Bulletin of Mathematical Biology

, Volume 81, Issue 12, pp 4951–4976 | Cite as

Modelling the Host Immune Response to Mature and Immature Dengue Viruses

  • Milen Borisov
  • Gabriel Dimitriu
  • Peter RashkovEmail author
Original Article


Immature dengue virions contained in patient blood samples are essentially not infectious because the uncleaved surface protein prM renders them incompetent for membrane fusion. However, the immature virions regain full infectivity when they interact with anti-prM antibodies, and once opsonised virion fusion into Fc receptor-expressing cells is facilitated. We propose a within-host mathematical model for the immune response which takes into account the dichotomy between mature infectious and immature noninfectious dengue virions. The model accounts for experimental observations on the different interactions of plasmacytoid dendritic cells with infected cells producing virions with different infectivity. We compute the basic reproduction number as a function of the proportion of infected cells producing noninfectious virions and use numerical simulations to compare the host’s immune response in a primary and a secondary dengue infections. The results can be placed in the immunoregulatory framework with plasmacytoid dendritic cells serving as a bridge between the innate and adaptive immune response, and pose questions for potential experimental work to validate hypothesis about the evolutionary context whereby the virus strives to maximise its chance for transmission from the human host to the mosquito vector.


Dengue Mathematical model Viral dynamics Immune response 

Mathematics Subject Classification

34A34 92B05 49Q12 



This publication is based on work from COST Action CA16227 Investigation & Mathematical Analysis of Avant-garde Disease Control via Mosquito Nano-Tech-Repellents, supported by COST (European Cooperation in Science and Technology). Weblink: Peter Rashkov would like to thank the Mathematical Biosciences Institute (funded from the National Science Foundation Division of Mathematical Sciences and supported by The Ohio State University) for the opportunity to participate in the Emphasis Semester on Infectious Diseases: Data, Modelling, Decisions (Spring 2018). The authors thank Libin Rong and Nikolay I. Nikolov for the helpful discussions during the manuscript revision.

Supplementary material

11538_2019_664_MOESM1_ESM.pdf (706 kb)
Supplementary material 1 (pdf 706 KB)


