Beyond ranking nodes: Predicting epidemic outbreak sizes by network centralities

Distribution of centrality measures on undirected random networks via the cavity method

The Katz centrality of a node in a complex network is a measure of the node's importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its "global" character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability [Formula: see text] that a random node in the ensemble of undirected random graphs has centrality [Formula: see text] satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank-[Formula: see text] projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.

A control measure for epidemic spread based on the susceptible-infectious-susceptible (SIS) model

When an epidemic occurs in a network, finding the important links and cutting them off is an effective measure for preventing the spread of the epidemic. Traditional methods that remove important links easily lead to a disconnected network, inevitably incurring high costs arising from quarantining individuals or communities in a real-world network. In this study, we combine the clustering coefficient and the eigenvector to identify the important links using the susceptible-infectious-susceptible (SIS) model. The results show that our approach can improve the epidemic threshold while maintaining the connectivity of the network to control the spread of the epidemic. Experiments on multiple real-world and synthetic networks of varying sizes, demonstrate the effectiveness and scalability of our approach.

Infection patterns in simple and complex contagion processes on networks

Contagion processes, representing the spread of infectious diseases, information, or social behaviors, are often schematized as taking place on networks, which encode for instance the interactions between individuals. The impact of the network structure on spreading process has been widely investigated, but not the reverse question: do different processes unfolding on a given network lead to different infection patterns? How do the infection patterns depend on a model's parameters or on the nature of the contagion processes? Here we address this issue by investigating the infection patterns for a variety of models. In simple contagion processes, where contagion events involve one connection at a time, we find that the infection patterns are extremely robust across models and parameters. In complex contagion models instead, in which multiple interactions are needed for a contagion event, non-trivial dependencies on models parameters emerge, as the infection pattern depends on the interplay between pairwise and group contagions. In models involving threshold mechanisms moreover, slight parameter changes can significantly impact the spreading paths. Our results show that it is possible to study crucial features of a spread from schematized models, and inform us on the variations between spreading patterns in processes of different nature.

Static graph approximations of dynamic contact networks for epidemic forecasting

Epidemic modeling is essential in understanding the spread of infectious diseases like COVID-19 and devising effective intervention strategies to control them. Recently, network-based disease models have integrated traditional compartment-based modeling with real-world contact graphs and shown promising results. However, in an ongoing epidemic, future contact network patterns are not observed yet. To address this, we use aggregated static networks to approximate future contacts for disease modeling. The standard method in the literature concatenates all edges from a dynamic graph into one collapsed graph, called the full static graph. However, the full static graph often leads to severe overestimation of key epidemic characteristics. Therefore, we propose two novel static network approximation methods, DegMST and EdgeMST, designed to preserve the sparsity of real world contact network while remaining connected. DegMST and EdgeMST use the frequency of temporal edges and the node degrees respectively to preserve sparsity. Our analysis show that our models more closely resemble the network characteristics of the dynamic graph compared to the full static ones. Moreover, our analysis on seven real-world contact networks suggests EdgeMST yield more accurate estimations of disease dynamics for epidemic forecasting when compared to the standard full static method.

The spatiotemporal analysis of the population migration network in China, 2021

Population migration is a critical component of large-scale spatiotemporal models of infectious disease transmission. Identifying the most influential spreaders in networks is vital to controlling and understanding the spreading process of infectious diseases. We used Baidu Migration data for the whole year of 2021 to build mobility networks. The nodes of the network represent cities, and the edges represent the population flow between cities. By applying the k-shell decomposition and the Louvain algorithm, we could get the k-shell values for each city and community partition. Then, we identified the most efficient nodes or pathways in a complex network by generating random networks. Furthermore, we analyzed the eigenvalue of the migration matrix to find the nodes that have the most impact on the network. We also found the consistency between k-shell value and eigenvalue through Kendall's τ test. The main result is that in Spring Festival and National Day, the network is at higher risk of an infectious disease outbreak and the Yangtze River Delta is at the highest risk of an epidemic all year around. Shanghai is the most significant node in both k-shell value and eigenvalue analysis. The spatiotemporal property of the network should be taken into account to model the transmission of infectious diseases more accurately.

