A framework for counterfactual analysis, strategy evaluation, and control of epidemics using reproduction number estimates

During pandemics, countries, regions, and communities develop various epidemic models to evaluate spread and guide mitigation policies. However, model uncertainties caused by complex transmission behaviors, contact-tracing networks, time-varying parameters, human factors, and limited data present significant challenges to model-based approaches. To address these issues, we propose a novel framework that centers around reproduction number estimates to perform counterfactual analysis, strategy evaluation, and feedback control of epidemics. The framework 1) introduces a mechanism to quantify the impact of the testing-for-isolation intervention strategy on the basic reproduction number. Building on this mechanism, the framework 2) proposes a method to reverse engineer the effective reproduction number under different strengths of the intervention strategy. In addition, based on the method that quantifies the impact of the testing-for-isolation strategy on the basic reproduction number, the framework 3) proposes a closed-loop control algorithm that uses the effective reproduction number both as feedback to indicate the severity of the spread and as the control goal to guide adjustments in the intensity of the intervention. We illustrate the framework, along with its three core methods, by addressing three key questions and validating its effectiveness using data collected during the COVID-19 pandemic at the University of Illinois Urbana-Champaign (UIUC) and Purdue University: 1) How severe would an outbreak have been without the implemented intervention strategies? 2) What impact would varying the intervention strength have had on an outbreak? 3) How can we adjust the intervention intensity based on the current state of an outbreak?Author summary: We propose a framework that centers around reproduction number estimates for counterfactual analysis, strategy evaluation, and feedback control of epidemics. The framework introduces a mechanism to quantify the impact of the testing-for-isolation intervention on the basic reproduction number first. It offers a method to reverse engineer the effective reproduction number under alternative strengths of this strategy, enabling the reconstruction of hypothetical spreading scenarios under different strength of intervention. Additionally, quantifying the impact of the testing-for-isolation intervention on the basic reproduction number facilitates the development of a closed-loop feedback control algorithm. This algorithm uses the effective reproduction number both as feedback to assess the severity of the spread and as the control goal to adjust the strength of the intervention. We leverage this framework to: 1) Analyze the effectiveness of the implemented intervention strategy by examining the connection between the testing-for-isolation intervention and the basic reproduction number; 2) Evaluate the impact of varying intervention intensities using a reverse engineering method to generate effective reproduction numbers of hypothetical spreading scenarios under different intervention strengths; and 3) Design a closed-loop feedback epidemic control framework for intervention intensity adaptation through the closed-loop control algorithm. This framework provides new insights into utilizing the reproduction number estimates to analyze hypothetical spreading scenarios under alternative levels of intervention strategies. Additionally, it uses the effective reproduction number as feedback information to design the closed-loop control strategy for dynamically adjusting the strength of the intervention to support epidemic mitigation efforts. Using COVID-19 data from UIUC and Purdue, we illustrate and validate our framework by conducting counterfactual analyses to evaluate the effectiveness of the implemented testing-for-isolation strategies. Additionally, we validate that our feedback control algorithm can effectively adjust the intervention strategy based on the severity of the epidemic.