Proof of conjecture in: The basic reproduction number obtained from Jacobian and next generation matrices—A case study of dengue transmission modelling

Hyun Mo Yang, David Greenhalgh

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The spectral radius of the next generation matrix provides an expression for the basic reproduction number. Instead of calculating the dominant eigenvalue of the characteristic equation corresponding to the next generation matrix, a threshold parameter can be obtained by handling the coefficients of this equation. Here we prove two conjectures presented in [9].
Original languageEnglish
Pages (from-to)103-107
Number of pages5
JournalApplied Mathematics and Computation
Early online date22 May 2015
Publication statusPublished - 15 Aug 2015


  • compartmental modelling
  • Routh–Hurwitz criteria
  • spectral radius
  • threshold
  • single infection
  • coinfection

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