Advertisement

Journal of Mathematical Biology

, Volume 69, Issue 6–7, pp 1773–1800 | Cite as

Virus antibody dynamics in primary and secondary dengue infections

  • Tanvi P. Gujarati
  • G. AmbikaEmail author
Article

Abstract

Dengue viral infections show unique infection patterns arising from its four serotypes, (DENV-1,2,3,4). Its effects range from simple fever in primary infections to potentially fatal secondary infections. We analytically and numerically analyse virus dynamics and humoral response in a host during primary and secondary dengue infection for long periods using micro-epidemic models. The models presented here incorporate time delays, antibody dependent enhancement, a dynamic switch and a correlation factor between different DENV serotypes. We find that the viral load goes down to undetectable levels within 7–14 days as is observed for dengue infection, in both cases. For primary infection, the stability analysis of steady states shows interesting dependence on the time delay involved in the production of antibodies from plasma cells. We demonstrate the existence of a critical value for the immune response parameter, beyond which the infection gets completely cured. For secondary infections with a different serotype, the homologous antibody production is enhanced due to the influence of heterologous antibodies. The antibody production is also controlled by the correlation factor, which is a measure of similarities between the different DENV serotypes involved. Our results agree with clinically observed humoral responses for primary and secondary infections.

Keywords

Humoral immune response Antibody dependent enhancement Correlation factor among serotypes Time delay  Stability analysis 

Mathematics Subject Classification (2010)

37N25 34A34 92B05 92C60 

Notes

Acknowledgments

We would like to thank Dr. Hedgewar Hospital, Aurangabad, Maharashtra for providing the ELISA data on Dengue infections. We thank the anonymous reviewers for their valuable comments.

