[Persistence and resurgence of sleeping sickness caused by Trypanosoma brucei gambiense in historic foci. Biomathematical approach of an epidemiologic enigma].

Since the end of the 19th century, historic endemic foci of Trypanosoma brucei gambiense sleeping sickness have proven very persistent. A five-compartment mathematical model with open vector populations was developed in order to study the dynamics of this disease in Central Africa. Of particular interest 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 halving/doubling time T(o) of the numbers infected; T(o) is a doubling time when the basic reproduction number Ro > 1 and a halving time when Ro < 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 brought about by an Ro either just above 1 (slow spread) or just below 1 (slow extinction). A resurgence of historical foci can then be caused by a small shift in parameter values that brings Ro well above 1 and decreases T(o). In addition, when Ro is less than 1 (in the absence of vector migrations), simulations show that a very small percentage of infected immigrant flies can bring about high prevalence rates in the human population. The model is validated with field data from historical Congolese, Central and West African foci of the past.