Stability and persistence in ODE models for populations with many stages

Guihong Fan, Yijun Lou, Horst R. Thieme, Jianhong Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)


A model of ordinary differential equations is formulated for populations which are structured by many stages. The model is motivated by ticks which are vectors of infectious diseases, but is general enough to apply to many other species. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions.
Original languageEnglish
Pages (from-to)661-686
Number of pages26
JournalMathematical Biosciences and Engineering
Issue number4
Publication statusPublished - 1 Jan 2015


  • And stability)
  • Basic reproduction number
  • Boundedness
  • Equilibria (existence
  • Extinction
  • Lyapunov functions
  • Persistence
  • Uniqueness

ASJC Scopus subject areas

  • General Medicine
  • Modelling and Simulation
  • General Agricultural and Biological Sciences
  • Computational Mathematics
  • Applied Mathematics


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