Stephen Eubank

Testing for nonlinearity in time series: the method of surrogate data

We describe a statistical approach for identifying nonlinearity in time series. The method first specifies some linear process as a null hypothesis, then generates surrogate data sets which are consistent with this null hypothesis, and finally computes a discriminating statistic for the original and for each of the surrogate data sets. If the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data, then the null hypothesis is rejected and nonlinearity is detected. We discuss various null hypotheses and discriminating statistics. The method is demonstrated for numerical data generated by known chaotic systems, and applied to a number of experimental time series which arise in the measurement of superfluids, brain waves, and sunspots; we evaluate the statistical significance of the evidence for nonlinear structure in each case, and illustrate aspects of the data which this approach identifies.

Modelling disease outbreaks in realistic urban social networks

Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. Here we explore the use of dynamic bipartite graphs to model the physical contact patterns that result from movements of individuals between specific locations. The graphs are generated by large-scale individual-based urban traffic simulations built on actual census, land-use and population-mobility data. We find that the contact network among people is a strongly connected small-world-like graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we then analyse the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.

Modeling targeted layered containment of an influenza pandemic in the United States

Planning a response to an outbreak of a pandemic strain of influenza is a high public health priority. Three research groups using different individual-based, stochastic simulation models have examined the consequences of intervention strategies chosen in consultation with U.S. public health workers. The first goal is to simulate the effectiveness of a set of potentially feasible intervention strategies. Combinations called targeted layered containment (TLC) of influenza antiviral treatment and prophylaxis and nonpharmaceutical interventions of quarantine, isolation, school closure, community social distancing, and workplace social distancing are considered. The second goal is to examine the robustness of the results to model assumptions. The comparisons focus on a pandemic outbreak in a population similar to that of Chicago, with ≈8.6 million people. The simulations suggest that at the expected transmissibility of a pandemic strain, timely implementation of a combination of targeted household antiviral prophylaxis, and social distancing measures could substantially lower the illness attack rate before a highly efficacious vaccine could become available. Timely initiation of measures and school closure play important roles. Because of the current lack of data on which to base such models, further field research is recommended to learn more about the sources of transmission and the effectiveness of social distancing measures in reducing influenza transmission.

EpiSimdemics: an efficient algorithm for simulating the spread of infectious disease over large realistic social networks

Preventing and controlling outbreaks of infectious diseases such as pandemic influenza is a top public health priority. We describe EpiSimdemics - a scalable parallel algorithm to simulate the spread of contagion in large, realistic social contact networks using individual-based models. EpiSimdemics is an interaction-based simulation of a certain class of stochastic reaction-diffusion processes. Straightforward simulations of such process do not scale well, limiting the use of individual-based models to very small populations. EpiSimdemics is specifically designed to scale to social networks with 100 million individuals. The scaling is obtained by exploiting the semantics of disease evolution and disease propagation in large networks. We evaluate an MPI-based parallel implementation of EpiSimdemics on a mid-sized HPC system, demonstrating that EpiSimdemics scales well. EpiSimdemics has been used in numerous sponsor defined case studies targeted at policy planning and course of action analysis, demonstrating the usefulness of EpiSimdemics in practical situations.

An analytic approach to practical state space reconstruction

We study the three standard methods for reconstructing a state space from a time series: delays, derivatives, and principal components. We derive a closed-form solution to principal component analysis in the limit of small window widths. This solution explains the relationship between delays, derivatives, and principal components, it shows how the singular spectrum scales with dimension and delay time, and it explains why the eigenvectors resemble the Legendre polynomials. Most importantly, the solution allows us to derive a guideline for choosing a good window width. Unlike previous suggestions, this guideline is based on first principles and simple quantities. We argue that discrete Legendre polynomials provide a quick and not-so-dirty substitute for principal component analysis, and that they are a good practical method for state space reconstruction.

Modeling the Impact of Interventions on an Epidemic of Ebola in Sierra Leone and Liberia

Background: An Ebola outbreak of unparalleled size is currently affecting several countries in West Africa, and international efforts to control the outbreak are underway. However, the efficacy of these interventions, and their likely impact on an Ebola epidemic of this size, is unknown. Forecasting and simulation of these interventions may inform public health efforts. Methods: We use existing data from Liberia and Sierra Leone to parameterize a mathematical model of Ebola and use this model to forecast the progression of the epidemic, as well as the efficacy of several interventions, including increased contact tracing, improved infection control practices, the use of a hypothetical pharmaceutical intervention to improve survival in hospitalized patients. Findings: Model forecasts until Dec. 31, 2014 show an increasingly severe epidemic with no sign of having reached a peak. Modeling results suggest that increased contact tracing, improved infection control, or a combination of the two can have a substantial impact on the number of Ebola cases, but these interventions are not sufficient to halt the progress of the epidemic. The hypothetical pharmaceutical intervention, while impacting mortality, had a smaller effect on the forecasted trajectory of the epidemic. Interpretation: Near-term, practical interventions to address the ongoing Ebola epidemic may have a beneficial impact on public health, but they will not result in the immediate halting, or even obvious slowing of the epidemic. A long-term commitment of resources and support will be necessary to address the outbreak.

