Dengue Transmission Model between Infantand Pregnant Woman with Antibody
Dengue, a disease found in most tropical and
subtropical areas of the world. It has become the most common
arboviral disease of humans. This disease is caused by any of four
serotypes of dengue virus (DEN1-DEN4). In many endemic
countries, the average age of getting dengue infection is shifting
upwards, dengue in pregnancy and infancy are likely to be
encountered more frequently. The dynamics of the disease is studied
by a compartmental model involving ordinary differential equations
for the pregnant, infant human and the vector populations. The
stability of each equilibrium point is given. The epidemic dynamic is
discussed. Moreover, the numerical results are shown for difference
values of dengue antibody.
[1] L. Esteva, and C. Vargas, "A model for dengue disease with variable
human population," J Math Bio., vol. 38, pp. 220-240, 1999.
[2] L. Esteva, and C. Vargas, "Coexistence of different serotypes of dengue
virus," J Math Bio., vol. 46, pp. 31-47, 2003.
[3] World Health Organization, Dengue Haemorrhagic fever: Diagnosis
treatment and control, Geneva, 1997.
[4] A. W. Smith, and E. Schwartz, "Dengue in travelers," N Engl J Med.,
vol. 353, pp. 924-32, 2005.
[5] D. J. Gubler, "Epidemic dengue/dengue hemorrhagic fever as a public
health, social and economic problem in the 21st century," Trends
Microbiol., vol. 10, pp. 100-3, 2002.
[6] Division of Vector-Born Infectious Disease, National Center for
Infectious Disease, Centers for Disease Control and Prevention, Dengue
fever. Available: (http://www.cdc.gov/ncidod/dvbid/dengue).
[7] M. G. Guzman, and G. Louri, "Dengue: an update," Lancet Infect Dis.,
vol. 2, pp. 23-42, 2002.
[8] F. P. Pinheiro, and S. J. Corber, "Global situation of dengue and dengue
haemorrhagic fever, and its emergence in the Americas," World Health
Stat Q., vol. 50, pp. 161-169, 1997.
[9] Division of Epidemiology, Ministry of Public Health, Thailand, Annual
Epidemiological Survillance Report, 1997-2007.
[10] KC. Shekhar, and OL. Hual, "Epidemiology of dengue/dengue
hemorrhagic fever in Malaysia-a retrospective epidemiological study
1973-1987 Part1: Dengue hemorrhagic fever (DHF)," Asia Pac J Public
Health., vol. 6, pp. 15-25, 1992.
[11] S. B. Halstead, "Observations related to pathogenesis of dengue
hemorrhagic. VI. Hypotheses and discussion," Yale J Biol Med., vol. 42,
pp. 350-362, 1970.
[12] D.J. Gubler, "Dengue and Dengue Hemorrhagic Fever," Clinical
Microbiology Review., vol. 11, pp.480-496, 1998.
[13] A. L. Rothman, and F. A. Ennis, "Immunopathogenesis of dengue
hemorrhagic fever," Virology, vol. 257, pp. 1-6, 1999.
[14] W. Veerachai, P. E. Timothy, S. Rudiwilai, K. Angkool, S. Sriluck, P.
Napuschon, A. Chanchai, W. V. David, HO. Cynthia, and N. Ananda,
"Transplacentally transferred maternal-infant antibodies to dengue
virus," J Trop Med Hyg., vol. 69, pp. 123-128, 2003.
[15] M Robert, Stability and Complexity in Model Ecosystems, Princeton
University Press, New Jersey, 1973.
[16] R. M. Anderson, and R. M. May, Infectious diseases of humans, Oxford:
Oxford University Press, 1991.
[17] K. Dietz, "The estimation of the basic reproduction number for
infectious disease," Stat Methods Med Res., vol. 2, pp. 23-41, 1993.
[18] R. M. Anderson, "Discussion: the Kermack-Mckendrick epidemic
threshold theorem," Bull Math Biol., vol. 53, pp. 3-32, 1991.
[1] L. Esteva, and C. Vargas, "A model for dengue disease with variable
human population," J Math Bio., vol. 38, pp. 220-240, 1999.
