Bulletin of Mathematical Biology

, Volume 80, Issue 5, pp 1059–1083 | Cite as

Ordinary Differential Equation Models for Adoptive Immunotherapy

  • Anne Talkington
  • Claudia Dantoin
  • Rick DurrettEmail author
Special Issue : Mathematical Oncology


Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.


Chimeric antigen receptor T cells ODE models Stability analysis Saturating response Acute lymphoblastic leukemia 



Funding was provided by National Science Foundation (Grant No. DMS 1505215).


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  • Anne Talkington
    • 1
  • Claudia Dantoin
    • 2
  • Rick Durrett
    • 3
    Email author
  1. 1.Bioinformatics and Computational BiologyUniversity of North CarolinaChapel HillUSA
  2. 2.Departments of Chemistry and Electrical and Computer EngineeringDuke UniversityDurhamUSA
  3. 3.Department of MathematicsDuke UniversityDurhamUSA

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