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The recent pandemic emphasized the need to consider the role of human behavior in shaping epidemic dynamics. In particular, it is necessary to extend beyond the classical epidemiological structures to fully capture the interplay between the spread of disease and how people respond. Here, we focus on the challenge of incorporating change in human behavior in the form of “risk response” into compartmental epidemiological models, where humans adapt their actions in response to their perceived risk of becoming infected. The review examines 37 papers containing over 40 compartmental models, categorizing them into two fundamentally distinct classes: exogenous and endogenous approaches to modeling risk response. While in exogenous approaches, human behavior is often included using different fixed parameter values for certain time periods, endogenous approaches seek for a mechanism internal to the model to explain changes in human behavior as a function of the state of disease. We further discuss two different formulations within endogenous models as implicit versus explicit representation of information diffusion. This analysis provides insights for modelers in selecting an appropriate framework for epidemic modeling. 

COVID-19 highlighted the importance of considering human behavior change when modeling disease dynamics. This led to developing various models that incorporate human behavior. Our objective is to contribute to an in-depth, mathematical examination of such models. Here, we consider a simple deterministic compartmental model with endogenous incorporation of human behavior (i.e., behavioral feedback) through transmission in a classic Susceptible–Exposed–Infectious–Recovered (SEIR) structure. Despite its simplicity, the SEIR structure with behavior (SEIRb) was shown to perform well in forecasting, especially compared to more complicated models. We contrast this model with an SEIR model that excludes endogenous incorporation of behavior. Both models assume permanent immunity to COVID-19, so we also consider a modification of the models which include waning immunity (SEIRS and SEIRSb). We perform equilibria, sensitivity, and identifiability analyses on all models and examine the fidelity of the models to replicate COVID-19 data across the United States. Endogenous incorporation of behavior significantly improves a model’s ability to produce realistic outbreaks. While the two endogenous models are similar with respect to identifiability and sensitivity, the SEIRSb model, with the more accurate assumption of the waning immunity, strengthens the initial SEIRb model by allowing for the existence of an endemic equilibrium, a realistic feature of COVID-19 dynamics. When fitting the model to data, we further consider the addition of simple seasonality affecting disease transmission to highlight the explanatory power of the models.