A data-driven analysis of the impact of non-compliant individuals on epidemic diffusion in urban settings

TL;DR

This work addresses how behavioural non-compliance alters epidemic diffusion in urban settings by developing a data-driven, two-layer city contact framework and a heterogeneous HeSIR model that distinguishes ordinary (O) and non-compliant (M) individuals. The authors implement a discrete-time, tile-based network for three Italian cities and compare uniform versus data-driven distributions of non-compliant individuals, finding that local clustering can create infection hotspots even when city-wide effects are modest. Key findings show that non-compliance accelerates spread and raises peaks at moderate transmission, with greater local impact driven by spatially concentrated non-compliant groups and by higher susceptibility. The results highlight the importance of monitoring local compliance and tailoring interventions to spatial patterns, while also revealing how network structure mediates the translation of behavioural heterogeneity into epidemic outcomes.

Abstract

Individuals who do not comply with public health safety measures pose a significant challenge to effective epidemic control, as their risky behaviours can undermine public health interventions. This is particularly relevant in urban environments because of their high population density and complex social interactions. In this study, we employ detailed contact networks, built using a data-driven approach, to examine the impact of non-compliant individuals on epidemic dynamics in three major Italian cities: Torino, Milano, and Palermo. We use a heterogeneous extension of the Susceptible-Infected-Recovered model that distinguishes between ordinary and non-compliant individuals, who are more infectious and/or more susceptible. By combining electoral data with recent findings on vaccine hesitancy, we obtain spatially heterogeneous distributions of non-compliance. Epidemic simulations demonstrate that even a small proportion of non-compliant individuals in the population can substantially increase the number of infections and accelerate the timing of their peak. Furthermore, the impact of non-compliance is greatest when disease transmission rates are moderate. Including the heterogeneous, data-driven distribution of non-compliance in the simulations results in infection hotspots forming with varying intensity according to the disease transmission rate. Overall, these findings emphasise the importance of monitoring behavioural compliance and tailoring public health interventions to address localised risks.

Figures (10)

• Figure 1: (a-c) Distribution of the population in tiles for the cities under analysis: each tile is colored according to the number of individuals (see color bar on the left). (d) Schematic representation of a tile, with household contacts in blue and social contacts in orange – some of the latter connect to tiles not visible in the diagram. The dashed gray lines indicate the boundaries of the tile.
• Figure 2: Flow diagram of the HeSIR process. The transition rate from Susceptible to Infectious depends on the classes of both the infector and the infected (with $\beta$ as the baseline transmission rate, and $a, b \geq 1$ representing increased infectivity and susceptibility, respectively). The recovery rate $\gamma$ is uniform across all individuals.
• Figure 3: Data-driven distribution of the proportion of non-compliant individuals, $r_i$, scaled such that $0$ represents the minimum level and $1$ the maximum level of non-compliance. Darker colors correspond to smaller values, using the same color normalization for the three cities.
• Figure 4: Simulations of the HeSIR model in the city of Milano with a uniform distribution of non-compliant individuals. Panels (a-c): total fraction of infected individuals (Attack Rate) as a function of the product of transmission rate $\beta$ and average graph degree $\left< k \right>$, for varying values of $a$, $b$, and $p_M$. Panels (d-f): difference in Attack Rates between the HeSIR and baseline SIR models, with the same $p_M$ as the panel above. In all panels, lines indicate the mean and shaded areas correspond to inter-quartile range.
• Figure 5: Epidemic outbreak simulations of the HeSIR model in the city of Milano with a uniform distribution of non-compliant individuals ($\beta \langle k \rangle = 0.1$). Panels (a-b): time evolution of the infected population fraction for two values of the non-compliant fraction $p_M$. Lines indicate median values and shaded areas the interquartile range. Panel (c): scatter plot of epidemic peak time versus peak amplitude, averaged over 100 simulations, for various combinations of model parameters. Points located in the upper-left region indicate more severe outbreaks (earlier and higher peaks). The baseline SIR scenario, with no behavioural heterogeneity ($a = b = 1$), is shown in grey.