Analysis For SEIQR Model With Continuous Vaccination

Three types of epidemic models with isolation and vaccination were introducedin this article. The local stability of the disease-free equilibrium and endemicequilibrium of system were researched. And the permanence of disease wasconsidered.First, an SEIQR epidemic model with infectious force in both latent period andinfected period was established. Using the theory of the limit system, afive-dimensional system of model was reduced to a three-dimensional the thresholdwhich determines the spread of the disease was found, the existence of thedisease-free equilibrium point and the endemic equilibrium point were obtained.Using Huritz criterion, the sufficient condition for the local stability of thedisease-free equilibrium point was obtained. Through the construction of theLiapunov function, the global asymptotical stability of the endemic equilibriumpoint was proved, the uniform permanence of the endemic equilibrium was studied.Using the theory of compound matrix, the sufficient condition for the globalasymptotical stability of the endemic equilibrium was obtained. Using the Matlabsoftware, the numerical simulation was presented. Combining with the feature oftuberculosis and applying the conclusions of this model, the influence of isolationand vaccination was studied. We put forward some rational suggestions on control ofdisease.Second, an non-autonomous SEIQR epidemic model with the constant inflowof susceptible, exposed and infected was researched. Using the theory of the limittheorem reduce system, the uniform permanence of the endemic equilibrium wasstudied. Through the construction of the Liapunov function and using principle offixed point, the existence and the stability of the periodic solution was proved. Usingthe Matlab software, the numerical simulation was presented. Analysis of the effectof immigration input to the disease. Apply the conclusion to hand, foot and mouthdisease, analysis the regular of disease and put forward the strategies.At last, an SEIQR epidemic model with nonlinear incidence and time delays was studied. Using the limit theorem reduce system again. A threshold whichdetermines the outcome of the disease was found out, the existence of thedisease-free equilibrium point and the endemic equilibrium point were obtained.Using the limit theory, the local stability of the disease-free equilibrium point wasproved. Using comparison principle, the existence of the model was proved. Usingthe Matlab software, analysis of time delay and nonlinear incidence for disease.