Spreading dynamics of forget-remember mechanism

Area of Science:

• Physics
• Epidemiology
• Complex Systems

Background:

• The forget-remember mechanism (FRM) is a model for message spreading.
• Specifying forget-remember functions can significantly alter spreading dynamics.

Purpose of the Study:

• To derive and analyze the master equation for FRM dynamics.
• To investigate steady states and epidemic thresholds in FRM.
• To explore the temporal nature of diseases like flu using FRM.

Main Methods:

• Derivation of the master equation for FRM.
• Application of mean-field techniques to determine steady states.
• Monte Carlo simulations for validation.
• Analytical derivation of forget and remember time distributions for linear and exponential functions.

Main Results:

• Steady states were reached under specific conditions, validated by simulations.
• Explicit distributions for forget and remember times were derived for linear and exponential FRM functions.
• An epidemic threshold was identified for time-dependent FRM.
• The critical transmissibility for FRM was bounded by those of the SIS and SIR models.

Conclusions:

• The forget-remember mechanism provides a flexible framework for modeling spreading phenomena.
• FRM dynamics can be analytically described and simulated.
• The study offers insights into the temporal dynamics of diseases and establishes bounds for epidemic thresholds.