graphic representation of the SEIRL-V model. Clinical stages for the population are: Susceptible (S), Exposed ($E_{\nu }$) where $\nu =0,1,2$ is the number of vaccine doses administered, Presymptomatic ($P_{S,\nu }$), Asymptomatic (A), Recovered (R), Mild infection (M), Severe infection (H), Critical infection (ICU), Dead (D), Vaccinated 1st dose ($V_1)$ and Vaccinated 2nd dose ($V_2)$ The intervention measures are represented by L

Fig. 3

Boxplot of MIRI values for the 10 realizations of the CRA. The evaluation function is the area under the curve of H

Fig. 4

Boxplot of MIRI values for the 10 realizations of the CRA. The evaluation function is the area under the curve of ICU

Fig. 5

Boxplot of MIRI values for the 10 realizations of the CRA. The evaluation function is the area under the curve of D

Fig. 6

Italy. Results of Scenario A: perturbation of parameters $\eta$ and $\delta$. (a–c). Total number of hospitalization for three different values of [$s_{06}$,$s_{07}$,$s_{08}$].(d–f). Total number of ICU patients for three different values of [$s_{06}$,$s_{07}$,$s_{08}$].(g–i). Maximum number of deaths for three different values of [$s_{06}$,$s_{07}$,$s_{08}$]. Data are normalized over the Italian population ($\sim$ $60$ million) and multiplied by ${10}^5$

Fig. 7

Italy. Predicted scenarios for different values of vaccine efficacy against infection. Parameter ${\rho }_1$, representing the efficacy of the first dose, is perturbed between 0.3 and 0.8 with a step size of 0.05. Parameter ${\rho }_2$, representing the efficacy of the second dose, is perturbed between 0.6 and 0.95 with a step size of 0.035. Higher values of ${\rho }_1$ and ${\rho }_2$ correspond to higher color curves of H, ICU and D