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Background: The COVID-19 pandemic has significantly affected social contact patterns worldwide. Particularly during the first epidemic wave, because of the lack of specific treatment or vaccine, most countries around the world enforced non-pharmaceutical interventions. Italy was one of the first countries to be strongly affected by the pandemic, imposing in the first epidemic wave a hard lockdown. During the second wave, the country implemented color-coded, progressively restrictive tiers at the regional level according to weekly epidemiological risk assessments. Methods: We analyze longitudinal surveys of a representative sample of the Italian population by age, gender, and region of residence, collected during the second epidemic wave. After presenting a statistical description of the sample, we compare variations in contact patterns according to a color-coded tier of interventions experienced by the participants. In particular, we use contact matrices to quantify the reduction in the number of contacts by age group and contact settings, focusing on the adult population. We also compare the results with the pre-pandemic baseline assessing the impact of tiered restrictions on contacts. Finally, we compute the reproduction number to evaluate the impact of the restrictions on the spreading of the disease.Results: The comparison with the pre-pandemic baseline, shows a significant decrease in the number of contacts, independently from the age group or contact settings. Moreover, we show that the decrease in the number of contacts significantly depends on the strictness of the non-pharmaceutical interventions. For all levels of strictness considered, the reduction in social mixing results in a reproduction number smaller than one. In particular, the impact of the restriction on the number of contacts decreases with the severity of the interventions. Conclusions: We showed that the progressive restriction tiers implemented in Italy reduced overall the reproduction number, with stricter interventions associated with higher reductions. Readily collected contact data can promptly inform the implementation of mitigation measures at the national level in epidemic emergencies to come.

The exposure and consumption of information during epidemic outbreaks may alter risk perception, trigger behavioural changes, and ultimately affect the evolution of the disease. It is thus of the uttermost importance to map information dissemination by mainstream media outlets and public response. However, our understanding of this exposure-response dynamic during COVID-19 pandemic is still limited. In this paper, we provide a characterization of media coverage and online collective attention to COVID-19 pandemic in four countries: Italy, United Kingdom, United States, and Canada. For this purpose, we collect an heterogeneous dataset including 227,768 online news articles and 13,448 Youtube videos published by mainstream media, 107,898 users posts and 3,829,309 comments on the social media platform Reddit, and 278,456,892 views to COVID-19 related Wikipedia pages. Our results show that public attention, quantified as users activity on Reddit and active searches on Wikipedia pages, is mainly driven by media coverage and declines rapidly, while news exposure and COVID-19 incidence remain high. Furthermore, by using an unsupervised, dynamical topic modeling approach, we show that while the attention dedicated to different topics by media and online users are in good accordance, interesting deviations emerge in their temporal patterns. Overall, our findings offer an additional key to interpret public perception/response to the current global health emergency and raise questions about the effects of attention saturation on collective awareness, risk perception and thus on tendencies towards behavioural changes.

