A two-patch model of Gambian sleeping sickness: application to vector control strategies in a village and plantations

A compartmental model is described for the spread of Gambian sleeping sickness in a spatially heterogeneous environment in which vector and human populations migrate between two "patches": the village and the plantations. The number of equilibrium points depends on two "summary parameters": gr the proportion removed among human infections, and R0, the basic reproduction number. The origin is stable for R0 < 1 and unstable for R0 > 1. Control strategies are assessed by studying the mix of vector control between the two patches that bring R0 below 1. The results demonstrate the importance of vector control in the plantations. For example if 20 percent of flies are in the village and the blood meal rate in the village is 10 percent, then a 20 percent added vector mortality in the village must be combined with a 9 percent added mortality in the plantations in order to bring R0 below 1. The results are quite insensitive to the blood meal rate in the village. Optimal strategies (that minimize the total number of flies trapped in both patches) are briefly discussed.