[2] L. Esteva, and C. Vargas, "Coexistence of different serotypes of dengue
virus," J Math Bio., vol. 46, pp. 31-47, 2003.
[3] World Health Organization, Dengue Haemorrhagic fever: Diagnosis
treatment and control, Geneva, 1997.
[4] A. W. Smith, and E. Schwartz, "Dengue in travelers," N Engl J Med.,
vol. 353, pp. 924-32, 2005.
[5] D. J. Gubler, "Epidemic dengue/dengue hemorrhagic fever as a public
health, social and economic problem in the 21st century," Trends
Microbiol., vol. 10, pp. 100-3, 2002.
[6] Division of Vector-Born Infectious Disease, National Center for
Infectious Disease, Centers for Disease Control and Prevention, Dengue
fever. Available: (http://www.cdc.gov/ncidod/dvbid/dengue).
[7] M. G. Guzman, and G. Louri, "Dengue: an update," Lancet Infect Dis.,
vol. 2, pp. 23-42, 2002.
[8] F. P. Pinheiro, and S. J. Corber, "Global situation of dengue and dengue
haemorrhagic fever, and its emergence in the Americas," World Health
Stat Q., vol. 50, pp. 161-169, 1997.
[9] Division of Epidemiology, Ministry of Public Health, Thailand, Annual
Epidemiological Survillance Report, 1997-2007.
[10] KC. Shekhar, and OL. Hual, "Epidemiology of dengue/dengue
hemorrhagic fever in Malaysia-a retrospective epidemiological study
1973-1987 Part1: Dengue hemorrhagic fever (DHF)," Asia Pac J Public
Health., vol. 6, pp. 15-25, 1992.
[11] S. B. Halstead, "Observations related to pathogenesis of dengue
hemorrhagic. VI. Hypotheses and discussion," Yale J Biol Med., vol. 42,
pp. 350-362, 1970.
[12] D.J. Gubler, "Dengue and Dengue Hemorrhagic Fever," Clinical
Microbiology Review., vol. 11, pp.480-496, 1998.
[13] A. L. Rothman, and F. A. Ennis, "Immunopathogenesis of dengue
hemorrhagic fever," Virology, vol. 257, pp. 1-6, 1999.
[14] W. Veerachai, P. E. Timothy, S. Rudiwilai, K. Angkool, S. Sriluck, P.
Napuschon, A. Chanchai, W. V. David, HO. Cynthia, and N. Ananda,
"Transplacentally transferred maternal-infant antibodies to dengue
virus," J Trop Med Hyg., vol. 69, pp. 123-128, 2003.
[15] M Robert, Stability and Complexity in Model Ecosystems, Princeton
University Press, New Jersey, 1973.
[16] R. M. Anderson, and R. M. May, Infectious diseases of humans, Oxford:
Oxford University Press, 1991.
[17] K. Dietz, "The estimation of the basic reproduction number for
infectious disease," Stat Methods Med Res., vol. 2, pp. 23-41, 1993.
[18] R. M. Anderson, "Discussion: the Kermack-Mckendrick epidemic
threshold theorem," Bull Math Biol., vol. 53, pp. 3-32, 1991.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:52383", author = "R. Kongnuy and P. Pongsumpun", title = "Dengue Transmission Model between Infantand Pregnant Woman with Antibody", abstract = "Dengue, a disease found in most tropical and
subtropical areas of the world. It has become the most common
arboviral disease of humans. This disease is caused by any of four
serotypes of dengue virus (DEN1-DEN4). In many endemic
countries, the average age of getting dengue infection is shifting
upwards, dengue in pregnancy and infancy are likely to be
encountered more frequently. The dynamics of the disease is studied
by a compartmental model involving ordinary differential equations
for the pregnant, infant human and the vector populations. The
stability of each equilibrium point is given. The epidemic dynamic is
discussed. Moreover, the numerical results are shown for difference
values of dengue antibody.", keywords = "Dengue antibody, infant, pregnant human,mathematical model.", volume = "2", number = "8", pages = "543-7", }