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Mathematical analysis of within-host dengue dynamics with innate and adaptive immune responsess

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Abstract

Dengue is among the most prevalent arboviral disease in humans worldwide. Infection with dengue can cause a wide spectrum of disease indications, from clinically inapparent infection to life threatening severe disease. Despite the increasing burden of dengue, development of an effective vaccine has rather remained elusive. One reason is the complex immunopathogenesis involved during an infection. To understand the viral dynamics and immune responses during dengue, we develop a mathematical model which describes the dynamics of healthy cells, infected cells and pathogens in the presence of innate and adaptive immune responses. A detailed analysis of the model was done and the most important model parameters were identified. The analytical findings were demonstrated by numerical simulations. It was observed that the model has five equilibria, namely, the disease free equilibrium, immunity induced viral clearance, no immune equilibrium, virus persistence in the absence of adaptive immune response and no antibody equilibrium. A detailed stability analysis of each equilibrium was implemented. It was observed that no antibody immune equilibrium is unstable for some parameter values. Thus it can be inferred from the detailed analysis, that the introduction of immune response strongly affects the stability of the system and antibodies plays a very important role in sha** dengue dynamics.

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References

  1. Bhatt, S., P.W. Gething, O.J. Brady, J.P. Messina, A.W. Farlow, C.L. Moyes, J.M. Drake, J.S. Brownstein, A.G. Hoen, and O. Sankoh. 2013. The global distribution and burden of dengue. Nature 496: 504–507.

    Article  Google Scholar 

  2. Diamond, M.S., and T.C. Pierson. 2015. Molecular insight into dengue virus pathogenesis and its implications for disease control. Cell 162: 488–492.

    Article  Google Scholar 

  3. World Health Organization: World Health Organization and Special Programme for Research and Training in Tropical Diseases- Dengue: Guideline for Diagnosis, Treatment, Prevention and Control. France (2009). World Health Organization

  4. Sun, P., and T.J. Kochel. 2013. The battle between infection and host immune responses of dengue virus and its implication in dengue disease pathogenesis. Scientific World Journal 2013: 843469.

    Article  Google Scholar 

  5. Halstead, S.B. 2007. Dengue. Lancet 370 (9599): 2–9.

    Article  Google Scholar 

  6. Moulton, S.L., et al. 2016. State-of-the-art monitoring in treatment of dengue shock syndrome: a case series. Journal of Medical Case Reports 10 (1): 233.

    Article  Google Scholar 

  7. Bäck, A.T., and A. Lundkvist. 2013. Dengue viruses - an overview. Infection Ecology and Epidemiology 3: 10–34023019839.

    Google Scholar 

  8. Perry, A.K., G. Chen, D. Zheng, H. Tang, and G. Cheng. 2005. The host type I interferon response to viral and bacterial infections. Cell Research 15: 407–422.

    Article  Google Scholar 

  9. Pawelek, K.A., G.T. Huynh, M. Quinlivan, A. Cullinane, L. Rong, and A.S. Perelson. 2012. Modeling within-host dynamics of influenza virus infection including immune responses. PLoS Computational Biology 8 (6): 1002588.

    Article  MathSciNet  Google Scholar 

  10. Navarro-Sánchez, E., P. Desprès, and L. Cedillo-Barrón. 2005. Innate immune responses to dengue virus. Archives of Medical Research 36: 425–435.

    Article  Google Scholar 

  11. Host Response to the Dengue Virus.http://www.nature.com/scitable/topicpage/host-response-to-the-dengue-virus-22402106. Accessed 9 Apr 2016.

  12. Gujarati, T.P., and G. Ambika. 2013. Virus antibody dynamics in primary and secondary dengue infections. Journal of Mathematical Biology 69: 1773–1800.

    Article  MathSciNet  MATH  Google Scholar 

  13. Nikin-Beers, R.P., and S.M. Ciupe. 2015. The role of antibody in enhancing dengue virus infection. Mathematical Biosciences 263: 83–92.

