Analysis of a Mathematical Model for Dengue Disease in Pregnant Cases
Dengue fever is an important human arboviral disease. Outbreaks are now reported quite often from many parts of the world. The number of cases involving pregnant women and infant cases are increasing every year. The illness is often severe and complications may occur. Deaths often occur because of the difficulties in early diagnosis and in the improper management of the diseases. Dengue antibodies from pregnant women are passed on to infants and this protects the infants from dengue infections. Antibodies from the mother are transferred to the fetus when it is still in the womb. In this study, we formulate a mathematical model to describe the transmission of this disease in pregnant women. The model is formulated by dividing the human population into pregnant women and non-pregnant human (men and non-pregnant women). Each class is subdivided into susceptible (S), infectious (I) and recovered (R) subclasses. We apply standard dynamical analysis to our model. Conditions for the local stability of the equilibrium points are given. The numerical simulations are shown. The bifurcation diagrams of our model are discussed. The control of this disease in pregnant women is discussed in terms of the threshold conditions.
[1] World Health Organization , Dengue Haemorrhagic fever:Diagnosis
treatment control., Geneva, 1997.
[2] J. K. Chye, C. T. Lim, J. M. Lim, R. George, and S. K. Lam, "Vertical
transmission of dengue," Clin Infect Dis.,vol 25, pp. 1374-7, 1997.
[3] L. Poli, E. Chungue, O. Soulignac, P. Kuo, and M. Papouin-Rauzy,
"Materno-Feral dengue," Bull Soc Path Exot, vol. 84 , pp. 513-521,
1991.
[4] P. Thaithumyanon, U. Thisyakorn, J. Deerojnawong, and B. L. Innis,
"Dengue infection complicated by severe hemorrhage and vertical
transmission in a parturient woman," Clin Infect Dis, vol. 18 , pp. 248-
249, 1994.
[5] T. Doussemart, P. Babe, G. Sibille, C. Neyret, and C. Berchel, "Prenatal
transmission of dengue:two new cases," J Perinatol, vol. 21 , pp. 255-
257, 2001.
[6] A. Kerdpanich, V. Watanaveeradej, R. Samakoses, S. Chumnanvanakij,
T. Chulyamitporn, P. Sumeksri, and et al, "Perinatal dengue infection,"
Southeast Asian J Trop Med Publ Health, vol. 32, pp. 488-493.
[7] L. Kabilan, S. Balasubramanian, S. M. Keshava, V. Thenmozhi, G.
Sehar, S. C. Tewari , and et al, "Dengue disease spectrum among infants
in the 2001 dengue epidemic in Chennai, Tamil Nadu, India," J.
Clin Microbiol, vol. 41, pp. 3919-3921, 2003.
[8] N. Malhotra, C. Chanana, and S. Kumar, "Dengue infection in
pregnancy," Int J Gynecol Obstet, vol. 94 , pp. 131-132, 2006.
[9] V. Wiwanitkit, "Dengue haemorrhagic fever in pregnancy:appraisal on
Thai cases," J Vector Borne Dis, vol. 43, pp. 203-205, 2006.
[10] V. Phupong, "Dengue fever in pregnancy:a case report," BMC
Pregnancy and Childbirth, vol. 1, pp. 1471-2393, 2001.
[11] K. Y. Chong, and K. C. Lin, A preliminary report of the fetal effects of
dengue infection in pregnancy, Gaoxiong Yi Xue Ke Xue Za Zhi, vol. 5,
pp. 31-34, 1989.
[12] L. T. Figueiredo, H. Carlucci, and G. Duarte, "Prospective study with
infants whose mothers had dengue during pregnancy," Rev Inst Med
Trop Sao Paulo, vol. 36, pp. 417-421, 1994.
[13] S. Bunyavejchevin, S. Tanawattanacharoen, N. Taechakraichana, U.
Thisyakorn, Y. Tannirandorn, and K. Limpaphayom, "Dengue
hemorrhagic fever during pregnancy: antepartum, intrapartum and
postpartum management," J Obstet Gynaecol Res, vol. 23, pp. 445-448,
1997.
