With Continuous Immunization Of The Seis Model With Saturating Contact Rate Seiv Model Dynamics Analysis,

According to The World Health Organization report, infective diseases are still the first killer for the human. The human are confronted with the menace of infective diseases for long-term. For the experimental methods are not permitted on study of the infective diseases, the theoretic analysis and simulation technology are required for mechanism of epidemic, law of spread and tendency of the epidemic diseases. The dynamic models have been taken an important role in studying infective diseases. According to the spread mechanisms of disease, the models are often divided into SI, SIR, SIS, SIRS, SEI, SEIR and other types.Vaccination is a commonly used method for controlling disease, e.g, hepatitis B, measles, or influenza, etc. In Chapter 2, a SEIV epidemic model with a standard incidence rate is investigated:The model exhibits two equilibrias, namely, the disease-free equilibrium and the endemic equilibrium. It is shown that if the basic reproduction numberσ<1, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist. Moreover, we show that if the basic reproduction numberσ>1, the disease is uniformly persistent and the unique endemic equilibrium of the system is globally asymptotically stable under certain conditions.The incidence of a disease is the number of new cases per unit time and plays an important role in the study of mathematical epidemiology. Thieme and Castillo-Chavez argued that the general form of a population size dependent incidence should be written asλ0C(N)S/NI.where S and I are respectively the numbers of susceptibles and infectives at time t,λ0 is the probability per unit time of transmitting the infection between two individuals taking part in a contact, and C(N) is the unknown probability for an individual to take part in a contact. In Chapter 3, the SEIV model with this saturating contact rate is studied:The model also exhibits two equilibrias, namely, the disease-free equilibrium and the endemic equilibrium. It is shown that if the basic reproduction number a< 1, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist. Moreover, we show that if the basic reproduction numberσ>1, the unique endemic equilibrium of the system is locally asymptotically stable. when there is no death because of the disease, the endemic equilibrium is globally asymptotically stable.