Journal Article

A model of Gambian sleeping sickness with open vector populations

Marc Artzrouni and Jean‐Paul Gouteux

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 18, issue 2, pages 99-117
Published in print June 2001 | ISSN: 1477-8599
Published online June 2001 | e-ISSN: 1477-8602 | DOI:
A model of Gambian sleeping sickness with open vector populations

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  • Applied Mathematics
  • Biomathematics and Statistics


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A compartmental model of Gambian sleeping sickness is described that takes into account density‐dependent migratory flows of infected flies. Equilibrium and stability theorems are given which show that with a basic reproduction number R0 below unity, then in the absence of reinvasion the disease goes to extinction. However, even a low prevalence rate among reinvading flies can then bring about significant equilibrium prevalence rates among humans. For a set of realistic parameter values we show that even in the case of a virulent parasite that keeps infected individuals in the first stage for as little as 4 or 8 months (durations for which there would be extinction with no infected reinvading flies) there is a prevalence rate in the range 13.0–36.9%, depending on whether 1 or 2% of reinvading flies are infected. A rate of convergence of the population dynamics is introduced and is interpreted in terms of a halving time of the infected population. It is argued that the persistence and/or extension of Gambian sleeping sickness foci could be due either to a continuous reinvasion of infected flies or to slow dynamics.

Keywords: sleeping sickness; model; differential equations; migration; vectors; reinvasion; extinction

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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