SEIHRDV: a multi-age multi-group epidemiological model and its validation on the COVID-19 epidemics in Italy

TL;DR

The paper introduces SEIHRDV, a multi-age, multi-context compartmental model for simulating COVID-19 dynamics in Italy, with 15 age groups and 7 exposure contexts derived from Mossong tables. It couples age- and context-specific transmission through a tensor $\beta_{ij}^{k}$ and incorporates vaccination via the $V$ compartment and Green Pass policies via a separate transmissibility $\beta_S$, calibrating to Italian death data using piecewise-constant time-varying rates $c(t)$ and $\beta(t)$. The authors demonstrate national and regional validation (Lombardy, Lazio) for Sept 2020–July 2021 and extend to Dec 2021 to assess Green Pass impacts, providing detailed insights into how NPIs and school reopenings shift exposure across ages and contexts. The model offers a granular framework for policy analysis and scenario planning, enabling what-if evaluations of vaccination strategies and containment measures in heterogeneous settings.

Abstract

We propose a novel epidemiological model, referred to as SEIHRDV, for the numerical simulation of the COVID-19 epidemic, which we validate using data from Italy starting in September 2020. SEIHRDV features the following compartments: Susceptible (S), Exposed (E), Infectious (I), Healing (H), Recovered (R), Deceased (D) and Vaccinated (V). The model is age-stratified, as it considers the population split into 15 age groups. Moreover, it takes into account 7 different contexts of exposition to the infection (family, home, school, work, transport, leisure, other contexts), which impact on the transmission mechanism. Thanks to these features, the model can address the analysis of the epidemics and the efficacy of non-pharmaceutical interventions, as well as possible vaccination strategies and the introduction of the Green Pass, a containment measure introduced in Italy in 2021. By leveraging on the SEIHRDV model, we successfully analyzed epidemic trends during the COVID-19 outbreak from September 2020 to July 2021. The model proved instrumental in conducting comprehensive what-if studies and scenario analyses tailored to Italy and its regions. Furthermore, SEIHRDV facilitated accurate forecasting of the future potential trajectory of the epidemic, providing critical information for informed decision making and public health strategies.

Figures (25)

• Figure 1: Sketch of SEIHRDV model ($S$ = Susceptible, $E$ = Exposed, $I$ = Infectious, $H$ = Healing, $R$ = Recovered, $D$ = Deceased, $V$ = Vaccinated).
• Figure 2: Sketch of the SEIHRV model in a single exposure context and two ages group.
• Figure 3: Interactions among the compartments in SEIHRDV multi-age and multi-group model, with $K=7$ contexts of exposition and $N_a=15$ age groups.
• Figure 4: POLYMOD matrices $M^{k}_{i,j}$, $k=1,...,7 = K$, $i,j = 1,...,15 = N_a$: total number of contacts that each individual has with individuals from the 15 age groups, in the seven contexts of exposition.
• Figure 5: Total number of contacts that each individual has with individuals from the 15 age groups at left, for each exposure context at right.