一类离散SIS传染病模型及flip分支研究

An Analysis of a Discrete-Time SIS Epidemic Model and Its Flip Bifurcation

讨论和研究了一类SIS传染病模型及其flip分支.在一定条件下,探讨了该模型平衡点的存在性、稳定性以及平衡点不稳定时可能出现的flip分支.经过计算和数值模拟,模型存在一个无病平衡点和一个正平衡点.理论证明了无病平衡点和正平衡点的稳定性,当正平衡点不稳定时,模型会存在flip分支,通过详细地计算和推导,得出flip分支是稳定的.

This paper discusses and studies a discrete-time SIS epidemic model and its flip bifurcation and,under given conditions,investigates the existence and stability of the model and the possible flip bifurcation of the model when the equilibrium point is unstable.Calculation and numerical simulation show that there is a disease-free equilibrium and a positive equilibrium in this model and they are stable.A detailed calculation and derivation shows that the flip bifurcation is stable.