creators_name: Nurani, N.,  
creators_name: Soewono, E.,  
creators_name: Sidarto, K.A.,  
creators_id: nuning@dns.math.itb.ac.id
creators_id: esoewono@lppm.itb.ac.id
creators_id: sidarto@dns.math.itb.ac.id
type: article
datestamp: 2007-12-17 05:07:03
lastmod: 2008-08-16 02:16:30
metadata_visibility: show
corp_creators: Institut Teknologi Bandung, Faculty of Mathematics and Natural Science, Industrial and Financial Mathematics Research Division
title: Mathematical Model of Dengue Disease Transmission with Severe DHF Compartment
ispublished: pub
subjects: Q
full_text_status: none
keywords: Severe DHF compartment, Type reproductive number, Equilibrium point.

abstract: An SIR model for dengue disease transmission is discussed here. It is assumed that two viruses namely strain 1 and strain 2 cause the disease and long lasting immunity from infection caused by one virus may not be valid with respect to a secondary infection by the other virus. Our interest here is to derive and analyse the model taking into account the severe DHF compartment in the transmission model. The aim would be to find a control measure to reduce the DHF patients in the population, or to keep the number of patients at an acceptable level. Analysis of this model reveals that there are four equilibria, one of them is the disease-free, the other three equilibria correspond to the presence of single serotype respectively, and the coexistence of two serotypes. Stability analysis of each equilibria and their relations with type reproductive numbers are shown. We also discuss the ratio between total number of severe DHF compartment with respect to the total number of first infection compartment and the total number of secondary infection compartment, respectively. This ratio is needed for practical control measure in order to predict the “real” intensity of the endemic phenomena since only data of severe DHF compartment is available in the field.


2000 Mathematics Subject Classification: 92D30
date: 2007
date_type: published
publication: Bulletin of the Malaysian Mathematical Sciences Society
volume: 30
number: 2
publisher: Penerbit Universiti Sains Malaysia
pagerange: 143-157
refereed: TRUE
issn: 0126-6705
official_url: http://math.usm.my/bulletin/pdf/v30n2/v30n2p7.pdf
related_url_url: http://math.usm.my/bulletin/html/vol30_2_7.htm
referencetext: [1] K. Atkinson, Introduction to Numerical Analysis, John Wiley and Sons, New York, 1989. 

[2] M. Derouich, A. Boutayeb and E.H. Twizell, A model of dengue fever, BioMedical Engineering OnLine (2003).

[3] L. Esteva and C. Vargas, A model for dengue disease with variable human population, J. Math. Biol. 38(1999), 220—240.

[4] L. Esteva and C. Vargas, Analysis of a dengue fever disease transmission model, Math. Biosci. 150(1998), 131—151.

[5] L. Esteva and C. Vargas, Coexistence of different serotypes of dengue virus, J. Math. Biol. 46(2003), 31—47.

[6] L. Esteva and C. Vargas, Influence of vertical and mechanical transmission on the dynamics of dengue disease, Math. Biosci. 167(2000), 51-64.

[7] Z. Feng and J.X. Velasco-Hernandez, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol. 35(1997), 523-544.

[8] R.R. Graham, M. Juffrie, R. Tan, C.G. Hayes, I. Laksono, C. Ma’roef, Sutaryo, Erlin, K.R. Porter and S.B. Halstead, Aprospective seroepidemiologic study on dengue in children four to nine years of age in Yogyakarta, Indonesia. Studies in 1995-1996, Am. J. Prop. Med. Hyg. 61(3)(1999), 412-419.

[9] D.J. Gubler, Epidemic dengue/dengue homorrhagic fever as public health, social and economic problem in the 21st century, Trends Microbiol. 10(2)(2002).

[10] M.G. Roberts and J.A.P. Heesterbeek, A new method for estimating the effort required to control an infections disease, Proc. R. Soc. Lond. B, The Royal Society (2003), 1359-1364.

[11] D.W. Vaughn, S. Green, S. Kalayanarooj, B.L. Innis, S. Nimmannitya, S. Suntayakorn, T.P. Endy, B. Raengsakulrach, A.L. Rothman, F.A. Ennis and A. Nisalak, Dengue viremia titer, antibody response pattern, and virus serotype correlate with disease severity, J. Infect. Dis. 181(2000), 2—9.

[12] World Health Organization, Dengue Haemorrhagic Fever: Diagnosis, Treatment, Prevention and Control, Geneva, 1997.
citation: Nurani, N., and Soewono, E., and Sidarto, K.A., (2007) Mathematical Model of Dengue Disease Transmission with Severe DHF Compartment. Bulletin of the Malaysian Mathematical Sciences Society, 30 (2). pp. 143-157. ISSN 0126-6705