  1. Anderson R, Wang S, Osiowy C, Issekutz AC (1997) Activation of endothelial cells via antibody-enhanced dengue virus infection of peripheral blood monocytes. J Virol 71(6):4226–4232Google Scholar
  2. Ansari N, Hesaaraki M (2012) A within host dengue infection model with immune response and Beddington–DeAngelis incidence rate. Appl Math 3:177–184MathSciNetGoogle Scholar
  3. Asselin-Paturel C, Brizard G, Chemin K, Boonstra A, O’Garra A, Vicari A, Trinchieri G (2005) Type I interferon dependence of plasmacytoid dendritic cell activation and migration. J Exp Med 201(7):1157–1167Google Scholar
  4. Beltramello M, Williams KL, Simmons CP, Macagno A, Simonelli L, Quyen N, Sukupolvi-Petty S, Navarro-Sanchez E, Young PR, de Silva AM, Rey FA, Varani L, Whitehead SS, Diamond MS, Harris E, Lanzavecchia A, Sallusto F (2010) The human immune response to dengue virus is dominated by highly cross-reactive antibodies endowed with neutralizing and enhancing activity. Cell Host Microbe 8(3):271–283Google Scholar
  5. Ben-Shachar R, Koelle K (2015) Minimal within-host dengue models highlight the specific roles of the immune response in primary and secondary dengue infections. J R Soc Interface 12:20140886Google Scholar
  6. Ben-Shachar R, Schmidler S, Koelle K (2016) Drivers of inter-individual variation in dengue viral load dynamics. PLoS Comput Biol 12(11):e1005194Google Scholar
  7. Bray M, Lai C (1991) Dengue virus premembrane and membrane proteins elicit a protective immune response. Virology 185(1):505–508Google Scholar
  8. Chen X, Liu X, Liu W, Guo W, Yu Q, Wang C (2013) Comparative analysis of dendritic cell numbers and subsets between smoking and control subjects in the peripheral blood. Int J Clin Exp Patho 6(2):290–296Google Scholar
  9. Clapham H, Tricou V, Van Vinh Chau N, Simmons C, Ferguson N (2014) Within-host viral dynamics of dengue serotype 1 infection. J R Soc Interface 11:20140094Google Scholar
  10. Costa VV, Fagundes CT, Souza DG, Teixeira MM (2013) Inflammatory and innate immune responses in dengue infection: protection versus disease induction. Am J Pathol 182(6):1950–1961Google Scholar
  11. Décembre E, Assil S, Hillaire MLB, Dejnirattisai W, Mongkolsapaya J, Screaton GR, Davidson AD, Dreux M (2014) Sensing of immature particles produced by dengue virus infected cells induces an antiviral response by plasmacytoid dendritic cells. PLoS Pathog 10(10):1004434Google Scholar
  12. Dejnirattisai W, Jumnainsong A, Onsirisakul N, Fitton P, Vasanawathana S, Limpitikul W, Puttikhunt C, Edwards C, Duangchinda T, Supasa S, Chawansuntati K, Malasit P, Mongkolsapaya J, Screaton G (2010) Cross-reacting antibodies enhance dengue virus infection in humans. Science 328(5979):745–748Google Scholar
  13. Dimitriu G, Lorenzi T, Ştefănescu R (2014) Evolutionary dynamics of cancer cell populations under immune selection pressure and optimal control of chemotherapy. Math Model Nat Phenom 9:88–104MathSciNetzbMATHGoogle Scholar
  14. van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180:29–48MathSciNetzbMATHGoogle Scholar
  15. Dung NTP, Duyen HTL, Thuy NTV, Ngoc TV, Chau NVV, Hien TT, Rowland-Jones SL, Dong T, Farrar J, Wills B, Simmons CP (2010) Timing of CD8+ T cell responses in relation to commencement of capillary leakage in children with dengue. J Immunol 184(12):7281–7287Google Scholar
  16. Duong V, Lambrechts L, Paul RE, Ly S, Lay RS, Long KC, Huy R, Tarantola A, Scott TW, Sakuntabhai A, Buchya P (2015) Asymptomatic humans transmit dengue virus to mosquitoes. Proc Natl Acad Sci USA 11:14688–14693Google Scholar
  17. Fitzgerald-Bocarsly P, Dai J, Singh S (2008) Plasmacytoid dendritic cells and type I IFN: 50 years of convergent history. Cytokine Growth F R 19(1):3–19Google Scholar
  18. Friberg H, Bashyam H, Toyosaki-Maeda T, Potts J, Greenough T, Kalayanarooj S, Gibbons R, Nisalak A, Srikiatkhachorn A, Green S, Stephens H, Rothman A, Mathew A (2011) Cross-reactivity and expansion of dengue-specific t cells during acute primary and secondary infections in humans. Sci Rep 1:51Google Scholar
  19. Gibbons JD, Chakraborti S (2010) Nonparametric statistical inference, 5th edn. Taylor and Francis, Boca Raton, FLzbMATHGoogle Scholar
  20. Green S, Pichyangkul S, Vaughn DW, Kalayanarooj S, Nimmannitya S, Nisalak A, Kurane I, Rothman AL, Ennis FA (1999) Early cd69 expression on peripheral blood lymphocytes from children with dengue hemorrhagic fever. J Infect Dis 180(5):1429–1435Google Scholar
