A Delayed SEIR Model With Birth And Death Rate

In the paper , a mathematical model with both born rate and death rate is established and studied, which is an SEIR type of Infectious disease model with time delay. The paper consists of six chapters.In the first paper, we introduce the basic theory of ordinary differential equations and delayed differential equations and explain how to certificate the local and global stability of equilibrium of delayed equations.In the second paper, the basic definitions of infectious disease and the basic dynamic models of infectious disease are introduced, so that better models are established.In the third paper, we compute the parameters of SIR model using the data of HK, and further we analysis the threshold of existence of infectious disease.In the fourth paper, we introduce discrete delay into the SIR model, compute the time delay and discuss the global stability of equilibrium.In the fifth paper, we introduce the born rate and death rate into the SEIR model. The threshold of existence of endemic equilibrium is found and the local stability of equilibrium is discussed. At the same time, Hopf bifurcation will not appear in this model and we come up with that the death rate influence the threshold of existence of endemic equilibrium.In the sixth paper, we compare the parameters of three models and at the same time the time delay will influence other parameters of three models.Our main effort is that we build the mathematical model on the base of SIR model, and introduce delay to the system to study the stability of equilibrium of delayed differential equations. Using the theory of Hopf bifurcation, we obtain the result that Hopf bifurcation will not appeal" in the model. At the meanwhile, according to the theory of numerical solution in functional differential equations, we obtain the graphs of equation solutions. The graphs of the simulation results are drown, and the simulation results are consistent with the practical situation in HK. In the paper, the threshold in the model varies after we introduce time delay and death rate to the system and these parameters will influence with each other in the model.