In this paper we describe the dynamics of a vector-borne relapsing disease, such as tick-borne relapsing fever, using the methods of compartmental models. After some motivation, model description, and a brief overview of the theory of compartmental models, we compute a general form of the reproductive ratio R0, which is the average number of new infections produced by a single infected individual. A disease free equilibrium undergoes a bifurcation at R0=1 and we show that for an arbitrary number of relapses it is a transcritical bifurcation with a single branch of endemic equilibria that is locally asymptotically stable for R0 sufficiently close to 1. We close with some discussion and directions for future research.
@article{arxiv.1605.07647,
title = {The Dynamics of Vector-Borne Relapsing Diseases},
author = {Cody Palmer and Erin Landguth and Emily Stone and Tammi Johnson},
journal= {arXiv preprint arXiv:1605.07647},
year = {2016}
}