  21. Gujarati T, Ambika G (2014) Virus antibody dynamics in primary and secondary dengue infections. J Math Biol 69:1773–1800MathSciNetzbMATHGoogle Scholar
  22. Halstead S, O’Rourke E (1977) Antibody-enhanced dengue virus infection in primate leukocytes. Nature 265(5596):739–741Google Scholar
  23. Heinz FX, Stiasny K, Pschner-Auer G, Holzmann H, Allison SL, Mandl CW, Kunz C (1994) Structural changes and functional control of the tick-borne encephalitis virus glycoprotein e by the heterodimeric association with protein prm. Virology 198(1):109–117Google Scholar
  24. Kurane I, Rothman AL, Livingston PG, Green S, Gagnon SJ, Janus J, Innis BL, Nimmannitya S, Nisalak A, Ennis FA (1994) Immunopathologic mechanisms of dengue hemorrhagic fever and dengue shock syndrome. In: Brinton MA, Calisher CH, Rueckert R (eds) Positive-strand RNA viruses, pp 59–64. Springer, ViennaGoogle Scholar
  25. Marino S, Hogue IB, Ray CJ, Kirschner DE (2008) A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254(1):178–196MathSciNetzbMATHGoogle Scholar
  26. Mathan T, Figdor C, Buschow S (2013) Human plasmacytoid dendritic cells: from molecules to intercellular communication network. Front Immunol 4:372Google Scholar
  27. Mathew A, Rothman AL (2008) Understanding the contribution of cellular immunity to dengue disease pathogenesis. Immunol Rev 225(1):300–313Google Scholar
  28. McKenna K, Beignon AS, Bhardwaj N (2005) Plasmacytoid dendritic cells: linking innate and adaptive immunity. J Virol 79(1):17–27Google Scholar
  29. Montoya M, Schiavoni G, Mattei F, Gresser I, Belardelli F, Borrow P, Tough DF (2002) Type i interferons produced by dendritic cells promote their phenotypic and functional activation. Blood 99(9):3263–3271Google Scholar
  30. Nikin-Beers R, Ciupe SM (2015) The role of antibody in enhancing dengue virus infection. Math Biosci 263:83–92MathSciNetzbMATHGoogle Scholar
  31. Nuraini N, Tasman H, Soewono E, Sidarto KA (2009) A with-in host dengue infection model with immune response. Math Comput Model 49(5):1148–1155MathSciNetzbMATHGoogle Scholar
  32. Pichyangkul S, Endy TP, Kalayanarooj S, Nisalak A, Yongvanitchit K, Green S, Rothman AL, Ennis FA, Libraty DH (2003) A blunted blood plasmacytoid dendritic cell response to an acute systemic viral infection is associated with increased disease severity. J Immunol 171(10):5571–5578Google Scholar
  33. Pierson TC, Diamond MS (2012) Degrees of maturity: the complex structure and biology of flaviviruses. Curr Opin Virol 2(2):168–175Google Scholar
  34. Rodenhuis-Zybert IA, van der Schaar HM, da Silva Voorham JM, van der Ende-Metselaar H, Lei HY, Wilschut J, Smit JM (2010) Immature dengue virus: a veiled pathogen? PLoS Pathog 6(1):1000718Google Scholar
  35. Rodenhuis-Zybert IA, Wilschut J, Smit JM (2011) Partial maturation: an immune-evasion strategy of dengue virus? Trends Microbiol 19(5):248–254Google Scholar
  36. Silveira GF, Wowk PF, Cataneo AHD, dos Santos PF, Delgobo M, Stimamiglio MA, Lo Sarzi M, Thomazelli APFS, Conchon-Costa I, Pavanelli WR, Antonelli LRV, Báfica A, Mansur DS, dos Santos CND, Bordignon J (2018) Human T lymphocytes are permissive for dengue virus replication. J Virol 92(10):e02181Google Scholar
  37. Tough D (2012) Modulation of T-cell function by type I interferon. Immunol Cell Biol 90:492–497Google Scholar
  38. Waggoner JJ, Balmaseda A, Gresh L, Sahoo MK, Montoya M, Wang C, Abeynayake J, Kuan G, Pinsky BA, Harris E (2016) Homotypic dengue virus reinfections in Nicaraguan children. J Infect Dis 214(7):986–993Google Scholar
  39. Wang S, Wang X, Liu M, Bai O (2018) Blastic plasmacytoid dendritic cell neoplasm: update on therapy especially novel agents. Ann Hematol 97:563–572Google Scholar
  40. Webster B, Werneke SW, Zafirova B, This S, Coléon S, Décembre E, Paidassi H, Bouvier I, Joubert PE, Duffy D, Walzer T, Albert ML, Dreux M (2018) Plasmacytoid dendritic cells control dengue and chikungunya virus infections via IRF7-regulated interferon responses. eLife 7:e34273Google Scholar
  41. Zybert IA, van der Ende-Metselaar H, Wilschut J, Smit JM (2008) Functional importance of dengue virus maturation: infectious properties of immature virions. J Gen Virol 89(12):3047–3051Google Scholar

Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.University of Medicine and Pharmacy “Grigore T. Popa”, Universitatii 16IaşiRomania

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