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


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.


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

Mathematics Subject Classification (2010)

37N25 34A34 92B05 92C60 



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.


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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

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