Caterina M. Scoglio - US grants

The objective of this proposed exploratory and potentially transformative research is to use complex network theory to model and analyze the spread of epidemics in rural regions, with special emphasis on the study of graph characteristics and dynamics, and their impact on the speed and direction of the epidemic.

The social and economic costs of epidemics may be less well understood today than ever, yet infection of only a few animals or humans can have serious implications for international trade and policies. Furthermore, the loss of far greater numbers of livestock or people is quite possible, with inherently
enormous social and economic costs. Moreover, methods for detecting and forecasting epidemics that may have worked in the past in urban or rural overseas regions may not apply to rural regions in the Plains states today.
The overarching goal of this research is to develop optimized guidelines that administrators can use to establish procedures and realign resources to help mitigate the effects of an outbreak in rural regions, caused by a malicious attack or by natural occurrences.

The research team will start working on the following four research tasks:
(1) collect empirical data on rural Kansas and create the underlying networks, (2) extend the underlying network to families of graphs and study the graph-theoretical metrics of those networks to predict their behavior and dynamics during an epidemic,
(3) create accurate and portable simulators running on PCs, and
(4) develop optimized guidelines to control outbreaks.

Intellectual merit. This research is intended to lead to scientific breakthroughs in complex network theory and analysis. In particular, families of networks will be analyzed to determine critical structures for the spread of epidemics. New metrics will be proposed to quantitatively measure the network robustness relative to epidemic spreading. Additionally, a new type of analysis for the rate at which an infection spreads will also be generated using weighted and asymmetric networks. This new analysis should provide greater accuracy in predicting the spread of an epidemic. This knowledge can then be incorporated into policies/plans to curb the spread of an infectious disease.

Broader impacts. This research is intended to have a broad impact on society and related research. For example, society will benefit by having more effective policies to decrease the effects of an epidemic. To clarify, in all cases, disease epidemics in human or animal populations may cause extensive social and economic losses. Being able to have an environment that is intrinsically robust to these type of attacks would provide a strong defense against malicious individuals as well as protection against natural events/disasters. Thus, the proposed work will foster interdisciplinary collaboration among rural sociologists and network experts. Finally, the research team will continue to mentor and recruit minorities and females into their research group, which is an interdisciplinary team.

The PI proposes to study several problems in geometric function theory that have as common underlying theme "conformal invariants" such as the hyperbolic and Kobayashi metric, harmonic measure, Green's functions, and modulus of path families. One such problem consists in studying dimensionality properties of p-Harmonic measure on domains beyond simply-connected ones. A second question deals with generalizations of the Chang-Marshall theorem in space, namely with exponential integrability properties for the trace of analytic functions, and their quasiregular counterparts in higher dimensions, when restricted to the boundary. A third problems studies iteration of analytic functions in one and several dimensions with a focus on the interplay between complex dynamics and the hyperbolic geometry of the unit disk in the complex plane and of the unit ball in higher dimensions.

This research will also draw on the properties of conformal invariants mentioned above to obtain concrete applications in the study of large networks. This is an area that has become more salient with the advent of the internet and the need to analyze large databases (so-called massive data-sets). One example that most people are familiar with is search-engines. The way internet searches work is through random processes that continually sample the web and periodically return averages and other statistics. The simplest such process is called a random crawler or walker and the mathematics that governs its behavior is derived from the study of conformal invariants in geometric function theory. The PI is conducting research that is expected to bring new tools to the task of comparing the behavior of such random processes to the geometry of the data-set. Because of the large applicability of such results the PI will also study the problem of epidemic outbreaks. In this context the PI has already obtained initial funding from the Center for Engagement and Community Development at Kansas State University for a joint project with Professor Scoglio in the Department of Electrical and Computing Engineering and Professor Schumm in the Department of Family Studies. Our team collected data in the city of Chanute, Kansas, and has already built a "contact" network, which is now being analyzed using the conformal invariants mentioned above. The ultimate goal is to provide the city of Chanute with a concrete set of directions that could help its city officials mitigate and manage an epidemic outbreak, especially one of zoonotic nature, originating on a farm.

