### Abstract

Language | English |
---|---|

Pages | 103-107 |

Number of pages | 5 |

Journal | Applied Mathematics and Computation |

Volume | 265 |

Early online date | 22 May 2015 |

DOIs | |

Publication status | Published - 15 Aug 2015 |

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### Keywords

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

### Cite this

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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.** / Yang, Hyun Mo; Greenhalgh, David.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Proof of conjecture in

T2 - Applied Mathematics and Computation

AU - Yang, Hyun Mo

AU - Greenhalgh, David

PY - 2015/8/15

Y1 - 2015/8/15

N2 - 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].

AB - 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].

KW - compartmental modelling

KW - Routh–Hurwitz criteria

KW - spectral radius

KW - threshold

KW - single infection

KW - coinfection

UR - http://www.sciencedirect.com/science/article/pii/S0096300315005743

U2 - 10.1016/j.amc.2015.04.112

DO - 10.1016/j.amc.2015.04.112

M3 - Article

VL - 265

SP - 103

EP - 107

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -