Mathematical analysis of local and global dynamics of a new epidemic model

ÇAKAN S.

TURKISH JOURNAL OF MATHEMATICS, vol.46, pp.533-551, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 46
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-mat-2107-41
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.533-551
  • Keywords: Lyapunov function, LaSalle's invariance principle, the second additive compound matrix, Li-Muldowney geometric approach, next generation matrix method, basic reproduction number, Jacobian matrix, Routh-Hurwitz criteria
  • Inonu University Affiliated: Yes

Abstract

In this paper, we construct a new SEIR epidemic model reflecting the spread of infectious diseases. After calculating basic reproduction number R-0 by the next generation matrix method, we examine the stability of the model. The model exhibits threshold behavior according to whether the basic reproduction number R-0 is greater than unity or not. By using well-known Routh-Hurwitz criteria, we deal with local asymptotic stability of equilibrium points of the model according to R-0. Also, we present a mathematical analysis for the global dynamics in the equilibrium points of this model using LaSalle's Invariance Principle associated with Lyapunov functional technique and Li-Muldowney geometric approach, respectively.