Periodic Reporting for period 1 - REACT (Reliable Epidemic monitoring And Control under geographic and demographic heTerogeneities)
Reporting period: 2022-09-01 to 2024-08-31
The COVID-19 pandemic highlighted the critical need for robust and timely epidemic monitoring systems. Traditional methods often proved inadequate, unable to accurately predict disease outbreaks or provide robust and actionable insights for policymakers. These limitations stem from the inherent complexities of epidemic dynamics, including nonlinearity and heterogeneity, and the challenges of effectively handling model and data uncertainties. Moreover, the epidemic monitoring process is fraught with uncertainties, as human behavior influences every aspect of an epidemic, from the spread of the disease to the accuracy of daily reported data.
This project aims to develop a novel approach to address these shortcomings by integrating physics-informed neural networks (PINNs) with robust system-theoretic tools. PINNs offer a powerful framework for estimating unknown nonlinear functions, such as disease transmission rates, by leveraging both physical models and historical epidemiological data. Combining PINNS with rigorous system-theoretic analysis, the proposed approach enables more accurate and reliable modeling of epidemic spread, which is essential for effective decision-making.
By incorporating a closed-loop structure of nonlinear observers (state estimators), the project aims to create a self-correcting system. Predictions generated by the PINN-based observer can be compared to real-world data, allowing for continuous refinement of the model and adaptation to changing circumstances in the epidemic process. For instance, both social adaptations to virus spread and virus mutations affect the disease transmission rates. Therefore, by continuously adapting and timely predicting the changing parameters of epidemic models, our feedback mechanism enhances the robustness and accuracy of the monitoring system, ensuring that it remains relevant and effective even in the face of complexity and uncertainty. The information derived from the PINN-based observer is utilized by an optimal controller to develop evidence-based policy recommendations. By considering socio-economic constraints and geographic and demographic heterogeneities, the controller can help to balance the need for epidemic mitigation with the broader societal and economic impacts of interventions.
The project's ultimate goal is to develop a comprehensive and scalable framework for epidemic monitoring and control that can be applied to a wide range of infectious diseases. By addressing the limitations of existing approaches, this work has the potential to significantly improve our ability to respond to future public health crises and protect public health.
This project aims to develop a novel approach to address these shortcomings by integrating physics-informed neural networks (PINNs) with robust system-theoretic tools. PINNs offer a powerful framework for estimating unknown nonlinear functions, such as disease transmission rates, by leveraging both physical models and historical epidemiological data. Combining PINNS with rigorous system-theoretic analysis, the proposed approach enables more accurate and reliable modeling of epidemic spread, which is essential for effective decision-making.
By incorporating a closed-loop structure of nonlinear observers (state estimators), the project aims to create a self-correcting system. Predictions generated by the PINN-based observer can be compared to real-world data, allowing for continuous refinement of the model and adaptation to changing circumstances in the epidemic process. For instance, both social adaptations to virus spread and virus mutations affect the disease transmission rates. Therefore, by continuously adapting and timely predicting the changing parameters of epidemic models, our feedback mechanism enhances the robustness and accuracy of the monitoring system, ensuring that it remains relevant and effective even in the face of complexity and uncertainty. The information derived from the PINN-based observer is utilized by an optimal controller to develop evidence-based policy recommendations. By considering socio-economic constraints and geographic and demographic heterogeneities, the controller can help to balance the need for epidemic mitigation with the broader societal and economic impacts of interventions.
The project's ultimate goal is to develop a comprehensive and scalable framework for epidemic monitoring and control that can be applied to a wide range of infectious diseases. By addressing the limitations of existing approaches, this work has the potential to significantly improve our ability to respond to future public health crises and protect public health.
In response to the ongoing challenges posed by the COVID-19 pandemic and to be well-prepared for future epidemics, we have made significant progress in developing robust, data-informed mechanisms for epidemic estimation, forecasting, and control. In the following, we summarize our key achievements and advancements across three interconnected scientific objectives.
