具有疫苗接种和无症状患者感染的SVEAIR模型的稳定性分析

SVEAIR infectious disease dynamics model for a class of infectious diseases w- ith vaccinated and asymptomatic patients is developed and investigated. Firstly, the positivi- ty and boundedness of the model solutions are proved, secondly, the disease-free equilibrium point $W^{0}$ and the basic regeneration number $R_{0}$ are given for the model, respectively, and it is proved that there exists a unique positive endemic equilibrium point of the model when $R_{0}$ $>1$, and local stability of the disease-free equilibrium point $W^{1}$ is proved. Then, we prove t- he local stability of the disease-free equilibrium point $W^{0}$ and the local stability of the endem- ic equilibrium point $W^{1}$ through LaSalle's invariant set principle and the construction of Lya- punov's generalized function, and finally, we draw conclusions from the theoretical results of the model.