Threshold and Stability Results of a New Mathematical Model for Infectious Diseases Having Effective Preventive Vaccine

Abstract

This paper evaluates the impact of an effective preventive vaccine on the control of some infectious diseases by using a new deterministic mathematical model. The model is based on the fact that the immunity acquired by a fully effective vaccination is permanent. Threshold $mathcal{R}_{0}$, defined as the basic reproduction number, is critical indicator in the extinction or spread of any disease in any population, and so it has a very important role for the course of the disease that caused to an epidemic. In epidemic models, it is expected that the disease becomes extinct in the population if $mathcal{R}_{0}