Background: Ebola virus disease (EVD) has generated a large epidemic in West Africa since December 2013. This mini-review is aimed to clarify and illustrate different theoretical concepts of infectiousness in order to compare the infectiousness across different communicable diseases including EVD.

Methods: We employed a transmission model that rests on the renewal process in order to clarify theoretical concepts on infectiousness, namely the basic reproduction number, R₀, which measures the infectiousness per generation of cases, the force of infection (i.e. the hazard rate of infection), the intrinsic growth rate (i.e. infectiousness per unit time) and the per-contact probability of infection (i.e. infectiousness per effective contact).

Results: Whereas R₀ of EVD is similar to that of influenza, the growth rate (i.e. the measure of infectiousness per unit time) for EVD was shown to be comparatively lower than that for influenza. Moreover, EVD and influenza differ in mode of transmission whereby the probability of transmission per contact is lower for EVD compared to that of influenza.

Conclusions: The slow spread of EVD associated with the need for physical contact with body fluids supports social distancing measures including contact tracing and case isolation. Descriptions and interpretations of different variables quantifying infectiousness need to be used clearly and objectively in the scientific community and for risk communication.

Controlling complex networks has become a forefront research area in network science and engineering. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes. However, in realistic situations not every node is accessible or can be externally driven, raising the fundamental issue of control efficacy: if driving signals are applied to an arbitrary subset of nodes, how many other nodes can be controlled? We develop a framework to determine the control efficacy for undirected networks of arbitrary topology. Mathematically, based on non-singular transformation, we prove a theorem to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver nodes. Physically, we develop the picture of diffusion that views the control process as a signal diffused from input signals to the set of controllable nodes. The combination of mathematical theory and physical reasoning allows us not only to determine the control efficacy for model complex networks and a large number of empirical networks, but also to uncover phenomena in network control, e.g., hub nodes in general possess lower control centrality than an average node in undirected networks.

A challenging problem in network science is to control complex networks. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state is measured by the minimum number of required driver nodes. However, if we implement actual control by imposing input signals on the minimum set of driver nodes, an unexpected phenomenon arises: due to computational or experimental error there is a great probability that convergence to the final state cannot be achieved. In fact, the associated control cost can become unbearably large, effectively preventing actual control from being realized physically. The difficulty is particularly severe when the network is deemed controllable with a small number of drivers. Here we develop a physical controllability framework based on the probability of achieving actual control. Using a recently identified fundamental chain structure underlying the control energy, we offer strategies to turn physically uncontrollable networks into physically controllable ones by imposing slightly augmented set of input signals on properly chosen nodes. Our findings indicate that, although full control can be theoretically guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control cost to achieve physical control.

In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.

Network reconstruction is a fundamental problem for understanding many complex systems with unknown interaction structures. In many complex systems, there are indirect interactions between two individuals without immediate connection but with common neighbors. Despite recent advances in network reconstruction, we continue to lack an approach for reconstructing complex networks with indirect interactions. Here we introduce a two-step strategy to resolve the reconstruction problem, where in the first step, we recover both direct and indirect interactions by employing the Lasso to solve a sparse signal reconstruction problem, and in the second step, we use matrix transformation and optimization to distinguish between direct and indirect interactions. The network structure corresponding to direct interactions can be fully uncovered. We exploit the public goods game occurring on complex networks as a paradigm for characterizing indirect interactions and test our reconstruction approach. We find that high reconstruction accuracy can be achieved for both homogeneous and heterogeneous networks, and a number of empirical networks in spite of insufficient data measurement contaminated by noise. Although a general framework for reconstructing complex networks with arbitrary types of indirect interactions is yet lacking, our approach opens new routes to separate direct and indirect interactions in a representative complex system.

The ongoing Zika virus (ZIKV) epidemic in the Americas poses a major global public health emergency. While ZIKV is transmitted from human to human by bites of Aedes mosquitoes, recent evidence indicates that ZIKV can also be transmitted via sexual contact with cases of sexually transmitted ZIKV reported in Argentina, Canada, Chile, France, Italy, New Zealand, Peru, Portugal, and the USA. Yet, the role of sexual transmission on the spread and control of ZIKV infection is not well-understood. We introduce a mathematical model to investigate the impact of mosquito-borne and sexual transmission on the spread and control of ZIKV and calibrate the model to ZIKV epidemic data from Brazil, Colombia, and El Salvador. Parameter estimates yielded a basic reproduction number R_0 = 2.055 (95% CI: 0.523–6.300), in which the percentage contribution of sexual transmission is 3.044% (95% CI: 0.123–45.73). Our sensitivity analyses indicate that R_0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. Prevention and control efforts against ZIKV should target both the mosquito-borne and sexual transmission routes.

