The basic reproduction number obtained from Jacobian and next generation matrices - A case study of dengue transmission modelling

Autor(es)

Yang, Hyun Mo ^[1]

Afiliação do(s) autor(es)

^[1] UNICAMP IMECC DMA, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: BIOSYSTEMS; v. 126, p. 52-75, DEC 2014.
• Citações Web of Science: 14

Resumo

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. (C) 2014 Elsevier Ireland Ltd. All rights reserved. (AU)

• Processo FAPESP: 09/15098-0 - Avaliando controle de epidemias utilizando modelos matemáticos e computacionais
• Beneficiário: Hyun Mo Yang
• Modalidade de apoio: Auxílio à Pesquisa - Temático