# A Mathematical Model of Rift Valley Fever with Human Host

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DOI: 10.1007/s10441-011-9132-2

- Cite this article as:
- Mpeshe, S.C., Haario, H. & Tchuenche, J.M. Acta Biotheor (2011) 59: 231. doi:10.1007/s10441-011-9132-2

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## 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.