含有接种和非线性传染力的流行病模型的稳定性研究

研究一类含有接种和非线性传染力的SEIR流行病模型，通过分析得到了各类平衡点存在的阈值条件。利用Liapunove函数、Lasalle不变集原理、Hurwith判据证明了当基本再生数时，无病平衡点是全局渐近稳定的；当R₀>1时，此模型存在两个平衡点，其中无病平衡点是不稳定的，利用Hurwitz判别法证明了地方病平衡点的局部渐近稳定性。最后对模型进行数据模拟，分析了接种对疾病流行的影响，并对文中的主要结论进行了验证。

Study on Stability of Epidemic Model with Vaccination and Nonlinear Infectious Force

A class of SEIR infectious disease model with inoculation is studed, and obtains the threshold condition of the existence of various equilibrium points. By using Liapunove function, Lasalle invariance principle, Hurwith criterion is proved when the basic reproduction number is less than one, the disease-free equilibrium is globally asymptotically stable；when the basic reproduction number is greater than one, this model has two equilibria, the disease-free equilibrium is unstable, discriminant analysis proved the local asymptotic stability of the equilibrium point local disease by Hurwitz, further using the theory of matrix composite track stability and global asymptotic stability of the endemic equilibrium is proved. Finally, the model is simulated, and the effect of vaccination on the epidemic is analyzed, and the main conclusions are verified in this paper.