The Kermack-McKendrick epidemic model revisited

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• The foundational Kermack-McKendrick epidemic model (1927) is an age of infection model.
• It describes infectivity based on time since an individual became infected.
• A simplified two-dimensional ordinary differential equation system is often referred to as the Kermack-McKendrick model.

Purpose of the Study:

• To contextualize the Kermack-McKendrick model within modern epidemic modeling.
• To highlight its relevance in analyzing post-SARS epidemic models.
• To demonstrate the applicability of its analytical approach to contemporary disease dynamics.

Main Methods:

• Analysis of epidemic models as age of infection models.
• Application of the full Kermack-McKendrick model's analytical approach.
• Examination of models incorporating general contact rates, quarantine, and isolation.

Main Results:

• Modern epidemic models, including those developed post-SARS, can be viewed through the lens of age of infection models.
• The Kermack-McKendrick model's analytical framework is applicable to these diverse models.
• These models consistently exhibit a threshold for epidemic outbreaks and eventual disease extinction.

Conclusions:

• The principles of the Kermack-McKendrick model remain relevant for understanding infectious disease dynamics.
• Its analytical framework provides a unified approach to studying various epidemic models.
• Key properties like outbreak thresholds and self-limiting epidemics are fundamental across these models.