The coming Omicron waves and factors affecting its spread after China reopening borders

The Chinese government relaxed the Zero-COVID policy on Dec 15, 2022, and reopened the border on Jan 8, 2023. Therefore, COVID prevention in China is facing new challenges. Though there are plenty of prior studies on COVID, none is regarding the predictions on daily confirmed cases, and medical resources needs after China reopens its borders. To fill this gap, this study innovates a combination of the Erdos Renyl network, modified computational model [Formula: see text], and python code instead of only mathematical formulas or computer simulations in the previous studies. The research background in this study is Shanghai, a representative city in China. Therefore, the results in this study also demonstrate the situation in other regions of China. According to the population distribution and migration characteristics, we divided Shanghai into six epidemic research areas. We built a COVID spread model of the Erodos Renyl network. And then, we use python code to simulate COVID spread based on modified [Formula: see text] model. The results demonstrate that the second and third waves will occur in July-September and Oct-Dec, respectively. At the peak of the epidemic in 2023, the daily confirmed cases will be 340,000, and the cumulative death will be about 31,500. Moreover, 74,000 hospital beds and 3,700 Intensive Care Unit (ICU) beds will be occupied in Shanghai. Therefore, Shanghai faces a shortage of medical resources. In this simulation, daily confirmed cases predictions significantly rely on transmission, migration, and waning immunity rate. The study builds a mixed-effect model to verify further the three parameters' effect on the new confirmed cases. The results demonstrate that migration and waning immunity rates are two significant parameters in COVID spread and daily confirmed cases. This study offers theoretical evidence for the government to prevent COVID after China opened its borders.

A Two-Phase Feature Selection Method for Identifying Influential Spreaders of Disease Epidemics in Complex Networks

Network epidemiology plays a fundamental role in understanding the relationship between network structure and epidemic dynamics, among which identifying influential spreaders is especially important. Most previous studies aim to propose a centrality measure based on network topology to reflect the influence of spreaders, which manifest limited universality. Machine learning enhances the identification of influential spreaders by combining multiple centralities. However, several centrality measures utilized in machine learning methods, such as closeness centrality, exhibit high computational complexity when confronted with large network sizes. Here, we propose a two-phase feature selection method for identifying influential spreaders with a reduced feature dimension. Depending on the definition of influential spreaders, we obtain the optimal feature combination for different synthetic networks. Our results demonstrate that when the datasets are mildly or moderately imbalanced, for Barabasi-Albert (BA) scale-free networks, the centralities' combination with the two-hop neighborhood is fundamental, and for Erdős-Rényi (ER) random graphs, the centralities' combination with the degree centrality is essential. Meanwhile, for Watts-Strogatz (WS) small world networks, feature selection is unnecessary. We also conduct experiments on real-world networks, and the features selected display a high similarity with synthetic networks. Our method provides a new path for identifying superspreaders for the control of epidemics.

Characteristics of the 100 largest modern zoonotic disease outbreaks

Zoonotic disease outbreaks are an important threat to human health and numerous drivers have been recognized as contributing to their increasing frequency. Identifying and quantifying relationships between drivers of zoonotic disease outbreaks and outbreak severity is critical to developing targeted zoonotic disease surveillance and outbreak prevention strategies. However, quantitative studies of outbreak drivers on a global scale are lacking. Attributes of countries such as press freedom, surveillance capabilities and latitude also bias global outbreak data. To illustrate these issues, we review the characteristics of the 100 largest outbreaks in a global dataset (n = 4463 bacterial and viral zoonotic outbreaks), and compare them with 200 randomly chosen background controls. Large outbreaks tended to have more drivers than background outbreaks and were related to large-scale environmental and demographic factors such as changes in vector abundance, human population density, unusual weather conditions and water contamination. Pathogens of large outbreaks were more likely to be viral and vector-borne than background outbreaks. Overall, our case study shows that the characteristics of large zoonotic outbreaks with thousands to millions of cases differ consistently from those of more typical outbreaks. We also discuss the limitations of our work, hoping to pave the way for more comprehensive future studies. This article is part of the theme issue 'Infectious disease macroecology: parasite diversity and dynamics across the globe'.

