Persistence and resurgence of sleeping sickness foci. A biomathematical investigation.

Since the end of the 19th century, historic endemic foci of Trypanosoma bru cei gambiense sleeping sickness have proven very persistent. A five-compart ment mathematical model with open vector populations was developed in order to study the dynamics of this disease in Central Africa. Of particular int erest is the rate at which the disease spreads or goes to extinction at the beginning of an epidemic outbreak. A measure of this rate is the initial h alving/doubling time T-o of rile numbers infected; T-o is a doubling time w hen the basic reproduction number R-o > 1 and a halving time when R-o < 1. For realistic parameter values, T-o can be quite large (i.e. several years or even decades) which corresponds to a persistent low-level endemic brough t about by an R-o either just above 1 (slow spread) or just below 1 (slow e xtinction). A resurgence of historical foci can then be caused by a small s hift in parameter- values that brings R-o well above 1 and decreases T-o. I n addition, when R-o is less than 1 (in the absence of vector migrations), simulations show that a very small percentage of infected immigrant flies c an bring about high prevalence rates in the human population. The model is validated with field data from historical Congolese, Central and West Afric an foci of the past. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.