Analysis Of A SEIR Epidemic Model With Continuous And Impulsive Vaccination

In this paper, several types of SEIR epidemic model with vaccination hadbeen discussed, by analyzing the dynamics behavior of the model, the work wasdivided into the following sections.Firstly, a kind of the autonomous SEIR epidemic model of continuousvaccination was built to consider the effection of the factor of incubation period,saturated contact saturation, integral delay and vertical infection. By constructingLiapunov functional and using Liapunov-Lasella invariance principle, the modelof global stability was obtained; the sufficient conditions of the persistent modelwere obtained through the comparison principle. The accuracy of the model wasproved via the numerical simulation.Secondly, on the basis of the autonomous SEIR epidemic model ofcontinuous vaccination, a kind of continuous vaccination of noautonomous SEIRepidemic model was studied, by considering for all the functions which maketime as the parameters in the model. Using the property of continuous boundedfunction on the interval has the supremum and infimum, the problem of solvingthe noautonomous model was translated into solving the problem of autonomousmodel. The sufficient conditions of persistence and illnesses extinction wereobtained by using the comparison principle. The accuracy of the model wasproved by the numerical simulation.Finally, a kind of the autonomous SEIR epidemic model of impulsevaccination was established, after considering the effection of the factor ofincubation period, contact saturation, integral delay and vertical infection. Theglobal attractivity of the disease-free periodic solution was proved and thesufficient condition of persistence was gotten by applying the comparisonprinciple of the impulsive differential equations. The accuracy of the model’sconclusion was proved by numerical simulation. Under the background ofapplying the Pulse model into hepatitis B virus infections disease, through the numerical simulation, we can easily find that the inoculated treatment for thenewborns has the important significance on the control of hepatitis B virustransmission.