References

  1. Agur Z, Mehr R (1992) Use of modelling for elucidating trypanotolerance: preliminary considerations. In: Perry BD, Hansen JW (eds) Modelling vector borne and other parasitic diseases. ILRAD, NairobiGoogle Scholar
  2. Ambika G, Dahanukar N (2009) Virus immune drug dynamics. In: Daniel M, Rajasekar S (eds) Nonlinear dynamics. Narosa Publication, New DelhiGoogle Scholar
  3. Beauchamin CAA, Handel AA (2011) Review of mathematical models of influenza A infection within a host or cell culture: lessons learned and challenges ahead. BMC Public Health 11(suppl 1):S7CrossRefGoogle Scholar
  4. Bielefeldt-Ohmann H (1997) Pathogenesis of dengue virus disease: missing pieces in the jigsaw. Trends Microbiol 5:409–413CrossRefGoogle Scholar
  5. Chan KR, Zhang SLX, Tan HC, Chan YK, Chow A, Lim APC, Vasudevan SG, Hanson BJ, Ooib EE (2011) Ligation of Fc gamma receptor IIB inhibits antibody-dependent enhancement of dengue virus infection. Proc Natl Acad Sci USA 108(30):12479–12484CrossRefGoogle Scholar
  6. Chaturvedi UC, Tandon P, Mathur A, Kumar A (1978) Host defence mechanisms against dengue virus infection of mice. J Gen Virol 39:293–302CrossRefGoogle Scholar
  7. Chen IC, Wang SM, Yu CK, Liu CC (2013) Subneutralizing antibodies to enterovirus 71 induce antibody-dependent enhancement of infection in newborn mice. Med Microbiol Immunol 202(4):259–265CrossRefGoogle Scholar
  8. Derouich M, Boutayeb A (2006) Dengue fever: mathematical modelling and computer simulation. Appl Math Comput 177:528–544CrossRefzbMATHMathSciNetGoogle Scholar
  9. Dibrov BF, Livshits MA, Volkenstein MV (1977) Mathematical model of immune processes. J Theor Biol 65:609–631CrossRefMathSciNetGoogle Scholar
  10. Diekmann O, Heesterbeek JAP (2000) Mathematical epidemiology of infectious diseases, model builiding, analysis and interpretation. John Wiley, ChichesterGoogle Scholar
  11. Dietz K (1975) Transmission and control of arbovirus diseases. In: Ludwig D, Cooke KL (eds) Epidemiology. SIAM, Philadelphia, pp 104–121Google Scholar
  12. Esteva L, Vargas C (1998) Analysis of a dengue disease transmission model. Math Biosci 15:131–151CrossRefGoogle Scholar
  13. Esteva L, Vargas C (1999) A model for dengue disease with variable human population. J Math Biol 38:220–240CrossRefzbMATHMathSciNetGoogle Scholar
  14. Esteva L, Vargas C (2003) Coexistence of different serotypes of dengue virus. J Math Biol 46:31–47CrossRefzbMATHMathSciNetGoogle Scholar
  15. Feng Z, Velasco-Hernandez JK (1997) Competative exclusion in vector host-model for the dengue fever. J Math Biol 35:523–544Google Scholar
  16. Fink J, Gu F, Vasudevan SG (2006) Role of T cells, cytokines and antibody in dengue fever and dengue haemorrhagic fever. Rev Med Virol 16:263–275CrossRefGoogle Scholar
  17. Fischer DB, Halstead SB (1970) Observations related to pathogenesis of dengue hemorrhagic fever, V. Examination of age specific sequential infection rates using a mathematical model. Yale J Biol Med 42:329–349Google Scholar
  18. Fowler AC (1981) Approximate solution of a model of biological immune responses incorporating delay. J Math Biol 13:23–45CrossRefzbMATHMathSciNetGoogle Scholar
  19. Garba SM, Gumel AB, Abu Baker MR (2008) Backward bifurcations in dengue transmission dynamics. Math Biosci 215:11–25Google Scholar
  20. Gibbons RV, Vaughn DW (2002) Dengue: an escalating problem. Br Med J 324:1563–1566CrossRefGoogle Scholar
  21. Guzman MG, Kouri G, Valds L, Bravo J, Vzquez S, Halstead SB (2002) Enhanced severity of secondary dengue-2 infections: death rates in 1981 and 1997 Cuban outbreaks. Rev Panam Salud Publica 11(4): 223–227Google Scholar
  22. Halstead SB (1970) Observations related to pathogenesis of dengue haemorrhagic fever VI: hypothesis and discussion. Yale J Biol Med 42:350–362Google Scholar
  23. Halstead SB (1988) Pathogenesis of dengue: challenges to molecular biology. Science 239:476–481CrossRefGoogle Scholar
  24. Halstead SB (2003) Neutralization and antibody-dependent enhancement of dengue viruses. Adv Virus Res 60:421–467CrossRefGoogle Scholar
  25. Halstead SB (2007) Dengue. Lancet 370:1644–1652CrossRefGoogle Scholar
  26. Halstead SB (2009) Antibodies determine virulence in dengue. Ann N Y Acad Sci 1171(Suppl. 1):E48–56CrossRefGoogle Scholar
  27. Imrie A, Meeks J, Gurary A, Sukhbaatar M, Truong TT, Cropp CB, Effler P (2007) Antibody to dengue 1 detected more than 60 years after infection. Viral Immunol 20(4):672–675CrossRefGoogle Scholar
  28. Janeway CA, Travers P, Walport M, Shlomchik MJ (2001) Immunobiology: the immune system in health and disease, 5th edn. Garland Science, New YorkGoogle Scholar
  29. Jindadamrongwech S, Thepparit C, Smith DR (2004) Identification of GRP 78 (BiP) as a liver cell expressed receptor element for dengue virus serotype 2. Arch Virol 149:915–927CrossRefGoogle Scholar
  30. Julander J, Perry ST, Shresta S (2011) Important advances in the field of anti-dengue virus research. Antivir Chem Chemother 21:105–116CrossRefGoogle Scholar
  31. Kinney RM, Huang CY (2001) Development of new vaccines against dengue fever and Japanese enchephalitis. Intervirology 44(2–3):176–197CrossRefGoogle Scholar
  32. Kitchen CMR, Yeghiazarian L, Hoh R, McCune JM, Sinclair E, Martin JN, Deeks SG (2011) Immune activation, Cd4+T cell counts, and viremia exhibit oscillatory patterns over time in patients with highly resistant HIV infection. PLoS One 6:e21190CrossRefGoogle Scholar
