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Mathematical Epidemiology

These introductory notes are meant for the interested biostatistics or public health student. The mathematics prerequisite is high school algebra. This page is under construction, so not all the chapters are on the web site yet. Thanks to Tom Lietman and Tomas Aragon for their suggestions.

Chapters

Fundamental concepts
- Exponential Growth: Difference Equations
- Exponential Growth: Simple Examples
- Exponential Decay
- Flow Rates
- Exponential Growth: Continuous Time Models
- Exponential Decay. The concept of hazard
- Carrying Capacity and Logistic Growth
Introduction to epidemic models
- A Simple Epidemic
- Ross-MacDonald Malaria Model
- The Kermack-McKendrick Model
- The basic reproduction number, R₀
Compartment models
- Introduction to Compartment Models
- Distributed Delays
- Complex natural histories following infection
Simple stochastic models
- The pure-birth process
- Simple Birth and Death Processes
- The Galton-Watson Process
- The Reed-Frost Model
- R₀
- Discrete-event simulation
Examples
- Herd Immunity. Vaccination Programs
- Contact structure
- Pair formation
- Drug resistance
Age structure
- Simple models of aging
- Stable age distributions
- Epidemic models with age structure
- Raising the age of first infection
Pathogens in competition
- Competitive Exclusion
- Superinfection
- Simple evolution models