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The Kermack-McKendrick epidemic model revisited
1Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada. brauer@math.ubc.ca
Mathematical Biosciences
|September 2, 2005
Summary
The Kermack-McKendrick epidemic model, an age of infection model, provides a framework for understanding disease spread. Modern epidemic models, including those for SARS, build upon its principles, showing disease thresholds and eventual die-out.
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.