DEPARTMENT OF MATHEMATICAL & STATISTICAL SCIENCES
UNIVERSITY OF ALBERTA
  

MATHEMATICAL BIOLOGY SEMINAR
 

MONDAY NOVEMBER 3, 2003

3:00-4:00 p.m.

CAB 657

 

Dr. Pauline van den Driessche

Department of Mathematics and Statistics

University of Victoria

 

 

Epidemic Thresholds

 

Abstract:

 

A general compartmental disease transmission model is formulated as a system of ordinary differential equations. The basic reproduction number, R_0, is defined as the spectral radius of a nonnegative matrix product. This number is shown to act as a threshold, with the disease-free equilibrium being locally stable if R_0<1, but unstable if R_0>1. Results are illustrated by some specific examples including a treatment model for Tuberculosis, a model for SARS, and a spatial network model that includes travel between cities. Bifurcations for R_0 near one are analyzed, and an example given of backward bifurcation when vaccination is introduced.