Qualitative Analysis Of Two Kinds Of Infective Disease Model With Part Immunization Rates

The existence of infective diseases is a very common phenomenon. It exists widely not only in the human, but also in the animals and plants. Serious consequence of infective diseases causes great damage and influence for human society. Therefore, it’s better to study the produce factors and trend of infective diseases, and it will be good for formulate correct control methods and treatments to control the spread trend of the infective diseases.Infective diseases dynamics is a very important branch of biomathematics. In this paper, the mechanism of infective diseases is analyzed and the mathematical model is established, using the Liapunov function method, Hurwitz criterion, Lasalle’s Invariant Principle, asymptotic stability theory and so on. The basic productive number R0is obtained, and the global stability of the disease-free equilibrium and endemic equilibrium are discussed. The main research contents of this paper are as follows:First of all, assuming the population in the environment is constant, we vaccinate the latent and neonatal who have impermanent immunity after recovery, but the vaccination is not completely effective. A SVEIR epidemic model with latent immunization is established after vaccination and treatment with a mechanism of partial immunization rates of transmission of infectious diseases. Liapunov function is constructed through using a new undetermined coefficient, then the existence, the stability of disease-free equilibrium and endemic equilibrium are discussed by using stability theory of the differential equations.Secondly, assuming part of the vaccinated with partial immunization rates are recovered after treatment, an epidemic model with partial immunity and partial recovery is established. Liapunov function is constructed, and the global stability of the disease-free equilibrium and endemic equilibrium are gained by using Lasalle’s Invariant Principle and asymptotic stability theory.Finally, the further research of infective diseases model is put forward.