[14] G. Carles, H. Peiffer, and A. Talarmin, "Effects of dengue fever during
pregnancy in French Guiana," Clin Infect Dis, vol. 28, pp. 638-40,
1999.
[15] G. Carles, A. Talarmin, C. H. Peneau, and M. Bertsch, "Dengue fever
and pregnancy, A study of 38 cases in French Guiana," J Gynecol
Obstet , vol. 29, pp. 758-762, 2000.
[16] P. Witayathawornwong, "Parturient and perinatal dengue hemorrhagic
fever," Southeast Asian J Trop Med Publ Health, vol. 34, pp. 797-799,
2003.
[17] S. Ahmed, "Vertical transmission of dengue: first case report from
Bangladesh," Southeast Asian J Trop Med Publ Health, vol. 34, pp.
800-803, 2003.
[18] B. N. Restrepo, D. M. Isaza, C. L. Salazar, J. L. Ramirez, G. E. Upegui,
and M. Ospina, "Neonatal and postnatal effects of dengue infection
during pregnancy," Biomedica, vol. 23, pp. 416-423, 2003.
[19] U. Chotigeat, S. Kalayanarooj, and A. Nisalak, "Vertical transmission of
dengue , infection in Thai infant: two case reports," J Med Assoc Thai,
vol. 86, pp. 628-632, 2003.
[20] W. Janjindamai, and P. Pruekprasert, "Perinatal dengue infection: a case
report and review of literature," Southeast Asian J Trop Med Publ
Health, vol. 34, pp. 793-796, 2003.
[21] S. Sirinavin, P. Nuntnarumit, S. Supapannachart, S. Boonkasidecha, C.
Techasaensiri, and S. Yoksarn, Pediatr Infect Dis J,vol. 23, pp. 1024-
1027, 2004.
[22] W. Petdachai, J. Silaon, S. Nimmannitya, and A. Nisalak, "Neonatal
dengue infection: report of dengue fever in a 1-day-old infant,"
Southeast Asian J Trop Med Publ Health, vol. 35, pp. 403-407, 2004.
[23] NAM. Ismail, M. Kampan, Z. A. Mahdy, M. A. Jamil, and ZRM. Razi,
Dengue in pregnancy," Southeast Asian J Trop Med Publ Health, vol.
37, pp. 681-683, 2006.
[24] W. Ranmali, G. N. Malavige, M. Pradeepan, N. Chandrika, F. Sirimali,
and L. Suranjith, "Dengue infections during pregnancy: A case series
from Sri Lanka and review of the literature," J Clin Virol, vol. 37, pp.
27-33, 2006.
[25] G. W. Litman, J. P. Rast, M. J. Shamblott, R. N. Haire, M. Hulst, W.
Roess, and et al, "Phylogenetic diversification of immunoglobulin
genes and the antibody repertoire," Mol Biol Evol, vol. 10, pp. 60-72,
1993.
[26] R. Ross, The Prevention of Malaria, Second Edition, Murray, London.
[27] G. MacDonald, The Epidemiology and Control of Malaria, Oxford
University Press, London, 1957.
[28] F. E. McKenzie, "Why model malaria ?," Parasititology Today , vol. 16,
pp. 511-516, 2000.
[29] L. Esteva, and C. Vargas, "Analysis of a dengue disease transmission
model," Math Biosci, vol. 150, pp. 131-151, 1998.
[30] M. Robert, Stability and Complexity in Model Ecosystems, Princeton
University Press, New Jersey, 1973.
[31] 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 Publ Health, vol. 35, pp. 155-
159, 2004.
[32] P. Pongsumpun, and I. M . Tang, "Mathematical model for the
transmission of Plasmodium Vivax Malaria," Int J math models and
methods in applied sci, vol. 3, pp. 117-121, 2007.
[33] F. C. Coelho, C. T. Codeco, and C. J. Struchiner, "Complete treatment of
uncertainties in a model for dengue R0 estimation," Cad Saude Publica,
vol. 24, pp. 853-861, 2008.
[1] World Health Organization , Dengue Haemorrhagic fever:Diagnosis
treatment control., Geneva, 1997.