Comprendere il meccanismo di diffusione di una malattia è sempre stato un problema cruciale per la sanità e la società. In particolare la valutazione della soglia oltre la quale si verifica l'insorgenza di uno stato epidemico è uno dei problemi fondamentali per il controllo della sua diffusione. Dal punto di vista matematico, molti modelli sono stati formalizzati nel corso degli anni. In particolare l'introduzione della teoria dei networks ha migliorato significativamente sia l'analisi che la capacità di previsione di questi fenomeni, dando risultati più soddisfacenti. Molti degli studi sulle epidemie sono stati condotti su reti statiche, ma negli ultimi anni l'interesse verso i temporal networks è cresciuto rapidamente. Nonostante la maggiore complessità derivante dall'introduzione della variabile temporale, alcuni modelli consentono una comprensione analitica dei processi di diffusione. In particolare nel nostro lavoro prenderemo in considerazione il modello activity-driven in cui la variabile temporale è incorporata nella propensione di ogni individuo ad interagire con gli altri in un determinato momento. I rapporti sociali sono mossi anche dalla memoria che le persone hanno l'una dell'altra, preferendo interagire con le vecchie conoscenze a quelle nuove. In questo lavoro esploriamo gli effetti che il meccanismo della memoria in network variabile nel tempo ha su un processo di diffusione concentrandoci sulla dinamica delle epidemie. In particolare consideriamo due modelli epidemici standard: il suscettibile-infetto-suscettibile (SIS) e il suscettibile-infetto-recuperato (SIR), descrivendo rispettivamente malattie che non conferiscono o non conferiscono immunità dopo l'infezione. Formuliamo un approccio activity-based mean-field ottenendo analiticamente la soglia epidemica in funzione dei parametri che descrivono la distribuzione delle attività e la forza degli effetti della memoria. In particolare consideriamo il regime asintotico in cui l'infezione inizia solo quando le persone hanno avuto un numero sufficientemente elevato di connessioni nella propria cerchia sociale. In questo limite il processo dinamico può essere visto come un processo guidato dall'attività che evolve su un effective static network. I nostri risultati mostrano che la memoria amplifica le fluttuazioni di attività riducendo la soglia e aumentando la diffusione dell'epidemia sia nel modello SIS che nel modello SIR. Per dimostrare numericamente i risultati ottenuti simuliamo il processo epidemico sia sull'effective static network che sul network temporale, variando il parametro di memoria e il tempo di primo contagio. Confrontando il modello teorico con le simulazioni numeriche confermiamo le nostre previsioni nel limite asintotico. Dimostriamo inoltre che nel regime preasintotico ci sono forti effetti di aging che rendono la soglia epidemica profondamente influenzata dal momento di inizio del contagio. In particolare, per brevi tempi di inizio dell'infezione, le correlazioni indotte dalla memoria producono un forte effetto di backtracking sia nei processi SIS che SIR, abbassando o aumentando rispettivamente la soglia epidemica. Discutiamo in dettaglio l'origine delle correzioni preasintotiche dipendenti dal modello, ponendo le basi per potenziali metodi di controllo dell'epidemie su reti temporali fortemente correlate. Understanding the mechanism behind the diffusion of a disease has always been a crucial problem for health and society. In particular the evaluation of the threshold above which there is an emergence of an epidemic state is one of the fundamental problems for disease control. From the mathematical point of view, many models have been formalized over the years. In particular the introduction of networks science has significantly improved both the analysis and the prediction capability of these phenomena giving more compelling results. Many of the studies in epidemics have been carried on static networks, but in the last few years the interest toward time-varying networks has rapidly grown. Despite the increased complexity from the introduction of the time variable, some models allow an analytical understanding of the spreading processes. In particular in our work we will consider the activity-driven model in which the time variable is embedded in the propensity of each individual to interact at a certain time. Social ties are also driven by the memory people have of each other, preferring old acquaintances interactions to new ones. In this work we explore the effects that the memory mechanism in a time-varying network has on a spreading process focusing on the epidemic dynamics. We focus our attention on two standard epidemic models: the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered (SIR), describing respectively diseases that don't or do confer immunity after the infection. We formulate an activity-based mean-field approach obtaining analytically the epidemic threshold as a function of the parameters describing the distribution of activities and the strength of the memory effects. In particular we consider the asymptotic regime in which the infection starts only when the people have had a sufficiently large number of connections in their social circle. In this limit the dynamical process can be seen as an activity-driven process evolving on an effective static graph. Our results show that memory amplifies the activity fluctuations reducing the threshold and enhancing the epidemic spreading in both the SIS and SIR models. To numerically prove our findings we simulate the epidemic process on both the time-evolving and the effective static networks, varying the memory parameter and the starting time of the infection. Comparing the theoretical model with the numerical simulations we confirm our predictions in the asymptotic limit. We also show that in the preasymptotic regime there are strong aging effects making the epidemic threshold deeply affected by the starting time of the outbreak. In particular, for short starting times of the infection, the correlations induced by the memory produce strong backtracking effect in both the SIS and SIR processes, lowering or increasing the epidemic threshold respectively. We discuss in detail the origin of the model-dependent preasymptotic corrections, setting the bases for potential epidemics control methods on correlated temporal networks.

BackgroundMost 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.MethodsRepresentative (with respect to age, sex, and region of residence) longitudinal surveys of the Italian population were undertaken during the second epidemic wave. Epidemiologically relevant contact patterns were measured and compared with pre-pandemic levels and according to the level of interventions experienced by the participants. Contact matrices were used to quantify the reduction in the number of contacts by age group and contact setting. The reproduction number was estimated to evaluate the impact of restrictions on the spread of COVID-19.ResultsThe comparison with the pre-pandemic baseline shows a significant decrease in the number of contacts, independently from the age group or contact settings. This decrease in the number of contacts significantly depends on the strictness of the non-pharmaceutical interventions. For all levels of strictness considered, the reduction in social mixing results in a reproduction number smaller than one. In particular, the impact of the restriction on the number of contacts decreases with the severity of the interventions.ConclusionsThe progressive restriction tiers implemented in Italy reduced the reproduction number, with stricter interventions associated with higher reductions. Readily collected contact data can inform the implementation of mitigation measures at the national level in epidemic emergencies to come. This project has received funding from the European Union’s Horizon 2020 research and innovation program, EpiPose project (Grant agreement number 101003688). This work refects only the authors’ view. The European Commission is not responsible for any use that may be made of the information it contains. DP, MT, and AD acknowledge the support from the Lagrange Project of the Institute for Scientifc Interchange Foundation (ISI Foundation) funded by the Fondazione Cassa di Risparmio di Torino (Fondazione CRT).