A Mathematical Model of Rift Valley Fever with Human Host

Abstract

Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold $\mathcal{R}_0$ is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission $\mathcal{R}_0$ and the endemic equilibrium are determined. Both $\mathcal{R}_0$ and the disease prevalence in mosquitoes are more sensitive to the natural mosquito death rate, d _m . The disease prevalence in livestock and humans are more sensitive to livestock and human recruitment rates, $\Uppi_l$ and $\Uppi_h$, respectively, suggesting isolation of livestock from humans is a viable preventive strategy during an outbreak. Numerical simulations support the analytical results in further exploring theoretically the long-term dynamics of the disease at the population level.