Modeling Rift Valley Fever with Treatment and Trapping Control Strategies

Abstract

We consider a rift valley fever model with treatment in human and livestock populations and trapping in the vector (mosquito) population. The basic reproduction number R 0 is established and used to determine whether the disease dies out or is established in the three populations. When R 0 ≤ 1, the disease-free equilibrium is shown to be globally asymptotically stable and the disease does not spread and when R 0 > 1, a unique endemic equilibrium exists which is globally stable and the disease will spread. The mathematical model is analyzed analytically and numerically to obtain insight of the impact of intervention in reducing the burden of rift valley fever disease’s spread or epidemic and also to determine factors influencing the outcome of the epidemic. Sensitivity analysis for key parameters is also done.