[2] J. K. Chye, C. T. Lim, J. M. Lim, R. George, and S. K. Lam, "Vertical
transmission of dengue," Clin Infect Dis.,vol 25, pp. 1374-7, 1997.
[3] L. Poli, E. Chungue, O. Soulignac, P. Kuo, and M. Papouin-Rauzy,
"Materno-Feral dengue," Bull Soc Path Exot, vol. 84 , pp. 513-521,
1991.
[4] P. Thaithumyanon, U. Thisyakorn, J. Deerojnawong, and B. L. Innis,
"Dengue infection complicated by severe hemorrhage and vertical
transmission in a parturient woman," Clin Infect Dis, vol. 18 , pp. 248-
249, 1994.
[5] T. Doussemart, P. Babe, G. Sibille, C. Neyret, and C. Berchel, "Prenatal
transmission of dengue:two new cases," J Perinatol, vol. 21 , pp. 255-
257, 2001.
[6] A. Kerdpanich, V. Watanaveeradej, R. Samakoses, S. Chumnanvanakij,
T. Chulyamitporn, P. Sumeksri, and et al, "Perinatal dengue infection,"
Southeast Asian J Trop Med Publ Health, vol. 32, pp. 488-493.
[7] L. Kabilan, S. Balasubramanian, S. M. Keshava, V. Thenmozhi, G.
Sehar, S. C. Tewari , and et al, "Dengue disease spectrum among infants
in the 2001 dengue epidemic in Chennai, Tamil Nadu, India," J.
Clin Microbiol, vol. 41, pp. 3919-3921, 2003.
[8] N. Malhotra, C. Chanana, and S. Kumar, "Dengue infection in
pregnancy," Int J Gynecol Obstet, vol. 94 , pp. 131-132, 2006.
[9] V. Wiwanitkit, "Dengue haemorrhagic fever in pregnancy:appraisal on
Thai cases," J Vector Borne Dis, vol. 43, pp. 203-205, 2006.
[10] V. Phupong, "Dengue fever in pregnancy:a case report," BMC
Pregnancy and Childbirth, vol. 1, pp. 1471-2393, 2001.
[11] K. Y. Chong, and K. C. Lin, A preliminary report of the fetal effects of
dengue infection in pregnancy, Gaoxiong Yi Xue Ke Xue Za Zhi, vol. 5,
pp. 31-34, 1989.
[12] L. T. Figueiredo, H. Carlucci, and G. Duarte, "Prospective study with
infants whose mothers had dengue during pregnancy," Rev Inst Med
Trop Sao Paulo, vol. 36, pp. 417-421, 1994.
[13] S. Bunyavejchevin, S. Tanawattanacharoen, N. Taechakraichana, U.
Thisyakorn, Y. Tannirandorn, and K. Limpaphayom, "Dengue
hemorrhagic fever during pregnancy: antepartum, intrapartum and
postpartum management," J Obstet Gynaecol Res, vol. 23, pp. 445-448,
1997.
[14] G. Carles, H. Peiffer, and A. Talarmin, "Effects of dengue fever during
pregnancy in French Guiana," Clin Infect Dis, vol. 28, pp. 638-40,
1999.
[15] G. Carles, A. Talarmin, C. H. Peneau, and M. Bertsch, "Dengue fever
and pregnancy, A study of 38 cases in French Guiana," J Gynecol
Obstet , vol. 29, pp. 758-762, 2000.
[16] P. Witayathawornwong, "Parturient and perinatal dengue hemorrhagic
fever," Southeast Asian J Trop Med Publ Health, vol. 34, pp. 797-799,
2003.
[17] S. Ahmed, "Vertical transmission of dengue: first case report from
Bangladesh," Southeast Asian J Trop Med Publ Health, vol. 34, pp.
800-803, 2003.
[18] B. N. Restrepo, D. M. Isaza, C. L. Salazar, J. L. Ramirez, G. E. Upegui,
and M. Ospina, "Neonatal and postnatal effects of dengue infection
during pregnancy," Biomedica, vol. 23, pp. 416-423, 2003.