This project advances the boundaries of network theory by analyzing spreading processes over multilayer and interconnected networks, which abound in nature and man-made infrastructures, and about which many interesting questions remain unanswered. Multilayer networks are an abstract representation where multiple types of links exist among nodes. Interconnected networks are an abstract representation where two or more simple networks, possibly with different and separate dynamics, are coupled to each other. The rationale for this project is that viral-spreading dynamics over multilayer and interconnected networks exhibit behaviors that cannot be attributed to single-network characteristics and play a highly relevant role in practice. The first part of the project extends the concept of the epidemic threshold value, which determines the conditions for outbreak, to the threshold curve for interconnected and multilayer networks. This research further develops measures for quantification of coupling strength in interconnected networks and seeks optimal interconnection designs for them. The second part of the project aims at predicting competitive spreading over multilayer networks and possible emergent phenomena. This research analyzes transient dynamics and steady-state behavior of multiple-virus competitive spreading in multilayer networks, and investigates competition policy in a game-theoretic framework. This project will use rigorous mathematical tools from network science, spectral graph theory, nonlinear dynamics, stochastic processes, control theory, game theory, and optimization.

Successful completion of this project will greatly advance the state of the art in network theory, with specific, relevant applications in communications and information technologies leading to more efficient and robust design of these complex networked systems. In a broader view, this research will contribute positively to society through a better understanding of how to prevent large-scale catastrophes, including cascading failures in power grids, financial contagions in market trading, infectious disease pandemics, and outbreaks of computer malware. Furthermore, the investigators will put forth significant effort to involve students from under-represented groups, and disseminate project outcomes in both general society and academia through publications, webinars, and public webpages.

The current outbreak of Ebola is the largest thus far, with more than 13,000 reported cases to date in West Africa. Secondary infections have also been reported in Spain and the United States, raising concerns about training of medical personnel and safety of the entire population. In an effort to stop the transmission of the virus within the USA during its very early stage, the Center for Disease Control and Prevention is adopting a "contact tracing" approach ? finding all individuals who have had close contact with an Ebola patient and monitoring the health status of those people for 21 days. This approach requires careful data collection, and is labor and cost intensive. A quantitative measure to evaluate the effectiveness of contact tracing is currently missing, due to the lack of previous experience of Ebola in the USA and insufficient supporting data from current cases. The goal of this project is to evaluate risk detection capabilities of contact tracing efforts for Ebola before the epidemic phase, and estimate the associated cost in potential scenarios. Not only will understanding the effectiveness of contact tracing be important for the current Ebola epidemic, but this project will also provide information for developing contact tracing guidelines and identifying critical circumstances hampering effective contact tracing in possible future epidemic threats.

This project will develop a network-based stochastic modeling framework of Ebola transmission for the local contact network of infected individuals (household, workplace, hospital, airplane, etc.). This simulation framework will allow investigators to synthesize scenarios and activities compatible with daily news about Ebola. "Missed- detection probability" versus "contact tracing cost" will be estimated through extensive simulations. Missed-detection probability, in this case, denotes the probability that a secondary infected individual is not detected before transmitting the infection to others. The team will perform sensitivity analysis to account for inherent uncertainties in different scenarios. The in-silico analysis will allow the following: 1) test performance and associated cost of contact tracing efforts in multiple realistic scenarios and different parameter spaces, 2) propose contact tracing guidelines under limited resources, and 3) identify critical circumstances for which contact tracing is not fully effective. A successful implementation of this project will have immediate benefits to USA public health and security against infectious disease.

Modern approaches to data analysis often involve network structures. For example, the spread of an epidemic in a specific population can be described using a contact network representing the nature and strength of interpersonal interactions among individuals. Historically, these models were intractable due to the complexity of individual behavior and, therefore, many early disease models utilized simplified representations involving population averages and statistics. By differentiating individuals, network models carry a large amount of additional information that has become more accessible thanks to increasingly powerful computer processors and the advent of fast computational algorithms. This project develops new mathematical theories and computational algorithms to capture the essential features of networks and applies them to models in epidemiology. Results from this project will allow researchers to identify a number of valuable patterns in the data, including the subpopulations at highest risk, vulnerable transmission pathways, and effective mitigation strategies.

