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**

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**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.