Analysis Of The Stability Of An Epidemic Model With Vaccination And Nonlinear Incidence Rate

With the development of globalization,the main cause of human deaths in the world today is still infectious diseases.It has caused serious disasters to the people of all countries in the world.However,since the beginning of the 21st century,vaccination has played an increasingly important role in controlling the spread of infectious diseases and reducing the incidence of infectious diseases.The type of incidence used in the study of infectious disease models should be based on specific diseases.With environmental and other factors,according to some available statistical data,the nonlin-ear incidence rate can more accurately reflect the transmission mechanism of infectious diseases than the linear incidence rate.Therefore,the inci-dence of vaccination and non-linearity is crucial for the study of infectious disease models.The full text is divided into three parts:The first part introduces the research background and status of infectious diseases and the research progress of infectious disease models.It gives the theoretical knowledge of the stability analysis of infectious disease models.The second part establishes a vaccine and nonlinearity.The SIVS epidemic model of mor-bidity rate gives the basic regeneration number of the model,and uses the Hurwitz criterion,the second additive composite matrix and the central manifold theory to analyze the local stability,global stability analysis,and branching of the equilibrium point.Analysis,and gives the system has the conditions of the backward branch.Data analysis shows that the overall dynamics of disease transmission is determined by the basic regeneration number R₀.If R₀<1,then the disease gradually disappears,the disease-free equilibrium It is locally asymptotically stable.If R₀>1,then the disease persists,and the endemic equilibrium is globally asymptotically stable in the feasible region.To support the results of the analysis,nu-merical simulations are performed using hypothetical data sets.The three parts propose some points for perfection in the paper in order to better apply the actual spread of the disease.