Hypergraphs naturally represent higher-order interactions, which persistently appear in social interactions, neural networks, and other natural systems. Although their importance is well recognized, a theoretical framework to describe general dynamical processes on hypergraphs is not available yet. In this paper, we derive expressions for the stability of dynamical systems defined on an arbitrary hypergraph. The framework allows us to reveal that, near the fixed point, the relevant structure is a weighted graph-projection of the hypergraph and that it is possible to identify the role of each structural order for a given process. We analytically solve two dynamics of general interest, namely, social contagion and diffusion processes, and show that the stability conditions can be decoupled in structural and dynamical components. Our results show that in social contagion process, only pairwise interactions play a role in the stability of the absorbing state, while for the diffusion dynamics, the order of the interactions plays a differential role. Our work provides a general framework for further exploration of dynamical processes on hypergraphs.

American Physical Society. Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we analyze the combined effect of these two ingredients on epidemic dynamics on networks. We study the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered (SIR) models on the recently introduced activity-driven networks with memory. By means of an activity-based mean-field approach, we derive, in the long-time limit, analytical predictions for the epidemic threshold as a function of the parameters describing the distribution of activities and the strength of the memory effects. Our results show that memory reduces the threshold, which is the same for SIS and SIR dynamics, therefore favoring epidemic spreading. The theoretical approach perfectly agrees with numerical simulations in the long-time asymptotic regime. Strong aging effects are present in the preasymptotic regime and the epidemic threshold is deeply affected by the starting time of the epidemics. We discuss in detail the origin of the model-dependent preasymptotic corrections, whose understanding could potentially allow for epidemic control on correlated temporal networks.

Most countries around the world enforced non-pharmaceutical interventions against COVID-19. Italy was one of the first countries to be affected by the pandemic, imposing a hard lockdown, in the first epidemic wave. During the second wave, the country implemented progressively restrictive tiers at the regional level according to weekly epidemiological risk assessments. This paper quantifies the impact of these restrictions on contacts and on the reproduction number.

SARS-CoV-2 has clearly shown that efficient management of infectious diseases requires a top-down approach which must be complemented with a bottom-up response to be effective. Here we investigate a novel approach to surveillance for transboundary animal diseases using African Swine (ASF) fever as a model. We collected data both at a population level and at the local level on information-seeking behavior respectively through digital data and targeted questionnaire-based surveys to relevant stakeholders such as pig farmers and veterinary authorities. Our study shows how information-seeking behavior and resulting public attention during an epidemic, can be identified through novel data streams from digital platforms such as Wikipedia. Leveraging attention in a critical moment can be key to providing the correct information at the right moment, especially to an interested cohort of people. We also bring evidence on how field surveys aimed at local workers and veterinary authorities remain a crucial tool to assess more in-depth preparedness and awareness among front-line actors. We conclude that these two tools should be used in combination to maximize the outcome of surveillance and prevention activities for selected transboundary animal diseases such as ASF.

Socioeconomic inequalities significantly influence infectious disease outcomes, as seen with COVID-19, but the pathways through which socioeconomic conditions affect transmission dynamics remain unclear. To address this, we conducted a survey representative of the Italian population, stratified by age, gender, geographical area, city size, employment status, and education level. The survey's final aim was to estimate differences in contact and protective behaviors across various population strata, both of which are crucial for understanding transmission dynamics. Our initial insights based on the survey indicate that years after the pandemic began, the perceived impact of COVID-19 on professional, economic, social, and psychological dimensions vary across socioeconomic strata, extending beyond the epidemiological outcomes. This reinforces the need for approaches that systematically consider socioeconomic determinants. In this context, using generalized linear models, we identified associations between socioeconomic factors and vaccination status for both COVID-19 and influenza, as well as the influence of socioeconomic conditions on mask-wearing and social distancing. Importantly, we also observed differences in contact behaviors based on employment status while education level did not show a significant association. These findings highlight the complex interplay of socioeconomic and demographic factors in shaping protective behavior and contact patterns. Understanding these dynamics can contribute to the improvement of epidemic models and better guide public health efforts for at-risk groups.