Firstly, we designed a feedback mechanism for enabling closed-loop, data-informed epidemic monitoring that is robust to model and data uncertainties. We have fully achieved this goal by developing innovative approaches that address the limitations of existing observer design techniques. Specifically, we proposed a nonlinear Luenberger-like observer 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, we developed two novel approaches for state estimation in 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. Our 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, we 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, we developed dynamic optimal control algorithms based on our previous epidemic monitoring methods to facilitate effective policy recommendations during epidemic outbreaks. We 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. We demonstrated the effectiveness of our method 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, we aimed to integrate geographic and demographic heterogeneities into the epidemic monitoring loop using large-scale networked and metapopulation epidemic models. We made significant progress by developing a closed-loop monitoring algorithm, known as a parametrization-free nonlinear observer, 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 our first objective, which were not suitable for large-scale systems with network-embedded nonlinearities. Although this objective is only partly achieved, our future work will focus on further integrating both geographic and demographic heterogeneities into epidemic models using large-scale, multi-layered architectures. This presents exciting opportunities for mathematical modeling and analysis, though it also poses significant challenges in terms of the computational complexity required to monitor such systems.
To conclude, our work 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.
Firstly, we designed a feedback mechanism for enabling closed-loop, data-informed epidemic monitoring that is robust to model and data uncertainties. We have fully achieved this goal by developing innovative approaches that address the limitations of existing observer design techniques. Specifically, we proposed a nonlinear Luenberger-like observer 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, we developed two novel approaches for state estimation in 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. Our 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, we 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, we developed dynamic optimal control algorithms based on our previous epidemic monitoring methods to facilitate effective policy recommendations during epidemic outbreaks. We 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. We demonstrated the effectiveness of our method 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, we aimed to integrate geographic and demographic heterogeneities into the epidemic monitoring loop using large-scale networked and metapopulation epidemic models. We made significant progress by developing a closed-loop monitoring algorithm, known as a parametrization-free nonlinear observer, 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 our first objective, which were not suitable for large-scale systems with network-embedded nonlinearities. Although this objective is only partly achieved, our future work will focus on further integrating both geographic and demographic heterogeneities into epidemic models using large-scale, multi-layered architectures. This presents exciting opportunities for mathematical modeling and analysis, though it also poses significant challenges in terms of the computational complexity required to monitor such systems.
To conclude, our work 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.
Results and potential impacts:
At the heart of our project lies a novel approach that combines the power of PINNs with rigorous system-theoretic analysis for epidemic monitoring and control. This integration enables more accurate and reliable modeling of epidemic spread, a crucial factor in effective decision-making during public health crises. Our project's cornerstone is the development of a self-correcting system utilizing a closed-loop structure of nonlinear observers. This innovative design allows for continuous refinement of the model, adapting to the ever-changing circumstances inherent in epidemic processes.
We have made significant progress in developing a unified framework for reliable epidemic monitoring and control based on feedback mechanisms that demonstrate robustness to model and data uncertainties. This achievement involved developing and integrating PINNs-based nonlinear observers into dynamic optimal control algorithms to facilitate effective policy recommendations during epidemic outbreaks. Our proposed method is designed to address uncertainties in epidemic models and robustly optimize epidemic control measures such as lockdowns, vaccination rates, and testing capacities. We have also laid the necessary groundwork for future advancements in incorporating both geographic and demographic heterogeneities in epidemic monitoring and control.
The potential impacts of this research are far-reaching. By improving the accuracy and reliability of epidemic estimation and forecasting, the project enhances our ability to respond effectively to public health crises. The balanced policy recommendations generated by the system consider both health and socioeconomic factors, potentially leading to reduced infections and deaths during outbreaks while minimizing economic disruptions.
Key needs to ensure further uptake and success:
To fully realize the potential of our groundbreaking work, several key needs must be addressed. Further research is required to integrate both geographic and demographic heterogeneities into epidemic models and tackle the computational challenges associated with monitoring large-scale systems. Moreover, since an epidemic process is a sociotechnical system, it is very crucial to develop appropriate incentive mechanisms that will allow public health agencies to engage with society, ensure its cooperation, and be able to control epidemics in a much more efficient way. We have carried out preliminary theoretical research on this aspect of our project, and we are determined to further investigate the integration of incentive mechanisms for epidemic mitigation and control.
