Developing Rift Valley Fever Model with Treatment and Trapping Control Strategies

Rift Valley Fever (RVF) is an infectious disease caused by the RVF virus of the genus Phlebovirus and family Bunyaviridae. RVF remains a threat to livestock keepers and nations where the disease is occurring due to its major economic implications through the costs of the measures taken at individual, collective and international levels to prevent or control infections and disease outbreaks.

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
is established and used to determine whether the disease dies out or is established in the three populations. When
, the disease-free equilibrium is shown to be globally asymptotically stable and the disease does not spread and when
, a unique endemic equilibrium exists that is globally stable and the disease will spread. The mathematical model is analyzed analytically and numerically to obtain insight into 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.

Finally, it is concluded that the Rift Valley Model formulated in this study is well-posed and exists in a feasible region where disease-free and endemic equilibrium points are obtained and their stability investigated.