A model of Gambian sleeping sickness with open vector populations.
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.
Artzrouni
M
M
Department of Applied Mathematics, University of Pau, France. marc.artzrouni@univ-pau.fr
Gouteux
J P
JP
D000818:Animals; D003198:Computer Simulation; D005714:Gambia / Q000453:epidemiology; D006801:Humans; D007303:Insect Vectors / Q000254:growth & development* / Q000469:parasitology; D008954:Models, Biological; D012424:Rural Population; D014346:Trypanosoma brucei brucei / Q000254:growth & development*; D014353:Trypanosomiasis, African / Q000453:epidemiology / Q000635:transmission*; D014370:Tsetse Flies / Q000254:growth & development* / Q000469:parasitology