[Contribution of a mathematical model in the control of a parasitosis: the case of human African trypanosomiasis due to Trypanosoma brucei gambiense].

Trypanosoma brucei gambiense sleeping sickness transmitted by tsetse flies (Glossina spp.) is lethal if not treated adequately. The endemicity was generally well under control in the sixties. However, since the seventies the disease is returning in most of its old foci, with alarming endemic levels in several areas. Mathematical modelling provides a rational basis for finding the optimal strategies to control these recrudescences. We present a deterministic model of the basic transmission of trypanosomiasis between human and vector hosts in natural situations. The parameters were quantified on the basis of available evidence from the literature. The model predicts a stable equilibrium state with very high prevalences: approximately 95% of humans and 27% of flies being infected. The model further shows that the build-up of an epidemic is initially very slow, and it takes several months before the equilibrium state is reached. Consequently communities have enough time to avoid catastrophic situations by migrating to safer areas. If is therefore unlikely that such high equilibrium situations will occur in practice. The expression of the basic reproductive rate R0, the number of new infections during the lifetime of an infected subject with high values of R0 implies that efforts to diminish transmission to levels where the disease cannot maintain itself in the population, have to be substantial. The necessary reduction of fly numbers in order to enable eradication, has been calculated. In almost all situations a reduction of at least 90% is necessary, which is in accordance with the field experiences of vector control programmes. The present model can be considered as a starting point in the further development of a complete simulation model, which could be applied in supporting decision making in trypanosomiasis control.