Implications of seasonal variations, host and vector migration on spatial spread of sleeping sickness: Insights from a mathematical model

Abstract

In this paper, we proposed and analyzed a non-autonomous sleeping sickness that incorporates host and vector movement in a periodic environment. The proposed model is a two patch framework that has three species-humans, animals and tsetse flies. In addition to seasonality and mobility aspects, the proposed model also incorporates vector-bias. Due to seasonal variation in forage and vegetation cover, we assumed that mobility of animals and vectors from one patch to another is assumed to vary seasonally while that of humans is considered to be constant. Analysis of the model has shown that there exists a threshold parameter, commonly known as the reproduction number, which plays a significant role on persistence and extinction of the disease. In particular, we have demonstrated that if the basic reproduction number is less than unity then the disease dies out. However, if the basic reproduction is greater than unity the model admits at least one positive periodic solution. Our results show that seasonality and migration plays an important role in shaping the long term dynamics of sleeping sickness, which subsequently impacts the design of its control strategies.

Keywords

• Sleeping sickness
• Mathematical model
• Seasonality
• Spatial spread