Adaptive human behavior and delays in information availability autonomously modulate epidemic waves

Abstract

The recurrence of epidemic waves has been a hallmark of infectious disease outbreaks. Repeated surges in infections pose significant challenges to public health systems, yet the mechanisms that drive these waves remain insufficiently understood. Most prior models attribute epidemic waves to exogenous factors, such as transmission seasonality, viral mutations, or implementation of public health interventions. We show that epidemic waves can emerge autonomously from the feedback loop between infection dynamics and human behavior. Our results are based on a behavioral framework in which individuals continuously adjust their level of risk mitigation subject to their perceived risk of infection, which depends on information availability and disease severity. We show that delayed behavioral responses alone can lead to the emergence of multiple epidemic waves. The magnitude and frequency of these waves depend on the interplay between behavioral factors (delay, severity, and sensitivity of responses) and disease factors (transmission and recovery rates). Notably, if the response is either too prompt or excessively delayed, multiple waves cannot emerge. Our results further align with previous observations that adaptive human behavior can produce nonmonotonic final epidemic sizes, shaped by the trade-offs between various biological and behavioral factors-namely, risk sensitivity, response stringency, and disease generation time. Interestingly, we found that the minimal final epidemic size occurs on regimes that exhibit a few damped oscillations. Altogether, our results emphasize the importance of integrating social and operational factors into infectious disease models, in order to capture the joint evolution of adaptive behavioral responses and epidemic dynamics.

Keywords: adaptive human behavior; behavioral epidemiology; infectious disease modeling; nonlinear dynamics; risk perception.

Fig. 1.

Delayed behavioral responses can induce epidemic waves. A) Linear-scaled logistic functions (solid green line) and log-scaled Hill functions (dotted lines) can both describe the disease prevalence-dependent behavioral response. The behavioral response midpoint for all exemplary functions is fixed at $c=2\mathrm{\%}$, while the sensitivity parameter ($k_h,k_l$, respectively) varies. B) Disease prevalence, C) effective reproduction number, and D) contact reduction over time, and for different behavioral responses: none as in the standard SIR model, immediate ($\tau =0$), delayed ($\tau =5$). E) Trajectory of the prevalence and contact reduction under an immediate and delayed behavioral response. The arrows indicate the direction of the change over time. B–E) All nonspecified parameters are at their default values listed in Table 1. Specifically, $c=2\mathrm{\%}$ and $k_h=16$.

Fig. 2.

Disease dynamics and population-wide contact reduction for a variety of delays and Hill response functions. Given a delay of τ days and a population-wide contact reduction function, parametrized by the behavioral response midpoint c and the sensitivity $k_h$, the A, C, E) disease prevalence and B, D, F) population-wide contact reduction is plotted over time for several A, B) τ-values, C, D) c-values and E,F) $k_h$-values. All nonspecified parameters are at their default values listed in Table 1. In all sub panels, the solid black line depicts the dynamics for $\tau =5,c=2\mathrm{\%},k_h=16$.

Fig. 3.

2D sensitivity analysis. The number of epidemic waves is shown for a range of values for the delay parameter (τ, x-axis) and another model parameter (y-axis): A) behavioral response midpoint c, B) behavioral response sensitivity $k_h$, C) transmission rate β, D) recovery rate γ. White lines connect the highest (in A, D) or lowest (in B, C) model parameter value and associated delay value that yields a specific number of multiple waves. All nonspecified parameters are at their default values listed in Table 1.

Fig. 4.

4D sensitivity analysis. A) The delay causing the maximal number of waves (color) and the corresponding number of waves (numbers in each cell) are shown for different basic reproduction numbers ${\mathcal{R}}_0$ (x-axis), different disease generation times modulated by the transmission rate β (y-axis), as well as for four different shapes of the population-wide behavioral response function, parametrized by the behavioral response midpoint c and the sensitivity $k_h$. Gray cells indicate that the model behaves as the standard SIR model and exhibits only a single epidemic wave, irrespective of the delay parameter. B, C) For a fixed ${\mathcal{R}}_0$ value and fixed behavioral response function ($c=2\mathrm{\%}$, $k_h=16$), the wave-maximizing delay (y-axis) is inversely proportional to B) the transmission rate β and thus directly proportional to C) the disease generation time. For each ${\mathcal{R}}_0$ value, the line only extends across those x-values that yield the respective maximal number of waves, which is indicated in the legend in (B).

Fig. 5.

Disease and behavior-related parameters affect the final epidemic size nonmonotonically. A–D) The final epidemic size is shown for a range of values for the delay parameter (τ, x-axis) and another model parameter (y-axis): A) behavioral response point c, B) behavioral response sensitivity $k_h$, C) transmission rate β, D) recovery rate γ. E, F) For a fixed value of E) the transmission rate β or F) the recovery rate γ, the color indicates the absolute reduction in the final epidemic size compared to the maximal epidemic size attained across all tested delay values (dark: no reduction, light: high reduction). A–F) White lines depict the thresholds where the number of waves changes, as shown in Fig. 3. All nonspecified parameters are at their default values listed in Table 1.