Mixing patterns between age groups in social networks

We present a method for estimating transmission matrices that describe the mixing and the probability of infection between age groups. Transmission matrices can be used to estimate age-dependent forces of infection in age-structured, compartmental models for the study of infectious diseases. We analyze the social network generated by the synthetic population of Portland and extract mixing patterns. Our results show that the mixing within the population consists of two groups, children and adults. Children interact most frequently with other children close to their own age, while adults interact with a wider range of age groups and the durations of typical adult contacts are shorter than typical contacts between children. Furthermore, the transmission matrix shows that children are more likely to acquire infection than adults.

What Factors Might Have Led to the Emergence of Ebola in West Africa

An Ebola outbreak of unprecedented scope emerged in West Africa in December 2013 and presently continues unabated in the countries of Guinea, Sierra Leone, and Liberia. Ebola is not new to Africa, and outbreaks have been confirmed as far back as 1976. The current West African Ebola outbreak is the largest ever recorded and differs dramatically from prior outbreaks in its duration, number of people affected, and geographic extent. The emergence of this deadly disease in West Africa invites many questions, foremost among these: why now, and why in West Africa? Here, we review the sociological, ecological, and environmental drivers that might have influenced the emergence of Ebola in this region of Africa and its spread throughout the region. Containment of the West African Ebola outbreak is the most pressing, immediate need. A comprehensive assessment of the drivers of Ebola emergence and sustained human-to-human transmission is also needed in order to prepare other countries for importation or emergence of this disease. Such assessment includes identification of country-level protocols and interagency policies for outbreak detection and rapid response, increased understanding of cultural and traditional risk factors within and between nations, delivery of culturally embedded public health education, and regional coordination and collaboration, particularly with governments and health ministries throughout Africa. Public health education is also urgently needed in countries outside of Africa in order to ensure that risk is properly understood and public concerns do not escalate unnecessarily. To prevent future outbreaks, coordinated, multiscale, early warning systems should be developed that make full use of these integrated assessments, partner with local communities in high-risk areas, and provide clearly defined response recommendations specific to the needs of each community.

Scalable, efficient epidemiological simulation

We describe the design and implementation of a system for simulating the spread of disease among individuals in a large urban population over the course of several weeks. In contrast to traditional approaches, we do not assume uniform mixing among large sub-populations or split the population into spatial or demographic subpopulations determined a priori. Instead, we rely on empirical estimates of the social network, or contact patterns, that are produced by TRANSIMS, a large-scale simulation of transportation systems.

Systems modeling of molecular mechanisms controlling cytokine-driven CD4+ T cell differentiation and phenotype plasticity.

Differentiation of CD4+ T cells into effector or regulatory phenotypes is tightly controlled by the cytokine milieu, complex intracellular signaling networks and numerous transcriptional regulators. We combined experimental approaches and computational modeling to investigate the mechanisms controlling differentiation and plasticity of CD4+ T cells in the gut of mice. Our computational model encompasses the major intracellular pathways involved in CD4+ T cell differentiation into T helper 1 (Th1), Th2, Th17 and induced regulatory T cells (iTreg). Our modeling efforts predicted a critical role for peroxisome proliferator-activated receptor gamma (PPARγ) in modulating plasticity between Th17 and iTreg cells. PPARγ regulates differentiation, activation and cytokine production, thereby controlling the induction of effector and regulatory responses, and is a promising therapeutic target for dysregulated immune responses and inflammation. Our modeling efforts predict that following PPARγ activation, Th17 cells undergo phenotype switch and become iTreg cells. This prediction was validated by results of adoptive transfer studies showing an increase of colonic iTreg and a decrease of Th17 cells in the gut mucosa of mice with colitis following pharmacological activation of PPARγ. Deletion of PPARγ in CD4+ T cells impaired mucosal iTreg and enhanced colitogenic Th17 responses in mice with CD4+ T cell-induced colitis. Thus, for the first time we provide novel molecular evidence in vivo demonstrating that PPARγ in addition to regulating CD4+ T cell differentiation also plays a major role controlling Th17 and iTreg plasticity in the gut mucosa.