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

This paper evaluates the impact of an effective preventive vaccine on control some infectious diseases by using a new deterministic mathematical model. The model is based fact that immunity acquired fully vaccination permanent. Threshold $\mathcal{R}_{0}$, defined as basic reproduction number, critical indicator in extinction or spread any disease population, and so it has very important role for course caused to epidemic. In epidemic models, expected becomes extinct population if $\mathcal{R}_{0}<1.$ addition, when $\mathcal{R}_{0}<1$ disease-free equilibrium point model, stable sense local global. this context, threshold value $\mathcal{R}_{0}$ regarding obtained. asymptotic stability examined with analyzing corresponding characteristic equation. Then, proved global attractivity equilibrium, shown equilibria globally asymptotically stable.