The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling

dc.creatorYang H.M.
dc.date2014
dc.date2015-06-25T18:03:19Z
dc.date2015-11-26T15:05:46Z
dc.date2015-06-25T18:03:19Z
dc.date2015-11-26T15:05:46Z
dc.date.accessioned2018-03-28T22:16:21Z
dc.date.available2018-03-28T22:16:21Z
dc.identifier
dc.identifierBiosystems. Elsevier Ireland Ltd, v. 126, n. , p. 52 - 75, 2014.
dc.identifier3032647
dc.identifier10.1016/j.biosystems.2014.10.002
dc.identifierhttp://www.scopus.com/inward/record.url?eid=2-s2.0-84910048029&partnerID=40&md5=73cf73b1530bfde2d771629caa0a620a
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/88023
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/88023
dc.identifier2-s2.0-84910048029
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1257109
dc.descriptionThe 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.
dc.description126
dc.description
dc.description52
dc.description75
dc.descriptionAdams, B., Boots, M., How important is vertical transmission in mosquitoes for the persistence of dengue? Insights from a mathematical model (2010) Epidemics, 2, pp. 1-10
dc.descriptionAnderson, R.M., May, R.M., (1991) Infectious Diseases of Human. Dynamics and Control, , Oxford University Press, Oxford/New York/Tokyo
dc.descriptionBerman, A., Plemmons, R.J., (1979) Nonnegtive Matrices in the Mathematical Sciences, , Academic Press, New York
dc.descriptionDiekmann, O., Heesterbeek, J.A.P., (2000) Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, , Wiley, New York
dc.descriptionDiekmann, O., Heesterbeek, J.A.P., Roberts, M.G., The construction of next-generation matrices for compartmental epidemic models (2010) J. R. Soc. Interface, 7, pp. 873-885
dc.descriptionEdelstein-Keshet, L., (1988) Mathematical Models in Biology. Birkhäuser Mathematics Series, , McGraw-Hill Inc, New York
dc.descriptionEsteva, L., Yang, H.M., Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique (2000) Math. Biosci., 198, pp. 132-147
dc.descriptionHeesterbeek, J.A.P., Roberts, M.G., The type-reproduction number T in models for infectious disease control (2007) Math. Biosci., 206, pp. 3-10
dc.descriptionHeffernan, J.M., Smith, R.J., Wahl, L.M., Perspectives on the basic reproductive ratio (2005) J. R. Soc. Interface, 2, pp. 281-293
dc.descriptionHyman, J.M., Li, J., The reproductive number for an HIV model with differential infectivity and staged progression (2005) Linear Algebra Appl., 398, pp. 101-116
dc.descriptionHyman, J.M., Li, J., Infection-age structured epidemic models with behavior change or treatment (2007) J. Biol. Dyn., 1 (1), pp. 109-131
dc.descriptionLeite, M.B.F., Bassanezi, R.C., Yang, H.M., The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response (2000) IMA J. Math. Appl. Med. Biol., 17 (1), pp. 15-31
dc.descriptionLi, J., Blakeley, D., Smith, R.J., The failure of R0 (2011) Comput. Math. Methods Med., 2011, p. 527610
dc.descriptionMonath, T.P., (1989) The Arboviruses: Epidemiology and Ecology, 5. , (Ed).CRC Press, Boca Raton, FL
dc.descriptionNåsell, I., On eradication of schistosomiasis (1976) Theor. Popul. Biol., 10, pp. 133-144
dc.descriptionRaimundo, S.M., Massad, E., Yang, H.M., Modelling congenital transmission of Chagas' disease (2010) Biosystems, 99, pp. 215-222
dc.descriptionRaimundo, S.M., Yang, H.M., Venturino, E., Theoretical assessment of the relative incidence of sensitive and resistant tuberculosis epidemic in presence of drug treatment (2014) Math. Biosci. Eng., 11 (4), pp. 971-993
