A FRACTIONAL ORDER SEIR MODEL WITH DENSITY DEPENDENT DEATH RATE

DEMİRCİ E., ÜNAL A., ÖZALP N.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.40, no.2, pp.287-295, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 2
  • Publication Date: 2011
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.287-295
  • Keywords: Fractional derivative, Initial value problem, SEIR model, Stability, Numerical solution
  • Ankara University Affiliated: Yes

Abstract

In this paper, we introduce a fractional order SEIR epidemic model with vertical transmission, where the death rate of the population is density dependent, i.e., dependent on the population size. It is also assumed that there exists an infection related death rate. We show the existence of nonnegative solutions of the model, and also give a detailed stability analysis of disease free and positive fixed points. A numerical example is also presented.