Joint Mathematics Colloquium

University of Idaho

Washington State University

Fall 2013

Thursday,  November 21, 4:10-5:00 pm, room Neill Hall 5W

Refreshments in Neill 216 Hacker Reading Lounge at 2:00 p.m.

Spatially Heterogeneous Cholera Models


Pauline van den Driessche

Department of Mathematics and Statistics

University of Victoria, BC, Canada


Spatial heterogeneity of both humans and water may influence the spread of cholera, which is an infectious disease caused by an aquatic bacterium. To incorporate spatial effects, two cholera models are proposed that both include direct (rapid) and indirect (environmental/water) transmission. The first is a multi-group model and the second is a multi-patch model. Matrix theory and new mathematical tools from graph theory are used to understand the dynamics of both these heterogeneous cholera models, and to show that each model (under certain assumptions) satisfies a sharp threshold property. Specifically, Kirchhoff's matrix tree theorem is used to investigate the dependence of the disease threshold on the patch connectivity and water movement (multi-patch model), and also to establish the global dynamics of both models.