Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model.

Area of Science:

• Epidemiology
• Mathematical Biology
• Complex Systems

Background:

• Human societal processes, including epidemic evolution, are significantly impacted by memory.
• Real-world epidemic dynamics are non-Markovian, with memory effects playing a crucial role in disease spread.

Purpose of the Study:

• To investigate the dynamics of the Susceptible-Infected-Recovered (SIR) epidemic model incorporating memory effects using fractional derivatives.
• To analyze how memory decay influences epidemic thresholds in both well-mixed populations and structured networks.

Main Methods:

• Utilizing fractional calculus to introduce memory effects into the SIR model, specifically nonlinear fractional differential equations.
• Assuming a "fully mixed" approximation and analyzing the SIR model on structured networks to study topological effects.

Main Results:

• The memory-prone SIR model demonstrates a shift in the epidemic threshold to higher values compared to memoryless systems, dependent on the memory decay exponent.
• The study explores the impact of network topology on epidemic threshold points within a non-Markovian dynamics framework.

Conclusions:

• Memory effects, quantified by fractional derivative order, are essential for accurately modeling epidemic spread.
• The findings highlight the importance of considering memory and network structure for precise epidemic prediction and control.