In this project, we evaluate the impact of an effective preventive vaccine on the control of someinfectious diseases by using the deterministic mathematical model. The model is based on the fact thatthe immunity acquired by a fully effective vaccination is permanent. Threshold , defined as thebasic reproduction number, is critical indicator in the extinction or spread of any disease in anypopulation, and so it has a very important role for this project of the infectious disease that caused to an epidemic. In epidemic models, it is expected that the disease becomes extinct in thepopulation if . It is expected that the disease-free equilibrium point of the SVEIR model,and so the SVEIR model, is stable in the sense of local. And if , then it is the existence ofthe local endemic equilibrium point. So the threshold value regarding to the SVEIR model isobtained and also discussed the numerical simulation of the model.