Parameter estimation in behavioral epidemic models with endogenous societal risk-response

Behavioral epidemic models incorporating endogenous societal risk-response, where changes in risk perceptions prompt adjustments in contact rates, are crucial for predicting pandemic trajectories. Accurate parameter estimation in these models is vital for validation and precise projections. However, few studies have examined the problem of identifiability in models where disease and behavior parameters must be jointly estimated. To address this gap, we conduct simulation experiments to assess the effect on parameter estimation accuracy of a) delayed risk response, b) neglecting behavioral response in model structure, and c) integrating disease and public behavior data. Our findings reveal systematic biases in estimating behavior parameters even with comprehensive and accurate disease data and a well-structured simulation model when data are limited to the first wave. This is due to the significant delay between evolving risks and societal reactions, corresponding to the duration of a pandemic wave. Moreover, we demonstrate that conventional SEIR models, which disregard behavioral changes, may fit well in the early stages of a pandemic but exhibit significant errors after the initial peak. Furthermore, early on, relatively small data samples of public behavior, such as mobility, can significantly improve estimation accuracy. However, the marginal benefits decline as the pandemic progresses. These results highlight the challenges associated with the joint estimation of disease and behavior parameters in a behavioral epidemic model. Understanding how society's evolving risk perceptions alter social interactions and disease spread is key to building models that reliably project pandemic trajectories. This research focuses on systematic estimation of parameters in such models where disease dynamics and behavioral responses are intertwined. We find that even with perfect data and models, estimates of behavioral parameters are biased early in the pandemic, and data for at least one full wave of the disease are needed to have reliable estimates. This is mainly related to the time delay between pandemic risks, perceived risks, and public response. Our findings also show that conventional models that ignore risk response dynamics may replicate data well early on but eventually fail to uncover future waves. Additionally, incorporating small amounts of public behavior data (such as data samples from public mobility patterns) for model calibration significantly improves model accuracy, especially early in a pandemic. Moreover, the marginal benefit of additional behavioral data diminishes as the pandemic progresses. By understanding the challenges of estimating key parameters, we can build more reliable models for informed decision making during public health emergencies.