On a class of nonlocal SIR models

Area of Science:

• Epidemiology
• Mathematical Biology
• Dynamical Systems

Background:

• The susceptible-infected-recovered (SIR) model is a foundational tool in epidemiology.
• Nonlocal variations of the SIR model offer more complex dynamics.
• Understanding epidemic spread requires robust analytical and approximation methods.

Purpose of the Study:

• To derive exact analytical solutions for the classic SIR model.
• To analyze approximations for recently developed nonlocal SIR models.
• To investigate the emergence of multiple peak solutions in nonlocal epidemic models.

Main Methods:

• Development of novel analytical solution techniques for SIR models.
• Analysis of effective approximations in the context of nonlocal SIR dynamics.
• Rigorous mathematical investigation of peak solution existence and asymptotics.

Main Results:

• Exact analytical solutions were derived for the classical SIR model.
• Approximation methods were analyzed for nonlocal SIR models.
• Nonlocal SIR models exhibit multiple peak solutions for the infected population, a novel finding compared to the classic model.
• Conditions for the existence and non-existence of these peak solutions were established.

Conclusions:

• Nonlocal SIR models present richer dynamics, including multiple infection peaks.
• The developed methods provide a framework for analyzing complex epidemic models.
• Further research into nonlocal models is crucial for understanding diverse epidemic behaviors.