Reconstructing propagation networks with natural diversity and identifying hidden sources

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large number of model and real networks, finding that a full reconstruction of inhomogeneous interactions can be achieved from small amounts of polarized (binary) data, a virtue of compressed sensing. Further, we demonstrate that a hidden source that triggers the spreading process but is externally inaccessible can be ascertained and located with high confidence in the absence of direct routes of propagation from it. Our approach thus establishes a paradigm for tracing and controlling epidemic invasion and information diffusion in complex networked systems.Comment: 20 pages and 5 figures. For Supplementary information, please see http://www.nature.com/ncomms/2014/140711/ncomms5323/full/ncomms5323.html#

Reconstructing the recent West Nile virus lineage 2 epidemic in Europe and Italy using discrete and continuous phylogeography

West Nile virus lineage 2 (WNV-2) was mainly confined to sub-Saharan Africa until the early 2000s, when it was identified for the first time in Central Europe causing outbreaks of human and animal infection. The aim of this study was to reconstruct the origin and dispersion of WNV-2 in Central Europe and Italy on a phylodynamic and phylogeographical basis. To this aim, discrete and continuous space phylogeographical models were applied to a total of 33 newly characterised full-length viral genomes obtained from mosquitoes, birds and humans in Northern Italy in the years 2013-2015 aligned with 64 complete sequences isolated mainly in Europe. The European isolates segregated into two highly significant clades: a small one including three sequences and a large clade including the majority of isolates obtained in Central Europe since 2004. Discrete phylogeographical analysis showed that the most probable location of the root of the largest European clade was in Hungary a mean 12.78 years ago. The European clade bifurcated into two highly supported subclades: one including most of the Central/East European isolates and the other encompassing all of the isolates obtained in Greece. The continuous space phylogeographical analysis of the Italian clade showed that WNV-2 entered Italy in about 2008, probably by crossing the Adriatic sea and reaching a central area of the Po Valley. The epidemic then spread simultaneously eastward, to reach the region of the Po delta in 2013, and westward to the border area between Lombardy and Piedmont in 2014; later, the western strain changed direction southward, and reached the central area of the Po valley once again in 2015. Over a period of about seven years, the virus spread all over an area of northern Italy by following the Po river and its main tributaries

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

A Bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data

We describe a statistical framework for reconstructing the sequence of transmission events between observed cases of an endemic infectious disease using genetic, temporal and spatial information. Previous approaches to reconstructing transmission trees have assumed all infections in the study area originated from a single introduction and that a large fraction of cases were observed. There are as yet no approaches appropriate for endemic situations in which a disease is already well established in a host population and in which there may be multiple origins of infection, or that can enumerate unobserved infections missing from the sample. Our proposed framework addresses these shortcomings, enabling reconstruction of partially observed transmission trees and estimating the number of cases missing from the sample. Analyses of simulated datasets show the method to be accurate in identifying direct transmissions, while introductions and transmissions via one or more unsampled intermediate cases could be identified at high to moderate levels of case detection. When applied to partial genome sequences of rabies virus sampled from an endemic region of South Africa, our method reveals several distinct transmission cycles with little contact between them, and direct transmission over long distances suggesting significant anthropogenic influence in the movement of infected dogs

Effects of memory on the shapes of simple outbreak trees

Genomic tools, including phylogenetic trees derived from sequence data, are increasingly used to understand outbreaks of infectious diseases. One challenge is to link phylogenetic trees to patterns of transmission. Particularly in bacteria that cause chronic infections, this inference is affected by variable infectious periods and infectivity over time. It is known that non-exponential infectious periods can have substantial effects on pathogens’ transmission dynamics. Here we ask how this non-Markovian nature of an outbreak process affects the branching trees describing that process, with particular focus on tree shapes. We simulate Crump-Mode-Jagers branching processes and compare different patterns of infectivity over time. We find that memory (non-Markovian-ness) in the process can have a pronounced effect on the shapes of the outbreak’s branching pattern. However, memory also has a pronounced effect on the sizes of the trees, even when the duration of the simulation is fixed. When the sizes of the trees are constrained to a constant value, memory in our processes has little direct effect on tree shapes, but can bias inference of the birth rate from trees. We compare simulated branching trees to phylogenetic trees from an outbreak of tuberculosis in Canada, and discuss the relevance of memory to this dataset

Emerging Challenges and Opportunities in Infectious Disease Epidemiology.

Much of the intellectual tradition of modern epidemiology stems from efforts to understand and combat chronic diseases persisting through the 20th century epidemiologic transition of countries such as the United States and United Kingdom. After decades of relative obscurity, infectious disease epidemiology has undergone an intellectual rebirth in recent years amid increasing recognition of the threat posed by both new and familiar pathogens. Here, we review the emerging coalescence of infectious disease epidemiology around a core set of study designs and statistical methods bearing little resemblance to the chronic disease epidemiology toolkit. We offer our outlook on challenges and opportunities facing the field, including the integration of novel molecular and digital information sources into disease surveillance, the assimilation of such data into models of pathogen spread, and the increasing contribution of models to public health practice. We next consider emerging paradigms in causal inference for infectious diseases, ranging from approaches to evaluating vaccines and antimicrobial therapies to the task of ascribing clinical syndromes to etiologic microorganisms, an age-old problem transformed by our increasing ability to characterize human-associated microbiota. These areas represent an increasingly important component of epidemiology training programs for future generations of researchers and practitioners

Temporal similarity metrics for latent network reconstruction: The role of time-lag decay

When investigating the spreading of a piece of information or the diffusion of an innovation, we often lack information on the underlying propagation network. Reconstructing the hidden propagation paths based on the observed diffusion process is a challenging problem which has recently attracted attention from diverse research fields. To address this reconstruction problem, based on static similarity metrics commonly used in the link prediction literature, we introduce new node-node temporal similarity metrics. The new metrics take as input the time-series of multiple independent spreading processes, based on the hypothesis that two nodes are more likely to be connected if they were often infected at similar points in time. This hypothesis is implemented by introducing a time-lag function which penalizes distant infection times. We find that the choice of this time-lag strongly affects the metrics' reconstruction accuracy, depending on the network's clustering coefficient and we provide an extensive comparative analysis of static and temporal similarity metrics for network reconstruction. Our findings shed new light on the notion of similarity between pairs of nodes in complex networks

Inference for Ecological Dynamical Systems: A Case Study of Two Endemic Diseases

A Bayesian Markov chain Monte Carlo method is used to infer parameters for an open stochastic epidemiological model: the Markovian susceptible-infected-recovered (SIR) model, which is suitable for modeling and simulating recurrent epidemics. This allows exploring two major problems of inference appearing in many mechanistic population models. First, trajectories of these processes are often only partly observed. For example, during an epidemic the transmission process is only partly observable: one cannot record infection times. Therefore, one only records cases (infections) as the observations. As a result some means of imputing or reconstructing individuals in the susceptible cases class must be accomplished. Second, the official reporting of observations (cases in epidemiology) is typically done not as they are actually recorded but at some temporal interval over which they have been aggregated. To address these issues, this paper investigates the following problems. Parameter inference for a perfectly sampled open Markovian SIR is first considered. Next inference for an imperfectly observed sample path of the system is studied. Although this second problem has been solved for the case of closed epidemics, it has proven quite difficult for the case of open recurrent epidemics. Lastly, application of the statistical theory is made to measles and pertussis epidemic time series data from 60 UK cities