Theory in Biosciences

, Volume 137, Issue 1, pp 67–78 | Cite as

Mathematical modeling of cancer–immune system, considering the role of antibodies

  • Sumana Ghosh
  • Sandip Banerjee
Original Article


A mathematical model for the quantitative analysis of cancer–immune interaction, considering the role of antibodies has been proposed in this paper. The model is based on the clinical evidence, which states that antibodies can directly kill cancerous cells (Ivano et al. in J Clin Investig 119(8):2143–2159, 2009). The existence of transcritical bifurcation, which has been proved using Sotomayor theorem, provides strong biological implications. Through numerical simulations, it has been illustrated that under certain therapy (like monoclonal antibody therapy), which is capable of altering the parameters of the system, cancer-free state can be obtained.


Cancer cells B cells Plasma cells Antibodies Global stability Transcritical bifurcation 



We are grateful to the anonymous reviewers for their comments and useful suggestions to improve the quality of the paper. This study was supported by the Indo-French Centre for Applied Mathematics (IFCAM) (Grant No. MA/IFCAM/13/120) and the Ministry of Human Resource Development (MHRD) (Grant No. MHR02-41-113-429).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia

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