The Dynamics of Vector-Borne Relapsing Diseases

Document Type

Presentation Abstract

Presentation Date

11-30-2015

Abstract

Relapsing fever is a disease spread by lice and ticks among humans and other mammals. As the name suggests it is characterized by 3-4 relapsing periods of fever and muscle aches. Clinical descriptions of the disease date back to the ancient Greeks and it was a problem among troops during the World Wars. Tick-borne Relapsing Fever (TBRF) occurs in the Pacific Northwest and has recently been used to motivate models for vector-borne relapsing diseases.

In this talk we will be concerned with the effect that the number of relapses have on the dynamics of the disease. We quantify this by computing the fundamental reproductive number R0, the average number of new infections caused by a single infected individual.

We will be introducing and using the compartmental model of disease spread developed by van den Dreissche and Watmough to find a form for R0 as a function of the number of relapses.

Also of interest are the existence and stability to endemic equilibria (EE), fixed points of the system where only a portion of the population are infected. We will show the existence of EE for R0 sufficiently close to 1.

Additional Details

Monday, November 30, 2015 at 3:10 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

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