一类非线性传染率的SIRI模型的稳定性

The Stability of SIRI Model with Nonlinear Incidence Rate

考虑具有非线性及时滞的传染率为φ(S)I(t-τ)的SIRI传染病模型的动力学行为{dI/dt=φ(b/d-I-R)I(t-τ)-(γ+d)I+αI dR/dt=γI-(d+α)R首先,借助于Dulac函数和线性化方法,获得无时滞情形(τ=0)的各个平衡点的全局稳定性;其次,应用线性化系统的方法证明系统的局部稳定性;最后,利用Lyapunov泛函方法研究无病平衡点的全局稳定性得到结论,推广了H.N.Moreira & Yuquan Wang所做的工作。

In this paper, we consider dynamical behaviors of an SIRI epidemic model with nonlinear incidence rate and delay situation dI/dt=φ（b/d-I-R）I（t-r）-（y＋d）I＋αl dI/dt=yI-（d＋α）RFirstly, By employing the Dulac function and the method of linearization of this equations of each equilibrium, we obtain the global stability of each equilibrium without delay. Secondly, by using the method of linearization of this equations, we prove the local stability of each equilibrium for the systems with delay. Finally, by Lyapunov functional we derive global stability of the disease-free equilibrium.