# Coast to Coast Seminar Series: "Differential Equation Models of Infectious Disease Dynamics"

*Dr. James Watmough*

### Abstract

The early disease transmission model of Kermack and McKendrick established two main results that are still at the core of most disease transmission models today: the basic reproduction number, Ro, as a threshold for disease spread in a population; and the final size of an epidemic. This early model consisted of a single integral equation for the incidence of infection over time. As models become more complex, the relationships between disease spread, final size and Ro are not as clear; yet Ro remains the main object of study when comparing control measures. This talk will formulate Ro for more complex models and outline results for the final size and bifurcations from the disease-free solution.