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The Dynamic Behavior of a Discrete Vertical and Horizontal Transmitted Disease Model under Constant Vaccination

¹ School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, China
² School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, China
³ School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, China

International Journal of Modern Nonlinear Theory and Application·Volume 05 (2016)·Pages 171–184·Published 10 November 2016·DOI10.4236/ijmnta.2016.54017

Abstract

In this paper, a class of discrete vertical and horizontal transmitted disease model under constant vaccination is researched. Under the hypothesis of population being constant size, the model is transformed into a planar map and its equilibrium points and the corresponding eigenvalues are solved out. By discussing the influence of coefficient parameters on the eigenvalues, the hyperbolicity of equilibrium points is determined. By getting the equations of flows on center manifold, the direction and stability of the transcritical bifurcation and flip bifurcation are discussed.

KeywordsVertical and Horizontal TransmissionVaccinationCenter ManifoldTranscritical BifurcationFlip Bifurcation

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The Dynamic Behavior of a Discrete Vertical and Horizontal Transmitted Disease Model under Constant Vaccination

Abstract

References (16)