In response to the ongoing challenges posed by the COVID-19 pandemic and to be well-prepared for future epidemics, the project made significant progress in developing robust, data-informed mechanisms for epidemic estimation, forecasting, and control. In the following, the key achievements and advancements across three interconnected scientific objectives have been summarized.
Firstly, the project developed a feedback mechanism for enabling closed-loop, data-informed epidemic monitoring that is robust to model and data uncertainties. This goal was achieved by developing innovative approaches that address the limitations of existing observer design techniques. Specifically, a nonlinear Luenberger-like observer was proposed that combines feedback and feedforward injection of measured data, overcoming challenges posed by nonlinearities and sparsity in compartmental epidemic models. To further enhance robustness against uncertainties, two novel approaches were developed for state estimation of uncertain nonlinear systems. The first approach leveraged physics-informed learning to design a Kazantzis-Kravaris/Luenberger (KKL) observer, utilizing neural networks to learn an injective map and its inverse. This learning-based KKL observer provides global guarantees for robust state estimation, effectively handling measurement and model uncertainties, as well as learning errors. The second approach employed zonotopic filtering to address bounded uncertainties, estimating a compact set guaranteed to contain the true state of the epidemic model. By integrating these approaches, the algorithm obtained both an estimate of the epidemic state and a formal guarantee of the estimate’s accuracy, which proved crucial in designing robust feedback control mechanisms to mitigate epidemic spread.
Secondly, dynamic optimal control algorithms were developed based on the previous epidemic monitoring methods to facilitate effective policy recommendations during epidemic outbreaks. The project developed a unified framework for epidemic control that integrates robust state estimation with optimal control techniques. This approach addresses uncertainties in epidemic models by proposing a robust output feedback control mechanism using a nonlinear observer, effectively overcoming the limitations of traditional methods like the extended Kalman filter, which provides only local guarantees. The effectiveness of the proposed method was demonstrated using a modified SIR model, showing its ability to mitigate uncertainties and optimize control measures such as lockdowns, vaccination rates, and testing capacities. The optimal policies generated by this approach minimize a cost function that accounts for various epidemic compartments, resulting in significant reductions in infections and deaths.
Lastly, the project integrated geographic and demographic heterogeneities into the epidemic monitoring loop using large-scale networked and metapopulation epidemic models. A closed-loop monitoring algorithm, known as a parametrization-free nonlinear observer, was developed for estimating the state of large-scale networked epidemic processes that incorporate geographic heterogeneities. This advancement addressed the limitations of the techniques and methods developed for the first objective, which were not suitable for large-scale systems with network-embedded nonlinearities. In this objective, a distributed estimation approach was developed that provides a state estimate of a large-scale system within a prescribed time by dividing the computational tasks among multiple sensor nodes. This development presents exciting opportunities for mathematical modeling and analysis.
To conclude, the work performed in this project represents substantial progress in the field of epidemic control and management. The development of robust state estimation techniques, the integration of geographic and demographic heterogeneities, and the creation of a unified framework for epidemic control all contribute to more reliable, data-informed epidemic modeling and policy-making. These achievements pave the way for more effective responses to future epidemic outbreaks, with the potential to save lives and reduce the socioeconomic impact of such crises.
