Acta Biotheoretica

, Volume 59, Issue 3–4, pp 231–250 | Cite as

A Mathematical Model of Rift Valley Fever with Human Host

  • Saul C. Mpeshe
  • Heikki Haario
  • Jean M. Tchuenche
Regular Article

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, dm. 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.

Keywords

Rift Valley fever Stability Sensitivity analysis 

Mathematics Subject Classification (2000)

92B05 92D30 92C60 93D05 93D20 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Saul C. Mpeshe
    • 1
    • 3
  • Heikki Haario
    • 2
  • Jean M. Tchuenche
    • 3
  1. 1.Department of MathematicsTumaini University, Iringa University CollegeIringaTanzania
  2. 2.Department of Mathematics and PhysicsLappeenranta University of TechnologyLappeenrantaFinland
  3. 3.Department of MathematicsUniversity of Dar es SalaamDar es SalaamTanzania

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