Optimal test-kit-based intervention strategy of epidemic spreading in heterogeneous complex networks

We propose a deterministic compartmental model of infectious disease that considers the test kits as an important ingredient for the suppression and mitigation of epidemics. A rigorous simulation (with an analytical argument) is provided to reveal the effective reduction of the final outbreak size and the peak of infection as a function of basic reproduction number in a single patch. Furthermore, to study the impact of long and short-distance human migration among the patches, we consider heterogeneous networks where the linear diffusive connectivity is determined by the network link structure. We numerically confirm that implementation of test kits in a fraction of nodes (patches) having larger degrees or betweenness centralities can reduce the peak of infection (as well as the final outbreak size) significantly. A next-generation matrix-based analytical treatment is provided to find out the critical transmission probability in the entire network for the onset of epidemics. Finally, the optimal intervention strategy is validated in two real networks: the global airport network and the transportation network of Kolkata, India.

Unraveling the dynamic importance of county-level features in trajectory of COVID-19

The objective of this study was to investigate the importance of multiple county-level features in the trajectory of COVID-19. We examined feature importance across 2787 counties in the United States using data-driven machine learning models. Existing mathematical models of disease spread usually focused on the case prediction with different infection rates without incorporating multiple heterogeneous features that could impact the spatial and temporal trajectory of COVID-19. Recognizing this, we trained a data-driven model using 23 features representing six key influencing factors affecting the pandemic spread: social demographics of counties, population activities, mobility within the counties, movement across counties, disease attributes, and social network structure. Also, we categorized counties into multiple groups according to their population densities, and we divided the trajectory of COVID-19 into three stages: the outbreak stage, the social distancing stage, and the reopening stage. The study aimed to answer two research questions: (1) The extent to which the importance of heterogeneous features evolved at different stages; (2) The extent to which the importance of heterogeneous features varied across counties with different characteristics. We fitted a set of random forest models to determine weekly feature importance. The results showed that: (1) Social demographic features, such as gross domestic product, population density, and minority status maintained high-importance features throughout stages of COVID-19 across 2787 studied counties; (2) Within-county mobility features had the highest importance in counties with higher population densities; (3) The feature reflecting the social network structure (Facebook, social connectedness index), had higher importance for counties with higher population densities. The results showed that the data-driven machine learning models could provide important insights to inform policymakers regarding feature importance for counties with various population densities and at different stages of a pandemic life cycle.

Top influencers can be identified universally by combining classical centralities

Information flow, opinion, and epidemics spread over structured networks. When using node centrality indicators to predict which nodes will be among the top influencers or superspreaders, no single centrality is a consistently good ranker across networks. We show that statistical classifiers using two or more centralities are instead consistently predictive over many diverse, static real-world topologies. Certain pairs of centralities cooperate particularly well in drawing the statistical boundary between the superspreaders and the rest: a local centrality measuring the size of a node's neighbourhood gains from the addition of a global centrality such as the eigenvector centrality, closeness, or the core number. Intuitively, this is because a local centrality may rank highly nodes which are located in locally dense, but globally peripheral regions of the network. The additional global centrality indicator guides the prediction towards more central regions. The superspreaders usually jointly maximise the values of both centralities. As a result of the interplay between centrality indicators, training classifiers with seven classical indicators leads to a nearly maximum average precision function (0.995) across the networks in this study.