    Article  MathSciNet  MATH  Google Scholar 

  14. Pan American Health Organization, Scientific Publication No. 548: Dengue and Dengue Hemorrhagic Fever in the Americas: Guidelines for Prevention and Control. Washington, DC (1994). Pan American Health Organization, Scientific Publication No. 548

  15. Vaughn, D., Green, S., Kalayanarooj, S., Innis, B.L., Nimmannitya, S., Suntayakorn, S.E.A. 2000. Dengue viremia titer, antibody response pattern, and virus serotype correlate with disease severity. The Journal of infectious diseases 181(1), 2–9

  16. Murphy, B.R., and S.S. Whitehead. 2011. Immune response to dengue virus and prospects for a vaccine. Annual Review of Immunology 29: 587–619.

    Article  Google Scholar 

  17. WHO-VMI Dengue Vaccine Modeling Group. 2012. Assessing the potential of a candidate dengue vaccine with mathematical modeling. PLOS Neglected Tropical Diseases 6 (3): 1–6. https://doi.org/10.1371/journal.pntd.0001450.

    Article  Google Scholar 

  18. Ben-Shachar, R., and K. Koelle. 2015. Minimal within-host dengue models highlight the specific roles of the immune response in primary and secondary dengue infections. Journal of the Royal Society Interface 12: 20140886.

    Article  Google Scholar 

  19. Clapham, H.E., Tricou, V., Chau, N.V.V., Simmons, C.P., Ferguson, N.M. 2014 Within-host viral dynamics of dengue serotype 1 infection. Journal of the Royal Society Interface 11: 20140094

  20. Nuraini, N., H. Tasman, E. Soewono, and K.A. Sidarto. 2009. A with-in host dengue infection model with immune response. Mathematical and Computer Modelling 49: 1148–1155.

    Article  MathSciNet  MATH  Google Scholar 

  21. Nikin-Beers, R.P., and S.M. Ciupe. 2017. Modelling original antigenic sin in dengue viral infection. Mathematical Medicine and Biology. 35 (2): 257–272.

    Article  MathSciNet  MATH  Google Scholar 

  22. Perera, S.D., Perera, S.S.N. 2018 Simulation model for dynamics of dengue with innate and humoral immune responses. computational and mathematical methods in medicine 2018. https://doi.org/10.1155/2018/8798057

  23. Shechter, Y., L. Preciado-Patt, G. Schreiber, and M. Fridkin. 2001. Prolonging the half-life of human interferonalpha 2 in circulation: design, preparation, and analysis of (2-sulfo-9-fluorenylmethoxycarbonyl)7-interferon-alpha 2. Proceedings of the National Academy of Sciences 98: 1212–1217.

    Article  Google Scholar 

  24. Perera, S.D., Perera, S.S.N. 2019 Mathematical Modeling and Analysis of innate and humoral immune responses to dengue infections. International Journal of Biomathematics 12(7) . https://doi.org/10.1142/S1793524519500773

  25. Nowak, M.A., and R.M. May. 2000. Virus dynamics: mathematical principles of immunology and virology. New York: Oxford University Press.

    MATH  Google Scholar 

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Author notes

  1. S. S. N. Perera contributed to this work.

Authors and Affiliations

  1. Department of Decision Sciences, Faculty of Business, University of Moratuwa, Moratuwa, 10040, Sri Lanka

    Sulanie Perera

  2. Department of Mathematics, Faculty of Science, University of Colombo, Colombo, 00300, Sri Lanka

    S. S. N. Perera

Authors
  1. Sulanie Perera
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Correspondence to Sulanie Perera.

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Communicated by S Ponnusamy.

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Perera, S., Perera, S.S.N. Mathematical analysis of within-host dengue dynamics with innate and adaptive immune responsess. J Anal 31, 1687–1706 (2023). https://doi.org/10.1007/s41478-022-00514-x

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