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Background Human behavioral responses to changes in risks are often delayed. Methods for estimating these delayed responses either rely on rigid assumptions about the delay distribution (e.g., Erlang distribution), producing a poor fit, or yield period-specific estimates (e.g., estimates from the Autoregressive Distributed Lag (ARDL) model) that are difficult to integrate into simulation models. We propose a hybrid ARDL–Erlang approach that yields an interpretable summary of behavioral responses suitable for incorporation into simulation models. Method We apply the ARDL–Erlang approach to estimate the effect of COVID-19 deaths on mobility across US counties from October 2020 to July 2021. A standard panel autoregressive distributed lag (ARDL) model first estimates the effect of past deaths and past mobility on current mobility. The ARDL model is then transformed into an Infinite Distributed Lag (IDL) model consisting of only past deaths. The coefficients of the past deaths are aggregated into an overall effect and fit to an Erlang distribution, summarized by average delay length and shape parameter. Results Our results show that on the national level, a one-standard-deviation permanent increase in weekly deaths per 100,000 population (log-transformed) is associated with a 0.46-standard-deviation decrease in human mobility in the long run, where the delay distribution follows a first-order Erlang distribution, and the average delay length is about 3.2 weeks. However, there is much heterogeneity across states, with first- to third-order Erlang delays and 2 to 18 weeks of average delay providing a theoretically cogent summary of how mobility followed changes in deaths during the first year and a half of the pandemic. Conclusion This study provides a novel approach to estimating delayed human responses to health risks using a hybrid ARDL-Erlang model. Our findings highlight significant variability in the impact and timing of responses across states, underscoring the need for tailored public health policies. This study can also serve as guidelines and an example for identifying delayed human behavior in other settings. 

The transmission dynamics of infectious diseases and human responses are intertwined, forming complex feedback loops. However, many epidemic models fail to endogenously represent human behavior change. In this study, we introduce a novel behavioral epidemic model that incorporates various behavioral phenomena into SEIR models, including risk-response dynamics, shifts in containment policies, adherence fatigue, and societal learning, alongside disease transmission dynamics. By testing our model against data from 8 countries, where extensive behavioral data were available, we simultaneously replicate death rates, mobility trends, fatigue levels, and policy changes, both in-sample and out-of-sample. Our model offers a comprehensive depiction of changes in multiple behavioral measures along with the spread of the disease. We assess the explanatory power of each model mechanism in capturing data variability. Our findings demonstrate that the comprehensive model that includes all mechanisms provides the most insightful perspective for understanding the influence of human behavior during pandemics. 

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.