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 [Formula: see text] 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 [Formula: see text] and the endemic equilibrium are determined. Both [Formula: see text] 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, [Formula: see text] and [Formula: see text], 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.