一类流感模型的动力学分析与数值模拟

研究了一种具有抗病性的SEIR流感模型，利用求再生矩阵最大特征值的方法计算了模型的基本再生数，并证明了当Rc<1时只有无病平衡点，且无病平衡点局部渐近稳定；当Rc>1时，方程组存在唯一的地方病平衡点。构造了Lyapunov函数证明了地方病平衡点的全局稳定性，且利用有限元法进行了数值模拟，模拟结果与理论分析结果相吻合，并与Runge-Kutta法进行了对比分析，为传染病分析提供了一个新思路。

A Dynamic Analysis and Numerical Simulation of a Certain Influenza Model

A study has been made of a SEIR influenza model with disease resistance in this paper, followed by a calculation of the basic reproduction number of the model by using the method of finding the maximum eigenvalue of the reproduction matrix. It is testified that under the condition of Rc<1, there is only a disease free equilibrium point, with the disease free equilibrium point locally asymptotically stable. When Rc>1, there is a unique endemic equilibrium point in the equation system, with Lyapunov function constructed to confirm the global stability of the endemic equilibrium point. For the first time, the finite element method is used for a numerical simulation, which is consistent with the theoretical analysis. Meanwhile, when compared with the Runge-Kutta method, the proposed process provides a new method for the analysis of infectious diseases.