The basic reproduction number of African trypanosomiasis disease with a periodic vector population and vertical transmission

African trypanosomiasis is a vector-borne disease transmitted to humans by tsetse flies. Assuming that the tsetse fly population’s growth rate is a periodic function, an African trypanosomiasis epidemic model with seasonality, vertical transmission and latent period is proposed. It is common knowledge that the basic reproduction number plays a vital role in a epidemic model which determines whether the disease is eradicated or not. We derive a basic reproduction number R0 which is adapted to periodic environments. Parameters are estimated from the province of Kinshasa, Democratic Republic of Congo. This model suggests that the epidemic could be stopped if the vector population were reduced by a factor R20 = 2.80.