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

Yıl 2021, , 56 - 64, 31.08.2021

Sümeyye Çakan

https://doi.org/10.33187/jmsm.884304

Öz

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.

Anahtar Kelimeler

Vaccine Effect, Diseasefree Equilibrium Point, Basic Reproduction Number, Local Asymptotic Stability, Global Attractivity, Global Asymptotic Stability

Kaynakça

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