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The Stability of an Epidemic Model With Piecewise Constant Argument by Lyapunov-Razumikhin Method
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Author(s): Nur Cengiz (Süleyman Demirel University, Turkey)and Duygu Aruğaslan-Çinçin (Süleyman Demirel University, Turkey)
Copyright: 2020
Pages: 24
Source title:
Emerging Applications of Differential Equations and Game Theory
Source Author(s)/Editor(s): Sırma Zeynep Alparslan Gök (Süleyman Demirel University, Turkey)and Duygu Aruğaslan Çinçin (Süleyman Demirel University, Turkey)
DOI: 10.4018/978-1-7998-0134-4.ch011
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Abstract
The authors propose a nonlinear epidemic model by developing it with generalized piecewise constant argument (GPCA) introduced by Akhmet. The authors investigate invariance region for the considered model. For the taken model into consideration, they obtain a useful inequality concerning relation between the values of the solutions at the deviation argument and at any time for the epidemic model. The authors reach sufficient conditions for the existence and uniqueness of the solutions. Then, based on Lyapunov-Razumikhin method developed by Akhmet and Aruğaslan for the differential equations with generalized piecewise constant argument (EPCAG), sufficient conditions for the stability of the trivial equilibrium and the positive equilibrium are investigated. Thus, the theoretical results concerning the uniform stability of the equilibriums are given.
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