A model of Gambian sleeping sickness with open vector populations. Application to the Nola-Bilolo focus (Central African Republic)

A compartmental model of sleeping sickness is improved by incorporating vec tor migration and reinvasion. The emigration rate is constant and reinvasio n (of both susceptible and infected flies) occurs only when the vector popu lation drops below a threshold value. The vector and human populations conv erge to equilibrium values that depend on the parameters values (mortality, emigration rates, and intensity of reinvasion). With a basic reproduction number less than 1, a less than one percent infection rate among reinvading flies can cause high human prevalence rates between 8% and 35%, depending on the assumed duration of the asymptomatic stage of the disease. The halvi ng time of the epidemic is introduced and is useful in assessing the long-t erm dynamics of the disease. The model is successfully tested for the Nola- Bilolo focus of the Central African Republic.