**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30075

##### Mathematical Model for Dengue Disease with Maternal Antibodies

**Authors:**
Rujira Kongnuy,
Puntani Pongsumpun,
I-Ming Tang

**Abstract:**

**Keywords:**
Dengue infection,
equilibrium states,
maternalantibodies,
pregnancy and infancy.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1079412

**References:**

[1] E. A. Henchal, and J.R. Putnak, "The dengue viruses," Clin Microbiol Rev., vol. 3, pp. 376-396, 1990.

[2] World Health Organization , Dengue Haemorrhagic fever:Diagnosis treatment and control., Geneva, 1997.

[3] K. B. Platt, K. J. Linthicum, K. S. Myint, B. L. Innis, K. Lerdthusnee, and D. W.Vaughn, "Impact of dengue virus infection on feeding behavior of Aedes aegypti," Am J Trop Med Hyg., vol. 57, pp. 119-125, 1997.

[4] P. K. Russell, S. Udomsakdi, and S. B. Halstead, "Antibody response in dengue and dengue hemorrhagic fever," Jpn J Med Sci Biol., vol. 20(suppl.), pp. 103-108, 1967.

[5] R. M. Scott, and P. K. Russell, "Complement fixation blocking activity of antidengue IgM antibody," J Immunol., vol. 109, pp. 875-881, 1972.

[6] OHP. Pepper, "A note of David Bylon and dengue," Annals of Int Med History., vol. 3, pp. 363-368, 1941.

[7] N. Bhamarapravate, V. Boonpucknavig, S. Boonpucknavig, and B.Petchclai, "Immune complexes in dengue hemorrhagic fever," J Med Assoc Thailand., vol. 61(suppl 3), pp. 62-66, 1978.

[8] S. Nimmannitya, "Clinical spectrum and management of dengue hemorrhagic fever," Southeast Asian J Trop Med Publ Health., vol. 18, pp. 392-397, 1987.

[9] S. B. Halstead, "Dengue:hematologic aspects," Seminars in Hematology., vol. 19, pp. 116-131, 1982.

[10] Division of Epidemiology, Ministry of Public Health, Thailand, Annual Epidemiological Survillance Report., 1997-2007.

[11] S. B. Halstead, S. Nimmannitya, and S. N. Cohen, "Observations related to pathogenesis of dengue hemorrhagic fever, IV.Relation of disease severity to antibody response and virus recovered," Yale J Biol Med., vol. 42, pp. 311-328, 1970.

[12] S. C. Kliks, S. Nimmanitya, A. Nisalak, and D.S. Burke, "Evidence that maternal dengue antibodies are important in the development of dengue hemorrhagic fever in infants," Am J Trop Med Hyg., vol. 38, pp. 411-419, 1988.

[13] D. J. Gubler, "The global pandemic of dengue/dengue hemorrhagic fever:current status and prospects for the future," Ann Acad Med Singapore., vol. 27, pp. 227-234, 1998.

[14] S. B. Halstead, "Observations related to pathogenesis of dengue hemorrhagic fever, IV.Relation of disease severity to antibody response and virus recovered," Yale J Biol Med., vol. 42, pp. 350-362, 1970.

[15] D. J. Gubler, "Dengue and dengue hemorrhagic fever," Clin Microbiol Rev., vol. 11, pp. 480-496, 1998.

[16] A. L. Rothman, and F. A. Ennis, "Immunopathogenesis of dengue hemorrhagic fever," Virology., vol. 257, pp. 1-6, 1999.

[17] L. Kabilan, S. Balasubramanian, S. M. Keshava, V. Thenmozhi, G. Sehar, S. C. Tewari, N. Arunachalam, R. Rajendran, and K. Satyanarayana, "Dengue disease spectrum among infants in the 2001 dengue epidemic in Chennai, Tamil Nadu, India," J Clin Microbiol., vol. 41, pp. 3919-3921, 2003.

[18] H. W. Hethcote, Three basic epidemiological models in Applied Mathematical Ecology., Springer-Verlag, Berlin, pp. 119-144, 1989.

[19] H. W. Hethcote, and J. W. Van Ark, Modeling HIV Transmission and AIDS in the United States., Lecture Notes in Biomath, Springer-Verlag, Berlin, 1992.

[20] L. Esteva, and C. Vargas, "Analysis of a dengue disease transmission model," Math Biosci., vol. 150, pp. 131-151, 1998.

[21] R. Kongnuy, P. Pongsumpun, and I-Ming Tang, "Analysis of a Mathematical Model for Dengue Disease in Pregnant Cases," Int J Biomed Sci., vol. 3, pp. 192-199, 2008.

[22] R. Ross , The Prevention of Malaria, Second Edition, Murray, London.

[23] M. Robert, Stability and Complexity in Model Ecosystems, Princeton University Press, New Jersey, 1973.

[24] P. Pongsumpun, and I-Ming 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.

[25] P. Pongsumpun , and R. Kongnuy, "Model for the transmission of dengue disease in pregnant and non-pregnant patients," Int J math models and methods in applied sci., vol. 3, pp. 127-132, 2007.

[26] 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.

[27] P. Pongsumpun, and I-Ming Tang, "Transmission Model for Plasmodium Vivax Malaria:Conditions for Bifurcation," Int J Biomed Sci., vol. 3, pp. 161-168, 2008.

[28] P. Pongsumpun, and I-Ming Tang, "Mathematical Model for the Transmission for P. Falciparum and P. Vivax Malaria along the Thai- Myanmar Border," Int J Biomed Sci., vol. 3, pp. 200-207, 2008.

[29] P. Pongsumpun, and I-Ming Tang, "Effect of the Seasonal Variation in the Extrinsic Incubation Period on the Long Term Behavior of the Dengue Hemorrhagic Fever Epidemic," Int J Biomed Sci., vol. 3, pp. 208-214, 2008.