S-I-R model with directed spatial diffusion

Fabio A. Milner, Ruijun Zhao

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


A S-I-R epidemic model is described in which susceptible individuals move away from foci of infection, and all individuals move away from overcrowded regions. It consists of hyperbolic partial differential equations, the sum of these equations being parabolic. Positivity and regularity of solutions are discussed and finite time blow-up of some solutions is illustrated through numerical simulations. A numerical test of the finite time blow-up of solutions is proposed.

Original languageEnglish (US)
Pages (from-to)160-181
Number of pages22
JournalMathematical population studies
Issue number3
StatePublished - Jul 2008
Externally publishedYes


  • Directed spatial diffusion
  • Finite time blow-up
  • S-I-R

ASJC Scopus subject areas

  • Demography
  • Geography, Planning and Development
  • General Agricultural and Biological Sciences
  • General Mathematics


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