Integrability of a SIS model

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


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
Publication statusPublished - 1 Aug 2008


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


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