# Existence and global behaviour of solutions of a nonlinear system modelling some epidemic diseases

Volume 7, Issue 1, pp 26--40
Publication Date: August 08, 2022 Submission Date: May 29, 2021 Revision Date: June 17, 2021 Accteptance Date: July 26, 2021
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### Authors

U. Cakan - Inonu University, Department of Mathematics, Malatya, Turkey. E. Laz - Ministry of Education, , Diyarbakir, Turkey.

### Abstract

In this study, we introduce a new mathematical model with a vaccination strategy in which different levels of susceptibility of individuals to an epidemic are considered. This model, which also takes into account the latent period, consists of a delay differential equation system. After showing the uniqueness of solution of the system, we present the equilibrium points of the model and the reproduction number $\mathcal{R}_{0}$ which is a vital threshold in spread of diseases. Then by using Lyapunov function and LaSalle Invariance Principle \cite LaSalle, we give some results about the global stabilities of the equilibrium points ofthe model according to $\mathcal{R}_{0}$.

### Share and Cite

##### ISRP Style

U. Cakan, E. Laz, Existence and global behaviour of solutions of a nonlinear system modelling some epidemic diseases, Mathematics in Natural Science, 7 (2021), no. 1, 26--40

##### AMA Style

Cakan U., Laz E., Existence and global behaviour of solutions of a nonlinear system modelling some epidemic diseases. Math. Nat. Sci. (2021); 7(1):26--40

##### Chicago/Turabian Style

Cakan, U., Laz, E.. "Existence and global behaviour of solutions of a nonlinear system modelling some epidemic diseases." Mathematics in Natural Science, 7, no. 1 (2021): 26--40

### Keywords

• Global stability analysis
• Lyapunov function
• LaSalle invariance principle
• Mathematical epidemiology
• Vaccination strategy
• Covid 19

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