含有预防接种的霍乱时滞模型的稳定性和hopf分支分析

Stability and Hopf-bifurcation of a Delay Cholera Model with Vaccination and Insecticides

本文旨在建立一个包含预防接种并且具有复杂的传播途径的霍乱时滞模型.研究模型稳定性,以时滞为分支参数,通过分析相应特征方程根的分布,得出当时滞大小超过一个阙值时,系统稳定性发生变化,产生Hopf分支.其次利用中心流形定理和规范型理论研究分支方向,分支周期解稳定性和计算公式.最后以2008年津巴布韦霍乱为例进行模型数值模拟.

In this paper, we aim to propose a nonlinear delay cholera model with vaccination including both direct and indirect transmission pathways. We study the local stability of positive equilibrium by analyzing the corresponding characteristic equation. The model exhibits when the time delay exceeds some critical value, the system loses its stability and Hopf-bifurcation occurs. Furthermore, we derive the direction, stability of bifurcating periodic solutions by using the normal form theory and the center manifold theorem. Finally,we carry out numerical simulations to verify the analytical predictions by investigating the2008-2009 cholera outbreak in Zimbabwe.