dc.descriptionRoberts, M.G., Heesterbeek, J.P.A., A new method to estimate the effort required to control an infectious disease (2003) Proc. R. Soc. Lond. Ser. B, 270, pp. 1359-1364
dc.descriptionRoberts, M.G., The pluses and minuses of R0 (2007) J. R. Soc. Interface, 4, pp. 949-961
dc.descriptionvan den Driessche, P., Watmough, J., Reproduction number and sub-threshold endemic equilibria for compartimental models of disease transmission (2002) Math. Biosci., 180 (1-2), pp. 29-48
dc.descriptionWesley, C.L., Allen, L.J.S., Langlais, M., Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission (2010) Math. Biosci. Eng., 7 (1), pp. 195-211
dc.descriptionWilliams, C.B., The use of logarithms in the interpretation of certain entomological problems (1937) Ann. Appl. Biol., 24 (2), pp. 404-414
dc.descriptionYang, H.M., Silveira, A.S.B., The loss of immunity in directly transmitted infections modelling: effects on the epidemiological parameters (1998) Bull. Math. Biol., 60 (2), pp. 355-372
dc.descriptionYang, H.M., Coutinho, F.A.B., Acquired immunity on a schistosomiasis transmission model - analysis of the stabilizing effects (1999) J. Theor. Biol., 196, pp. 473-482
dc.descriptionYang, H.M., Della Negra, M., Lian, Y.C., Queiroz, W., Hotta, L.K., The serorevertion and the survival related to HIV infection among children: statistical modeling applied to retrospective data collection (2003) Math. Comput. Model., 38, pp. 251-267
dc.descriptionYang, H.M., Comparison between schistosomiasis transmission modelling considering acquired immunity and age-structured contact pattern with infested water (2003) Math. Biosci., 184, pp. 1-26
dc.descriptionYang, H.M., Macoris, M.L.G., Galvani, K.C., Andrighetti, M.T.M., Wanderely, D.M.V., Assessing the effects of temperature on dengue transmission (2009) Epidemiol. Infect., 137 (8), pp. 1179-1187
dc.descriptionYang, H.M., Raimundo, S.M., Assessing the effects of multiple infections and long latency in the dynamics of tuberculosis (2010) Theor. Biol. Med. Model., 7, p. 41
dc.descriptionYang, H.M., Macoris, M.L.G., Galvani, K.C., Andrighetti, M.T.M., Follow up estimation of Aedes aegypti entomological parameters and mathematical modellings (2011) Biosystems, 103, pp. 360-371
dc.descriptionYang, H.M., Mathematical modeling of solid cancer growth with angiogenesis (2012) Theor. Biol. Med. Model., 9, p. 2
dc.descriptionYang, H.M., Mathematical modelling of the interaction between Mycobacterium tuberculosis infection and cellular immune response (2012) Proceedings of BIOMAT 2011, pp. 309-330. , World Scientific, Singapore, R. Mondaini (Ed.)
dc.descriptionYang, H.M., Boldrini, J.L., Fassoni, A.C., Lima, K.K.B., Freitas, L.F.S., Gomez, M.C., Andrade, V.R., Freitas, A.R.R., Abiotic effects on population dynamics of mosquitoes and their influences on the dengue transmission (2014) Ecological Modelling Applied to Entomology, , Springer, Berlim, C.P. Ferreira, W.A.C. Godoy (Eds.)
dc.descriptionYang, H.M., Assessing the influence of quiescence eggs on the dynamics of mosquito Aedes aegypti (2014) Appl. Math., , (in press)
dc.descriptionYang, H.M., Assessing the contribution of transovarial transmission in the dynamics of dengue infection (2014) BioMed Res. Int., , (submitted for publication)
dc.languageen
dc.publisherElsevier Ireland Ltd
dc.relationBioSystems
dc.rightsfechado
dc.sourceScopus
dc.titleThe Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling
dc.typeArtículos de revistas


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