关键词: 传染病模型；平衡点；基本再生数；稳定性 ,

Abstract: Considering the existence of asymptomatic individuals, the existence of mutant individuals, and the direct transformation of susceptible individuals into immune individuals by other means, a new SAIVR infectious disease model is established based on the traditional infectious disease model. According to the propagation rules of the SAIVR model, the propagation dynamics equation of the model is given by using the differential equation theory, and the existence of the disease-free equilibrium point and the endemic equilibrium point of the model is analyzed. The next-generation matrix method is used to compute the basic reproduction number of the model at the equilibrium point of the disease. According to the Routh-Hurwitz criterion, the local asymptotic stability condition of the model at the equilibrium point is obtained, and the global stability of the model is proved by Lyapunov theory. Simulation experiments show that the addition of asymptomatic individuals and mutant individuals can affect the outbreak time, outbreak scale, and death time of infectious diseases. It can effectively control the spread of SAIVR infectious diseases by reducing the transmission rate of infectious diseases in the population and increasing the immunity rate of infected persons and mutants.

Key words: epidemic model, equilibrium point, basic regeneration number, stability