Background In the early months of 2020, a novel coronavirus disease (COVID-19) spread rapidly from China across multiple countries worldwide. As of March 17, 2020, COVID-19 was officially declared a pandemic by the World Health Organization. We collected data on COVID-19 cases outside China during the early phase of the pandemic and used them to predict trends in importations and quantify the proportion of undetected imported cases. Methods and findings Two hundred and eighty-eight cases have been confirmed out of China from January 3 to February 13, 2020. We collected and synthesized all available information on these cases from official sources and media. We analyzed importations that were successfully isolated and those leading to onward transmission. We modeled their number over time, in relation to the origin of travel (Hubei province, other Chinese provinces, other countries) and interventions. We characterized the importation timeline to assess the rapidity of isolation and epidemiologically linked clusters to estimate the rate of detection. We found a rapid exponential growth of importations from Hubei, corresponding to a doubling time of 2.8 days, combined with a slower growth from the other areas. We predicted a rebound of importations from South East Asia in the successive weeks. Time from travel to detection has considerably decreased since first importation, from 14.5 ± 5.5 days on January 5, 2020, to 6 ± 3.5 days on February 1, 2020. However, we estimated 36% of detection of imported cases. This study is restricted to the early phase of the pandemic, when China was the only large epicenter and foreign countries had not discovered extensive local transmission yet. Missing information in case history was accounted for through modeling and imputation. Conclusions Our findings indicate that travel bans and containment strategies adopted in China were effective in reducing the exportation growth rate. However, the risk of importation was estimated to increase again from other sources in South East Asia. Surveillance and management of traveling cases represented a priority in the early phase of the epidemic. With the majority of imported cases going undetected (6 out of 10), countries experienced several undetected clusters of chains of local transmissions, fueling silent epidemics in the community. These findings become again critical to prevent second waves, now that countries have reduced their epidemic activity and progressively phase out lockdown.
288 cases have been confirmed out of China from January 3 to February 13, 2020. We collected and synthesized all available information on these cases from official sources and media. We analyzed importations that were successfully isolated and those leading to onward transmission. We modeled their number over time, in relation to the origin of travel (Hubei province, other Chinese provinces, other countries) and interventions. We characterized importations timeline to assess the rapidity of isolation, and epidemiologically linked clusters to estimate the rate of detection. We found a rapid exponential growth of importations from Hubei, combined with a slower growth from the other areas. We predicted a rebound of importations from South East Asia in the upcoming weeks. Time from travel to detection has considerably decreased since the first importation, however 6 cases out of 10 were estimated to go undetected. Countries outside China should be prepared for the possible emergence of several undetected clusters of chains of local transmissions.
We study the effect of heterogeneous temporal activations on epidemic spreading in temporal networks. We focus on the susceptible-infected-susceptible (SIS) model on activity-driven networks with burstiness. By using an activity-based mean-field approach, we derive a closed analytical form for the epidemic threshold for arbitrary activity and inter-event time distributions. We show that, as expected, burstiness lowers the epidemic threshold while its effect on prevalence is twofold. In low-infective systems burstiness raises the average infection probability, while it weakens epidemic spreading for high infectivity. Our results can help clarify the conflicting effects of burstiness reported in the literature. We also discuss the scaling properties at the transition, showing that they are not affected by burstiness.as in Poisson processes but, typically, it features a fat tail, easily measured from large datasets [1,2].Recent studies have addressed the problem of the origin of this highly heterogeneous behavior, arising from the decision-based queuing process that humans apply in performing tasks and allocating their priority [5,6]. Besides, a large amount of work has been devoted to clarify the effects of intermittent patterns on the temporal structures of interactions, as described by temporal networks [7]. Bursty dynamics can indeed influence the structure of links on the local and on the global scale [8][9][10][11][12]. More importantly, heterogenous temporal patterns in the evolution of time-varying networks can affect in a non-trivial way dynamical processes. Analytical arguments [13][14][15] and numerical approaches [16,17] have indeed shown that burstiness can significantly modify processes mediated by interactions, such as random walks, epidemics, information diffusion, consensus formation, percolation. Among these, epidemic spreading is one of the most representative and widely applicable example [18]. Analytical results on epidemics in temporal network have focused on the epidemic threshold [19,20], in general pushed to lower values by bursty effects. In other works, burstiness is introduced on a static network as a non-Markovian effect in infection (or recovery) processes [21][22][23][24][25].Interestingly, when comparing bursty with Poisson dynamics in epidemics, conflicting observations have been reported. On the one hand, numerical results [14,16,17] and modeling techniques [15,24,26,27] provided strong evidence of a slowing down for the late time spreading in the presence of burstiness, while opposite effects are reported in the early-time dynamics [28]. In [14] and [16], burstiness is found to slow down spreading in early times, while other works observe the opposite effect [17,26].To understand such conflicting observations and keep track at the same time of the temporal evolution of interactions, in this paper we focus on the Susceptible-Infected-Susceptible (SIS) process in the presence of burstiness on activity-driven networks [29][30][31]. In activity-driven networks, the propensity to engage...
Isolation of symptomatic individuals, tracing and testing of their nonsymptomatic contacts are fundamental strategies for mitigating the current COVID-19 pandemic. The breaking of contagion chains relies on two complementary strategies: manual reconstruction of contacts based on interviews and a digital (app-based) privacy-preserving contact tracing. We compare their effectiveness using model parameters tailored to describe SARS-CoV-2 diffusion within the activity-driven model, a general empirically validated framework for network dynamics. We show that, even for equal probability of tracing a contact, manual tracing robustly performs better than the digital protocol, also taking into account the intrinsic delay and limited scalability of the manual procedure. This result is explained in terms of the stochastic sampling occurring during the case-by-case manual reconstruction of contacts, contrasted with the intrinsically prearranged nature of digital tracing, determined by the decision to adopt the app or not by each individual. The better performance of manual tracing is enhanced by heterogeneity in agent behavior: superspreaders not adopting the app are completely invisible to digital contact tracing, while they can be easily traced manually, due to their multiple contacts. We show that this intrinsic difference makes the manual procedure dominant in realistic hybrid protocols.
Effective contact tracing is crucial to containing epidemic spreading without disrupting societal activities, especially during a pandemic. Large gatherings play a key role, potentially favouring superspreading events. However, the effects of tracing in large groups have not been fully assessed so far. We show that in addition to forward tracing, which reconstructs to whom the disease spreads, and backward tracing, which searches from whom the disease spreads, a third ‘sideward’ tracing is always present, when tracing gatherings. This is an indirect tracing that detects infected asymptomatic individuals, even if they have been neither directly infected by nor directly transmitted the infection to the index case. We analyse this effect in a model of epidemic spreading for SARS-CoV-2, within the framework of simplicial activity-driven temporal networks. We determine the contribution of the three tracing mechanisms to the suppression of epidemic spreading, showing that sideward tracing induces a non-monotonic behaviour in the tracing efficiency, as a function of the size of the gatherings. Based on our results, we suggest an optimal choice for the sizes of the gatherings to be traced and we test the strategy on an empirical dataset of gatherings on a university campus.
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