Behavior-induced oscillations in epidemic outbreaks with distributed memory: beyond the linear chain trick using numerical methods

TL;DR

This paper models how behavior-driven memory effects can induce oscillations in epidemic outbreaks, extending analysis beyond traditional methods using numerical techniques to understand long-term dynamics and stability.

Contribution

It introduces a numerical approach to analyze epidemic models with distributed memory kernels, surpassing the linear chain trick limitations and exploring complex oscillatory behaviors.

Findings

Behavior adaptation can cause sustained epidemic waves without demographic factors.

Memory kernel shape influences epidemic wave period and peak.

Minimal contact levels affect the stability of the disease-free equilibrium.

Abstract

We considered a model for an infectious disease outbreak, when the depletion of susceptible individuals is negligible, and assumed that individuals adapt their behavior according to the information they receive about new cases. In line with the information index approach, we supposed that individuals react to past information according to a memory kernel that is continuously distributed in the past. We analyzed equilibria and their stability, with analytical results for selected cases. Thanks to the recently developed pseudospectral approximation of delay equations, we studied numerically the long-term dynamics of the model for memory kernels defined by gamma distributions with a general non-integer shape parameter, extending the analysis beyond what is allowed by the linear chain trick. In agreement with previous studies, we showed that behavior adaptation alone can cause sustained waves of infections even in an outbreak scenario, and notably in the absence of other processes like demographic turnover, seasonality, or waning immunity. Our analysis gives a more general insight into how the period and peak of epidemic waves depend on the shape of the memory kernel and how the level of minimal contact impacts the stability of the behavior-induced positive equilibrium.