Stability and Sensitivity Analysis of Yellow Fever Dynamics

Abstract

 Several West African countries have recently reported of Yellow Fever outbreaks. Ghana recently recorded an outbreak which lead to the death of three (3) people in the West Gonja District of the Northern Region. These indicate the re-emergence of the deadly disease. This research proposes a deterministic mathematical model through non-linear ordinary differential equations in order to gain an accurate insight into the dynamics of yellow fever between human beings and the vector Aedes mosquito in an unvaccinated area for the purpose of controlling the disease. The disease threshold parameter was obtained using the next generation matrix. The Gerschgorin theorem proved the disease-Free equilibrium and the Endemic equilibrium to be locally asymptotically stable for  and  respectively. The Lyapunov function proved the disease-Free Equilibrium to be globally asymptotically stable for . In order to study the effect of the model parameters to , the sensitivity analysis of the basic reproduction number with respect to epidemiological parameters was performed.