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.

Background: Hemorrhagic fever with renal syndrome (HFRS), a rodent-borne infectious disease, is one of the most serious public health threats in China. Increasing our understanding of the spatial and temporal patterns of HFRS infections could guide local prevention and control strategies.

Methodology/Principal Findings: We employed statistical models to analyze HFRS case data together with environmental data from the Dongting Lake district during 2005–2010. Specifically, time-specific ecologic niche models (ENMs) were used to quantify and identify risk factors associated with HFRS transmission as well as forecast seasonal variation in risk across geographic areas. Results showed that the Maximum Entropy model provided the best predictive ability (AUC = 0.755). Time-specific Maximum Entropy models showed that the potential risk areas of HFRS significantly varied across seasons. High-risk areas were mainly found in the southeastern and southwestern areas of the Dongting Lake district. Our findings based on models focused on the spring and winter seasons showed particularly good performance. The potential risk areas were smaller in March, May and August compared with those identified for June, July and October to December. Both normalized difference vegetation index (NDVI) and land use types were found to be the dominant risk factors.

Conclusions/Significance: Our findings indicate that time-specific ENMs provide a useful tool to forecast the spatial and temporal risk of HFRS.

Background:
Pandemic influenza is said to 'shift mortality' to younger age groups; but also to spare a subpopulation of the elderly population. Does one of these effects dominate? Might this have important ramifications?

Methods: We estimated age-specific excess mortality rates for all-years for which data were available in the 20th century for Australia, Canada, France, Japan, the UK, and the USA for people older than 44 years of age. We modeled variation with age, and standardized estimates to allow direct comparison across age groups and countries. Attack rate data for four pandemics were assembled.

Results: For nearly all seasons, an exponential model characterized mortality data extremely well. For seasons of emergence and a variable number of seasons following, however, a subpopulation above a threshold age invariably enjoyed reduced mortality. 'Immune escape', a stepwise increase in mortality among the oldest elderly, was observed a number of seasons after both the A(H2N2) and A(H3N2) pandemics. The number of seasons from emergence to escape varied by country. For the latter pandemic, mortality rates in four countries increased for younger age groups but only in the season following that of emergence. Adaptation to both emergent viruses was apparent as a progressive decrease in mortality rates, which, with two exceptions, was seen only in younger age groups. Pandemic attack rate variation with age was estimated to be similar across four pandemics with very different mortality impact.

Conclusions: In all influenza pandemics of the 20th century, emergent viruses resembled those that had circulated previously within the lifespan of then-living people. Such individuals were relatively immune to the emergent strain, but this immunity waned with mutation of the emergent virus. An immune subpopulation complicates and may invalidate vaccine trials. Pandemic influenza does not 'shift' mortality to younger age groups; rather, the mortality level is reset by the virulence of the emerging virus and is moderated by immunity of past experience. In this study, we found that after immune escape, older age groups showed no further mortality reduction, despite their being the principal target of conventional influenza vaccines. Vaccines incorporating variants of pandemic viruses seem to provide little benefit to those previously immune. If attack rates truly are similar across pandemics, it must be the case that immunity to the pandemic virus does not prevent infection, but only mitigates the consequences.

Background:
Theory suggests that individual behavioral responses impact the spread of flu-like illnesses, but this has been difficult to empirically characterize. Social distancing is an important component of behavioral response, though analyses have been limited by a lack of behavioral data. Our objective is to use media data to characterize social distancing behavior in order to empirically inform explanatory and predictive epidemiological models.

Methods:
We use data on variation in home television viewing as a proxy for variation in time spent in the home and, by extension, contact. This behavioral proxy is imperfect but appealing since information on a rich and representative sample is collected using consistent techniques across time and most major cities. We study the April-May 2009 outbreak of A/H1N1 in Central Mexico and examine the dynamic behavioral response in aggregate and contrast the observed patterns of various demographic subgroups. We develop and calibrate a dynamic behavioral model of disease transmission informed by the proxy data on daily variation in contact rates and compare it to a standard (non-adaptive) model and a fixed effects model that crudely captures behavior.

Results:
We find that after a demonstrable initial behavioral response (consistent with social distancing) at the onset of the outbreak, there was attenuation in the response before the conclusion of the public health intervention. We find substantial differences in the behavioral response across age subgroups and socioeconomic levels. We also find that the dynamic behavioral and fixed effects transmission models better account for variation in new confirmed cases, generate more stable estimates of the baseline rate of transmission over time and predict the number of new cases over a short horizon with substantially less error.

Conclusions:
Results suggest that A/H1N1 had an innate transmission potential greater than previously thought but this was masked by behavioral responses. Observed differences in behavioral response across demographic groups indicate a potential benefit from targeting social distancing outreach efforts.