Mathematical Model of Dengue Disease with the Incubation Period of Virus
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51191", author = "P. Pongsumpun", title = "Mathematical Model of Dengue Disease with the Incubation Period of Virus", 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.", volume = "2", number = "8", pages = "530-5", }