Joint Mathematics Colloquium
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Abstract |
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| 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.
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