Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/201798
Type: Artigo de periódico
Title: The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.
Author: Yang, Hyun Mo
Abstract: The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.
Subject: Compartmental Modelling
Geometric Mean
Partial Reproduction Numbers
Routh–hurwitz Criteria
Stability Analysis Of Disease Free Equilibrium
Rights: fechado
Identifier DOI: 10.1016/j.biosystems.2014.10.002
Address: http://www.ncbi.nlm.nih.gov/pubmed/25305542
Date Issue: 2014
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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