[19] U. Chotigeat, S. Kalayanarooj, and A. Nisalak, "Vertical transmission of
dengue , infection in Thai infant: two case reports," J Med Assoc Thai,
vol. 86, pp. 628-632, 2003.
[20] W. Janjindamai, and P. Pruekprasert, "Perinatal dengue infection: a case
report and review of literature," Southeast Asian J Trop Med Publ
Health, vol. 34, pp. 793-796, 2003.
[21] S. Sirinavin, P. Nuntnarumit, S. Supapannachart, S. Boonkasidecha, C.
Techasaensiri, and S. Yoksarn, Pediatr Infect Dis J,vol. 23, pp. 1024-
1027, 2004.
[22] W. Petdachai, J. Silaon, S. Nimmannitya, and A. Nisalak, "Neonatal
dengue infection: report of dengue fever in a 1-day-old infant,"
Southeast Asian J Trop Med Publ Health, vol. 35, pp. 403-407, 2004.
[23] NAM. Ismail, M. Kampan, Z. A. Mahdy, M. A. Jamil, and ZRM. Razi,
Dengue in pregnancy," Southeast Asian J Trop Med Publ Health, vol.
37, pp. 681-683, 2006.
[24] W. Ranmali, G. N. Malavige, M. Pradeepan, N. Chandrika, F. Sirimali,
and L. Suranjith, "Dengue infections during pregnancy: A case series
from Sri Lanka and review of the literature," J Clin Virol, vol. 37, pp.
27-33, 2006.
[25] G. W. Litman, J. P. Rast, M. J. Shamblott, R. N. Haire, M. Hulst, W.
Roess, and et al, "Phylogenetic diversification of immunoglobulin
genes and the antibody repertoire," Mol Biol Evol, vol. 10, pp. 60-72,
1993.
[26] R. Ross, The Prevention of Malaria, Second Edition, Murray, London.
[27] G. MacDonald, The Epidemiology and Control of Malaria, Oxford
University Press, London, 1957.
[28] F. E. McKenzie, "Why model malaria ?," Parasititology Today , vol. 16,
pp. 511-516, 2000.
[29] L. Esteva, and C. Vargas, "Analysis of a dengue disease transmission
model," Math Biosci, vol. 150, pp. 131-151, 1998.
[30] M. Robert, Stability and Complexity in Model Ecosystems, Princeton
University Press, New Jersey, 1973.
[31] 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 Publ Health, vol. 35, pp. 155-
159, 2004.
[32] P. Pongsumpun, and I. M . Tang, "Mathematical model for the
transmission of Plasmodium Vivax Malaria," Int J math models and
methods in applied sci, vol. 3, pp. 117-121, 2007.
[33] F. C. Coelho, C. T. Codeco, and C. J. Struchiner, "Complete treatment of
uncertainties in a model for dengue R0 estimation," Cad Saude Publica,
vol. 24, pp. 853-861, 2008.
@article{"International Journal of Medical, Medicine and Health Sciences:49543", author = "Rujira Kongnuy and Puntani Pongsumpun and I-Ming Tang", title = "Analysis of a Mathematical Model for Dengue Disease in Pregnant Cases", abstract = "Dengue fever is an important human arboviral disease. Outbreaks are now reported quite often from many parts of the world. The number of cases involving pregnant women and infant cases are increasing every year. The illness is often severe and complications may occur. Deaths often occur because of the difficulties in early diagnosis and in the improper management of the diseases. Dengue antibodies from pregnant women are passed on to infants and this protects the infants from dengue infections. Antibodies from the mother are transferred to the fetus when it is still in the womb. In this study, we formulate a mathematical model to describe the transmission of this disease in pregnant women. The model is formulated by dividing the human population into pregnant women and non-pregnant human (men and non-pregnant women). Each class is subdivided into susceptible (S), infectious (I) and recovered (R) subclasses. We apply standard dynamical analysis to our model. Conditions for the local stability of the equilibrium points are given. The numerical simulations are shown. The bifurcation diagrams of our model are discussed. The control of this disease in pregnant women is discussed in terms of the threshold conditions.
", keywords = "Dengue disease, local stability, mathematical model, pregnancy.", volume = "1", number = "5", pages = "214-8", }