  33. Klein P (1980) Mathematical models of antibody response. Folia Microbiol 25:430–438CrossRefGoogle Scholar
  34. Kliks SC, Nisalak A, Brandt WE, Wahl L, Burke DS (1989) Antibody-dependent enhancement of dengue virus growth in human monocytes as a risk factor for dengue haemorrhagic fever. Am J Trop Med Hyg 40:444–451Google Scholar
  35. Kyle JL, Balsitis SB, Zhang L, Beatty RP, Harris E (2008) Antibodies play a greater role than immune cells in heterologous protection against secondary dengue virus infection in mouse model. Virology 380(2):296–303CrossRefGoogle Scholar
  36. Lakshmanan M, Senthilkumar DV (2010) Dynamics of non-linear time delay systems. Springer-Verlag, BerlinGoogle Scholar
  37. Lei HY, Yeh TM, Liu HS, Lin YS, Chen SH, Liu C (2001) Immunopathogenesis of dengue virus infection. J Biomed Sci 8:377–388CrossRefGoogle Scholar
  38. Lindenbach D, Rice CM (2001) Flaviviridae: the viruses and their replication. In: Knipe D, Howley P (eds) Fields virology. Lippincott, Philadelphia, pp 991–1041Google Scholar
  39. Marchuk GM (1997) Mathematical modelling of immune response on infectious diseases. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  40. Murphy BR, Whitehead SS (2011) Immune response to dengue virus and prospects for a vaccine. Annu Rev Immunol 29:587–619CrossRefGoogle Scholar
  41. Noisakran S, Perng GC (2008) Alternate hypothesis on the pathogenesis of dengue hemorrhagic fever (DHF)/dengue shock syndrome (DSS) in dengue virus infection. Exp Biol Med 233:401–408CrossRefGoogle Scholar
  42. Nowak MA, May RM (2000) Virus dynamics: mathematical principles of immunology and virology. Oxford University Press, New YorkGoogle Scholar
  43. Nuraini N, Soewono E, Sidarto KA (2007) A mathematical model of dengue internal transmission process. J Indonesia Math Soc (MIHMI) 13–1:123–132MathSciNetGoogle Scholar
  44. Nuraini N, Tasman H, Soewono E, Sidarto KA (2009) A with-in host dengue infection model with immune response. Math Comput Model 49:1148–1155CrossRefzbMATHMathSciNetGoogle Scholar
  45. Porterfield JS (1986) Antibody-depenedent enhancement of viral infectivity. In: Maramorosch K (ed) Advances in virus research, vol 31. Academic Press, London, pp 335–355Google Scholar
  46. Rigau-Perez JG, Clark GG, Gubler DJ, Reiter P, Sanders EJ, Vorndam AV (1998) Dengue and dengue haemorrhagic fever. Lancet 352:971–977CrossRefGoogle Scholar
  47. Rotham AL (2011) Immunity to dengue virus: a tale of original antigenic sin and tropical cytokine storms. Nat Rev 11:532–543CrossRefGoogle Scholar
  48. Rothman AL (2004) Dengue: defining protective versus pathologic immunity. J Clin Invest 113:946–951CrossRefGoogle Scholar
  49. Rothman AL, Ennis FA (1999) Immunopathogenesis of dengue haemorrhagic fever. Virology 257:1–6CrossRefGoogle Scholar
  50. Run Tao H, Innis BL, Nisalak A, Usawattanakul W, Wang S, Kalayanarooj S, Anderson R (1995) Antibodies that block virus attachment to vero cells are a major component of the human neutralizing antibody response against dengue virus type 2. J Med Virol 45:451–461CrossRefGoogle Scholar
  51. Sabin AB (1959) Dengue. In: Rivers TM, Horsfall F (eds) Viral and rickettsial infections of man, 3rd edn, vol 361. Lippincott, PhiladelphiaGoogle Scholar
  52. Science Daily (1998) Global warming would foster spread of dengue fever into some temperate regions. http://www.sciencedaily.com/releases/1998/03/980310081157.htm/. Accessed 2 September 2013
  53. Scott TW, Morrison AC (2010) Vector dynamics and transmission of dengue virus: implications for dengue survelliance and prevention strategies. In: Rotham AL (ed) Dengue virus. Current topics in microbiology and immunology, vol 338. Springer, Berlin, pp 115–128Google Scholar
  54. Tassaneetrithep B, Burgess TH, Granelli-Piperno A, Trumpfheller C, Finke J, Sun W, Eller MA, Pattanapanyasat K, Sarasombath S, Birx DL, Steinman RM, Schlesinger S, Marovich MA (2003) DC SIGN (CD209) mediates dengue virus infection of human dendritic cells. J Exp Med 197:823–829CrossRefGoogle Scholar
  55. Vaughn DW, Green S, Kalayanarooj S, Innis BL, Nimmannitya S, Suntayakorn S, Endy TP, Raengsakulrach B, Rothman AL, Ennis FA, Nisalak A (2000) Dengue viremia titer, antibody response pattern, and virus serotype correlate with disease severity. J Infect Dis 181:2–9CrossRefGoogle Scholar
  56. Wahala WM, de Silva AM (2011) The human antibody response to dengue virus infection. Viruses 3(12):2374–2395Google Scholar
  57. WHO (2013) Dengue and dengue haemorrhagic fever. http://www.who.int/mediacentre/factsheets/fs117/en/. Accessed 6October 2013
  58. World Health Organisation (WHO) and Special programme for Research and Training in Tropical Diseases (TDR) (2009) Dengue-guidelines for diagnosis, treatment, prevention and control (ISBN 9789241547871)Google Scholar
  59. Wu SJ, Grouard-Vogel G, Sun W, Mascola JR, Brachtel E, Putvatana R, Louder MK, Filgueira L, Marovich MA, Wong HK, Blauvelt A, Murphy GS, Robb ML, Innes BL, Birx DL, Hayes CG, Frankel SS (2000) Human skin Langerhans cells are targets of dengue virus infection. Nat Med 6:816–820CrossRefGoogle Scholar
  60. Zhou H, Deem MW (2006) Sculpting the immunological response to dengue fever by polytopic vaccination. Vaccine 24:2451–2459CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Indian Institute of Science Education and Research, TVMThiruvananthapuramIndia
  2. 2.Indian Institute of Science Education and Research, PunePuneIndia

Personalised recommendations