Formulating human risk response in epidemic models: exogenous vs endogenous approaches

TL;DR

This work surveys how human risk response—driven by perceived disease risk and information diffusion—is incorporated into compartmental epidemic models, distinguishing exogenous versus endogenous formulations and implicit versus explicit diffusion. It argues that endogenous risk-response frameworks, especially with delayed information diffusion, can reproduce realistic epidemic waves and provide better long-term forecasts than exogenous models. The paper classifies models into three main families, details mathematical formulations, and presents simulations illustrating how risk feedback shapes outbreak size and timing. The study informs modelers on selecting frameworks aligned with their forecasting goals and public-health policy needs, while outlining avenues for incorporating broader behavioral mechanisms.

Abstract

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.

Figures (7)

• Figure 1: Flow diagram describing the general structure of exogenous SEIR models. Red dashed lines indicate influences on disease transmission. Solid lines denote movement of individuals. The compartments are: $S$, susceptible; $E$, exposed; $I$, infectious; $R$, removed.
• Figure 2: Flow diagram describing the model from N'konzi et al. (2022). Influence of behavior changes occurs endogenously via implicit information diffusion. Red color indicates contributions to risk response formulation. Solid lines denote movement of individuals, while dashed lines indicate information feedback. Compartments are $S$, susceptible; $E$, exposed; $I$, infectious; $R$, recovered.
• Figure 3: Flow diagram describing the model from Abbas et al. 2022). Red and blue coloring indicate contributions to risk response formulation with blue coloring for fear relaxation. Solid lines denote movement of individuals, while dashed lines indicate influence. Influence of behavior changes occurs endogenously via explicit information diffusion with split susceptible compartment. Compartments are $S$, susceptible; $S_f$, fearful susceptible; $I$, infectious; $Q$, quarantined; $R$, recovered.
• Figure 4: Flow diagram describing the model from Li & Xiao (2022). Red coloring indicates contributions to risk response formulation. Solid lines denote movement of individuals, while dashed lines indicate information feedback. Influence of behavior changes occurs endogenously via explicit information diffusion. Compartments are $S$, susceptible; $E$, exposed; $I$, infectious; $M$, media.
• Figure 5: Classical SEIR model without demographics. Top: Flow diagram of individuals through compartments $S$, susceptible; $E$, exposed/infected but not infectious; $I$, infectious; $R$, removed. Bottom Left: Variables and parameters. Bottom Right: System of differential equations for the base model.