TY  - JOUR
TI  - Threshold and Stability Results of a New Mathematical Model for Infectious Diseases Having Effective Preventive Vaccine
AB  - 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 $mathcal{R}_{0}<1.$ In addition, when $mathcal{R}_{0}<1$ it is expected that the disease-free equilibrium point of the model, and so the model, is stable in the sense of local and global. In this context, the threshold value $mathcal{R}_{0}$ regarding the model is obtained. The local asymptotic stability of the disease-free equilibrium is examined with analyzing the corresponding characteristic equation. Then, by proved the global attractivity of disease-free equilibrium, it is shown that this equilibria is globally asymptotically stable.
AU  - ÇAKAN, Sümeyye
DO  - 10.33187/jmsm.884304
PY  - 2021
JO  - Journal of mathematical sciences and modelling (Online)
VL  - 4
IS  - 2
SN  - 2636-8692
SP  - 56
EP  - 64
DB  - TRDizin
UR  - http://search/yayin/detay/450916
ER  -