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J. P. LaSalle, “Stability Theory for Ordinary Differential Equations,” Journal of Differential Equations, Vol. 4, No. 1, 1968, pp. 57-65.

has been cited by the following article:

• TITLE: The Dynamics of Vector-Host Feeding Contact Rate with Saturation: A Case of Malaria in Western Kenya

  AUTHORS: Josephine Wairimu, Ogana Wandera

  KEYWORDS: SIS Host-Vector Models; Malaria; Contact Rate with Saturation; Global Stability

  JOURNAL NAME: Applied Mathematics, Vol.4 No.10, October 4, 2013

  ABSTRACT: In this study, we develop an expression for a saturated mosquito feeding rate in an SIS malaria model to determine its effect on infection and transmission dynamics of malaria in the highlands of Western Kenya. The basic reproduction number is established as a sharp threshold that determines whether the disease dies out or persists in the population. Precisely, if , the disease-free equilibrium is globally asymptotically stable and the disease always dies out and if , there exists a unique endemic equilibrium which is globally stable and the disease persists. The contribution of the saturated contact rate to the basic reproduction number and the level of the endemic equilibrium are also analyzed.