Collaborative Research: A comprehensive approach to modeling, learning, analysis and control of epidemic processes over time-varying and multi-layer networks

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Numerous natural and engineered systems consist of underlying networked components over which dynamical processes evolve. Examples include the spread of infectious disease processes over human contact and international travel networks, the propagation of peak traffic phenomenon over the transportation infrastructure, the spread of viruses or worms over computer networks, and sharing and re-sharing of posted articles, tweets, or rumors over social media platforms. Engineered systems are increasingly interconnected over various levels of both local and large-scale networks. Developing a stronger understanding at fundamental and analytical levels of how viral processes evolve across different network structures, the rates at which they spread, how the occurrence of multiple viral types and multiple network layers affect the spread process dynamics, and how these processes can be suppressed and/or mitigated by employing deliberate control policies will greatly impact the health, safety and security of a vast variety of systems around the globe. The spread of COVID-19 has clearly had broad implications for the health of people on all six inhabited continents as well as the world's economy. The research proposed herein will substantially enhance our understanding of epidemics such as COVID-19 and lead to general policy guidelines that will help limit the loss of human life and reduce the economic impacts of the virus. The methods to be developed in this project will be beneficial for battling subsequent epidemic outbreaks, a second wave of COVID-19, and on a broader scale general viral process. Throughout this project the PIs will build on their past experiences to make every effort towards recruiting and mentoring students from under-represented groups, and will establish outreach efforts by including undergraduate and local high school student researchers.Although the dynamics of epidemic processes over networks have been extensively studied for the past 10-15 years, past work has been focused largely on SIS and SIR processes spreading over static networks. In the proposed project, our focus will be on modeling, analysis and control of dynamic epidemic processes over large and possibly time-varying networks, comprised of multiple layers at multiple scales. We will specifically consider data-informed modeling and analysis of SAIRS (susceptible-asymptomatic-infected-recovered-susceptible) processes over time-varying networks; this work will include stability and equilibria analysis of the nonlinear dynamics of networked epidemic process models, network structure identification, estimation of parameters and structure from imperfect and non-random data, and development of realizable control strategies from the agent level to societal levels. The research proposed will draw on and contribute to wide-ranging foundational results in mathematical modeling and analysis of infectious diseases, time-varying nonlinear and linear analysis methods, optimization and control-theoretic policy formulation, network inference and analysis, sequential sampling strategies with stochastic sample constraints, and mean-field games over networks.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.