Real-world testing and validation of the developed models and frameworks are essential to demonstrate their effectiveness. Moreover, access to public funding will be crucial for us to continue our efforts for more research and development. We have realized the need to develop algorithms that automatically adapt the models and frameworks to different geographic and cultural contexts. This requires collaborating with international health organizations for global implementation. We also aim to work with health authorities to establish standards for epidemic modeling and control, which is very crucial.
Access to high-quality, real-time epidemiological data is paramount to our project. Currently, freely available data on the internet is of very low quality. We believe in establishing collaborations and partnerships with health authorities for data access and developing protocols for data collection and sharing during outbreaks. Interdisciplinary collaboration between mathematicians, computer scientists, epidemiologists, and policymakers will be essential to refine and implement these systems effectively.
Lastly, ethical considerations must be at the forefront. Addressing concerns related to data use and policy recommendations, while ensuring transparency in model decision-making processes, will be crucial for public trust and acceptance.
By addressing the identified key needs, the innovative approaches developed in our project have the potential to transform the response to future epidemic outbreaks, ultimately saving lives and mitigating the socioeconomic impact of public health crises. As we move forward, continued investment in this research and its practical application will be vital in building a more resilient global health infrastructure.
At the heart of our project lies a novel approach that combines the power of PINNs with rigorous system-theoretic analysis for epidemic monitoring and control. This integration enables more accurate and reliable modeling of epidemic spread, a crucial factor in effective decision-making during public health crises. Our project's cornerstone is the development of a self-correcting system utilizing a closed-loop structure of nonlinear observers. This innovative design allows for continuous refinement of the model, adapting to the ever-changing circumstances inherent in epidemic processes.
We have made significant progress in developing a unified framework for reliable epidemic monitoring and control based on feedback mechanisms that demonstrate robustness to model and data uncertainties. This achievement involved developing and integrating PINNs-based nonlinear observers into dynamic optimal control algorithms to facilitate effective policy recommendations during epidemic outbreaks. Our proposed method is designed to address uncertainties in epidemic models and robustly optimize epidemic control measures such as lockdowns, vaccination rates, and testing capacities. We have also laid the necessary groundwork for future advancements in incorporating both geographic and demographic heterogeneities in epidemic monitoring and control.
The potential impacts of this research are far-reaching. By improving the accuracy and reliability of epidemic estimation and forecasting, the project enhances our ability to respond effectively to public health crises. The balanced policy recommendations generated by the system consider both health and socioeconomic factors, potentially leading to reduced infections and deaths during outbreaks while minimizing economic disruptions.
Key needs to ensure further uptake and success:
To fully realize the potential of our groundbreaking work, several key needs must be addressed. Further research is required to integrate both geographic and demographic heterogeneities into epidemic models and tackle the computational challenges associated with monitoring large-scale systems. Moreover, since an epidemic process is a sociotechnical system, it is very crucial to develop appropriate incentive mechanisms that will allow public health agencies to engage with society, ensure its cooperation, and be able to control epidemics in a much more efficient way. We have carried out preliminary theoretical research on this aspect of our project, and we are determined to further investigate the integration of incentive mechanisms for epidemic mitigation and control.
Real-world testing and validation of the developed models and frameworks are essential to demonstrate their effectiveness. Moreover, access to public funding will be crucial for us to continue our efforts for more research and development. We have realized the need to develop algorithms that automatically adapt the models and frameworks to different geographic and cultural contexts. This requires collaborating with international health organizations for global implementation. We also aim to work with health authorities to establish standards for epidemic modeling and control, which is very crucial.
Access to high-quality, real-time epidemiological data is paramount to our project. Currently, freely available data on the internet is of very low quality. We believe in establishing collaborations and partnerships with health authorities for data access and developing protocols for data collection and sharing during outbreaks. Interdisciplinary collaboration between mathematicians, computer scientists, epidemiologists, and policymakers will be essential to refine and implement these systems effectively.
Lastly, ethical considerations must be at the forefront. Addressing concerns related to data use and policy recommendations, while ensuring transparency in model decision-making processes, will be crucial for public trust and acceptance.
By addressing the identified key needs, the innovative approaches developed in our project have the potential to transform the response to future epidemic outbreaks, ultimately saving lives and mitigating the socioeconomic impact of public health crises. As we move forward, continued investment in this research and its practical application will be vital in building a more resilient global health infrastructure.