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

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  • Yang, Hyun Mo
  • Greenhalgh, David

Abstract

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].

Suggested Citation

  • Yang, Hyun Mo & Greenhalgh, David, 2015. "Proof of conjecture in: The basic reproduction number obtained from Jacobian and next generation matrices—A case study of dengue transmission modelling," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 103-107.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:103-107
    DOI: 10.1016/j.amc.2015.04.112
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    Cited by:

    1. Raimundo, Silvia Martorano & Yang, Hyun Mo & Rubio, Felipe Alves & Greenhalgh, David & Massad, Eduardo, 2023. "Modeling criminal careers of different levels of offence," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    2. Florin Avram & Rim Adenane & Lasko Basnarkov & Matthew D. Johnston, 2023. "Algorithmic Approach for a Unique Definition of the Next-Generation Matrix," Mathematics, MDPI, vol. 12(1), pages 1-40, December.

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