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Mathematical Model of Dengue Disease with the Incubation Period of Virus

Authors: P. Pongsumpun

Abstract:

Dengue virus is transmitted from person to person through the biting of infected Aedes Aegypti mosquitoes. DEN-1, DEN-2, DEN-3 and DEN-4 are four serotypes of this virus. Infection with one of these four serotypes apparently produces permanent immunity to it, but only temporary cross immunity to the others. The length of time during incubation of dengue virus in human and mosquito are considered in this study. The dengue patients are classified into infected and infectious classes. The infectious human can transmit dengue virus to susceptible mosquitoes but infected human can not. The transmission model of this disease is formulated. The human population is divided into susceptible, infected, infectious and recovered classes. The mosquito population is separated into susceptible, infected and infectious classes. Only infectious mosquitoes can transmit dengue virus to the susceptible human. We analyze this model by using dynamical analysis method. The threshold condition is discussed to reduce the outbreak of this disease.

Keywords: Transmission model, intrinsic incubation period, extrinsic incubation period, basic reproductive number, equilibriumstates, local stability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1056370

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[1] World Health Organization, Dengue Haemorrhagic fever: Diagnosis treatment and control, Geneva, 1997.
[2] D.J. Gubler, "Dengue and Dengue Hemorrhagic Fever", Clinical Microbiology Review, vol.11, pp.480-496, 1998.
[3] S.B.Halstead, "Pathogenesis of Dengue: Challenges to molecular biology", Science, vol.239 , pp.476-481, 1998.
[4] TropNetEurop Sentinel Surveillance, Dengue fever in 2002. Special Report 23.06.02, 2002.
[5] L.Esteva and C.Vargas, "Analysis of a dengue disease transmission model", Mathematical Bioscience, vol.150, pp.131-151, 1998.
[6] M.Robert., Stability and complexity in model ecosystem, Princeton University Press, 1973.
[7] E.K.Leah , Mathematical models in biology, Random House,Inc., (1988)
[8] J.S.Koopman, D.R.Prevots, M.A.V.Mann, H.G.Dantes, M.L.Z.Aquino, I.M.Longini, J.r. and Js. Amor, "Determinants and Predictors of dengue Infection in Mexico", American Journal of Epidemiology., vol.133, pp.1168-1178, 1991.
[9] L.Molineaux and G.Gramiccia, The Garki project : research on the epidemiology and control of malaria in the Sudan savanna of West Africa World Health Organization, Geneva, 1980.
[10] P. Pongsumpun, K. Patanarapelert, M. Sripom, S. Varamit and I.M. Tang, Infection risk to travelers going to dengue fever endemic regions, Southeast Asian J. Trop. Med. Pub. Health, vol.35, pp.155-159, 2004.
[11] P.Pongsumpun and R. Kongnuy, Model for the transmission of dengue disease in pregnant and non-pregnant patients, International journal of mathematical models and methods in applied sciences, vol.3, no.1, pp.127-132, 2007.