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Related Experiment Video

Updated: Jan 13, 2026

Generation of Local CA1 γ Oscillations by Tetanic Stimulation

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Published on: August 14, 2015

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

Alessia Andò^1,2, Simone De Reggi^3,2, Francesca Scarabel^4,2

¹Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze 206, 33100 Udine, Italy.

Mathematical Biosciences and Engineering : MBE

|January 6, 2026

Summary

Behavior adaptation to infectious disease information can create sustained infection waves. This study models how memory of past cases influences epidemic dynamics, even without other factors like seasonality.

Keywords:

MatCont behavioral epidemiology incidence-based social distancing infectious disease model linear chain trick periodic solutions pseudospectral approximation stability

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Area of Science:

Epidemiology
Mathematical Biology
Infectious Disease Modeling

Background:

Infectious disease outbreaks are influenced by individual behavior.
Understanding how information about new cases affects behavior is crucial for epidemic control.
Previous models often simplify behavioral responses to disease information.

Purpose of the Study:

To develop and analyze a mathematical model of infectious disease dynamics incorporating behavioral adaptation based on past case information.
To investigate the long-term dynamics and stability of epidemics driven by information-dependent behavior.
To explore the impact of memory kernel characteristics on epidemic wave patterns.

Main Methods:

Mathematical modeling of infectious disease spread with behavioral feedback.
Analysis of model equilibria and stability using analytical techniques.
Numerical simulation of long-term dynamics using pseudospectral approximation of delay equations.
Investigation of gamma-distributed memory kernels with non-integer shape parameters.

Main Results:

Behavioral adaptation alone can generate sustained epidemic waves, independent of demographic factors or seasonality.
The shape of the memory kernel significantly influences the period and peak of infection waves.
The level of minimal contact affects the stability of behavior-induced equilibria.
Pseudospectral methods allowed analysis beyond traditional modeling limitations.

Conclusions:

Individual behavior adaptation in response to disease information is a potent driver of epidemic persistence.
The characteristics of memory (how past information is retained and weighted) are critical determinants of epidemic wave dynamics.
The model provides a more general framework for understanding behavior-driven epidemics and their control.