Integrability of a SIS model

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

We prove that the classical model of an infectious disseise, which never kills and which does not induce autoimmunity, is integrable. This model can be written as x′ = - b x y - m x + c y + m k, y′ = b x y - (m + c) y with parameters b, c, k, m ∈ R. We provide the explicit expression of its first integrals and of the set of all its invariant algebraic curves. © 2008 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)574-578
JournalJournal of Mathematical Analysis and Applications
Volume344
DOIs
Publication statusPublished - 1 Aug 2008

Keywords

  • Darboux integrability
  • Darboux polynomials
  • Exponential factors
  • Invariant algebraic curves
  • SIS equation

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