With Nonlinear Infection Rate And Pulse Vaccination Of Infectious Disease Model

In this paper, three categories of infectious disease model, an SEIR EpidemicModel with Nonlinear Incidence Rate and vertical transmission, the other is theepidemic model with saturated infection rate Vaccination, using differential equationsanalysis, linesexual method has been disease-free equilibrium of the model isequivalent to local stability, the use of to Hurwitz discrimination to prove the localstability of endemic equilibrium point, use the Poincare-Bendixson nature, Lozinskilmeasure, and construct the composite second-order system, the Liapunovfunction toprove global asymptotic stability of the endemic equilibrium; the third category is thestudy of the SEIR epidemic model with pulse vaccination and vertical transmission,the use of the Floquet multiplier theorem and construct a more systematic proof of theglobal disease-free periodic solutionmore attractive.