A model of Gambian sleeping sickness with open vector populations

• Published in: IMA journal of mathematics applied in medicine and biology Vol. 18; no. 2; p. 99
• Main Authors: Artzrouni, M, Gouteux, J P
• Format: Journal Article
• Language: English
• Published: England 01.06.2001
• Subjects: Animals; Computer Simulation; Gambia - epidemiology; Humans; Insect Vectors - growth & development; Insect Vectors - parasitology; Models, Biological; Rural Population; Trypanosoma brucei brucei - growth & development; Trypanosomiasis, African - epidemiology; Trypanosomiasis, African - transmission; Tsetse Flies - growth & development; Tsetse Flies - parasitology; Gambia
• ISSN: 0265-0746

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.