Special Section on Mathematical Modeling, Analysis, and Control of Epidemics

Abstract

This special section of the SIAM Journal on Control and Optimization (SICON) addresses the fundamental challenges inherent in the mathematical modeling, analysis, and control of epidemics. The ongoing COVID-19 pandemic has brought into the spotlight the critical importance of understanding complex epidemic processes. Yet the modeling, analysis, estimation, and control of these processes presents several formidable challenges. Epidemics inherently exhibit nonlinear dynamics as they spread through populations, requiring analytical techniques that can accurately capture both the transient and the steady-state aspects of the disease. Furthermore, careful attention must be paid to the resolution at which to model the epidemics, ranging from coarse mass-action models to metapopulation and individual-level models. Each of these approaches provides different insights and challenges for analysis and control. Models that operate at finer resolutions will also come with an increase in complexity, necessitating tractable abstractions ranging from mean-field models to deterministic and stochastic ODEs and PDEs. In the context of estimation of epidemics, the key challenge is to determine the important parameters of the epidemic (often in real time) based on data gathered from the affected population, in conjunction with dynamical models of the spreading process. Finally, formulating techniques to optimally control and address an ongoing epidemic (through either a centralized intervention, decentralized incentive mechanisms, or resource allocation policies) remains a critical challenge. The special section gathers contributions from the intersection of the fields of systems and control theory and the mathematical study of epidemic spread processes. A total of 16 papers represents a wide range of topics in modeling, identification, dynamic analysis, control, and optimization. Regarding modeling problems, the section covers contributions on Polya contagion networks, networked bivirus epidemic models, and age-differentiated compartmental models. For dynamic analysis, the section highlights contributions on explicit solutions and control design for simplified models, convergence and equilibria analysis, as well as the role of delays and saturations in closed loop settings. For identification and estimation problems, contributions are offered on the identifiability of model parameters and on parameter estimation using limited measurements. Most of the contributed articles focus on control design, optimization, and game theoretic problems. Centralized and distributed strategies are proposed. Actuation mechanisms include edge deletion, test allocation, optimal incentives, optimal switching between lockdown and opening the economy, screening, and curing policies. We believe this special section presents an excellent cross section of current research and hope that it will be of great interest to the broad readership of SICON. We offer our deepest thanks to all authors who submitted their work and to all reviewers who contributed their time and energy to the peer-review process. We would also like to thank the proficient and timely editorial support provided by Brian Fauth and the insightful and gracious advice that we received from the SICON Editor-in-Chief George Yin. Carolyn Beck University of Illinois at Urbana-Champaign Francesco Bullo University of California, Santa Barbara Giacomo Como Politecnico di Torino Kimon Drakopoulos University of Southern California Dang H. Nguyen University of Alabama Cameron Nowzari George Mason University Victor M. Preciado University of Pennsylvania Shreyas Sundaram Purdue University, Guest editors