The investigator and his colleagues study the mathematical concept of p-modulus on networks, focusing on the analysis of theoretical properties, the development of numerical algorithms, and the study of applications to the spread of diseases in contact networks. This is an interdisciplinary project intended to enhance both the theoretical understanding of the ways in which diseases spread in an interconnected network of individuals or sub-populations, and the computational tools available to researchers interested in modeling, simulating, and predicting the behavior of epidemics. The theory of p-modulus was originally developed in the field of complex analysis and has a connection to the concept of effective resistance in the context of electrical networks. The p-modulus provides a method for quantifying the richness of a family of walks: families of many short walks have a larger modulus than families of few long ones. Therefore, the flexibility of p-modulus provides a means for extracting fine structure characteristics of linked data.

This EArly-concept Grant for Exploratory Research (EAGER) project will generate simulated data to model the behaviors of the interdependent beef production system and transportation infrastructure in southwestern Kansas, with due consideration of key social and economic factors. This process involves: i) modeling of the system as a multilayer network; ii) designing of an agent-based model incorporating all collected data and considering key social and economic aspects; iii) assessment of interdependencies between the beef production and transportation infrastructures, iv) evaluation of different scenarios and their impact on the infrastructure performance. The generated data will be organized and publicly shared with the final goal of increasing the understanding of these coupled systems. Benefits of this work include improved understanding of how to prevent and contain risks to these systems, thus contributing to the goal of greater safety and economic viability. Mentoring and training of a graduate student in the conduct of interdisciplinary research is an important component of the research. Project data and software will be publicly shared through websites and results disseminated through academic conferences and journals. The Center for Engagement and Community Development of Kansas State University will be utilized to distribute project results to target stakeholder audiences through the organization of a workshop in a critical location for the beef industry.

From a theoretical perspective, the expected outcomes will provide novel insights into the structural characteristics and the interdependencies of coupled infrastructures. New methods and models will be developed and made publicly available for scientists in the field to use in other regions and other contexts. From an application perspective, the data generated in this project will advance current knowledge of the beef production and transportation systems. Furthermore, the significant economic and social aspects of these interdependent systems will provide foundational elements for cross-disciplinary analysis in the domains of network science and social organization.

With COVID-19, the world has experienced the most significant pandemic of contemporary history. In an effort to reduce the virus transmission, different mitigation strategies have been proposed and implemented. In this situation, models of disease transmission have emerged as a key tool to predict current and future characteristics of COVID-19 spreading, with or without the implementation of mitigation strategies, and to guide policymaking decisions. Models however are accurate predictors if they are built upon reliable data and evidence-supported assumptions. Large swings in model predictions can be imputed to assumptions not supported by data or evidence, with consequences on the model reliability. One typical assumption is the exponential distribution of the transition times of individuals between different states of disease (i.e., compartments that mark individuals as susceptible, exposed, infected, and recovered). However, recent observations of COVID-19 data, highlight non-exponential distributions for some critical transition times, such as the infectious period. This directly impacts the accuracy of the models. With this in mind, the goals of this project are to: 1) develop network-based compartmental meta-population models that accept arbitrary distributions for the transition times of the individual between different compartments; 2) develop rigorous methodologies to estimate unknown parameters of the model using stochastic optimization methods; 3) determine contact networks tailored for regions receiving lower attention, such as rural areas. Successful completion of this project will provide benefits to the USA public health, in particular to the analysis and monitoring of COVID-19. More accurate model-based testing of mitigation strategies will help public health officials to select strategies and to gather trust and support around mitigation policies. This way, health policymakers, modelers, and the general public will share common goals toward eventually stopping COVID-19.

In this project, the team will develop non-Markovian models that are driven by empirically determined distributions of transition times as suggested by recent results from analyzing data for COVID-19, highlighting the non-exponential distributions for some critical transition times. This novel aspect of our proposed model produces more accurate estimates of the current and future outbreak characteristics. For example, we can estimate the number of undetected infected people more accurately than models assuming the exponential distribution. Furthermore, as any model has known and unknown parameters, the estimation of the unknown parameters is critical to the model accuracy. To estimate the unknown parameters for this COVID-19 pandemic in the USA, we plan to use epidemic curves generated using the meta-population model and stochastic optimization techniques. The increased model accuracy produces better estimates of the outbreak characteristics and in turn better predictions of the mitigation policies effectiveness. Finally, any network-based model requires to input of a network representing contacts or movements. While these contact networks are available for some cities affected by the pandemic, rural regions have been less analyzed, despite occasionally being hot spots. The team will work to determine data-driven contact networks for certain rural areas of interest, for which we will apply and test our modeling approaches.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.