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Updated: Sep 30, 2025

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Simple model of epidemic dynamics with memory effects.

Michael Bestehorn1, Thomas M Michelitsch2, Bernard A Collet2

  • 1Brandenburgische Technische Universität Cottbus-Senftenberg, Institut für Physik, Erich-Weinert-Straße 1, 03046 Cottbus, Germany.

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Summary
This summary is machine-generated.

A new compartment model with memory introduces a finite immunity duration, causing persistent oscillations in infected individuals. This memory effect, unlike standard SIR models, better reflects real-world epidemic dynamics and ongoing activity.

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Computational Physics

Background:

  • Classical Susceptible-Infected-Recovered (SIR) models assume permanent immunity.
  • Real-world epidemics often exhibit recurring waves and lack a steady state.
  • The duration of immunity is a critical factor in epidemic dynamics.

Purpose of the Study:

  • To introduce a compartment model with memory for epidemic spreading.
  • To investigate the impact of a finite, random duration of immunity on epidemic dynamics.
  • To analyze the space-time dynamics of epidemic spread using computer simulations.

Main Methods:

  • Development of a compartment model incorporating a random lifetime for immunity.
  • Implementation of the model using a multiple random walker's approach for computer simulations.
  • Analysis of infection probability upon contact between susceptible and infected individuals.

Main Results:

  • The finite duration of immunity introduces a memory effect, crucial for epidemic dynamics.
  • Persistent oscillations in infected individuals are observed, preventing a steady state.
  • Computer simulations identify key parameters influencing epidemic spread and extinction.

Conclusions:

  • The memory effect from finite immunity duration leads to ongoing epidemic activity and oscillations.
  • This model captures real-life epidemic behaviors not predicted by standard SIR models.
  • The findings highlight the importance of considering immunity duration in epidemic forecasting.