title: Ordinary Differential Equation Models for Adoptive Immunotherapy.
abstract: 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.
authors.affiliation: Bioinformatics and Computational Biology, University of North Carolina, Chapel Hill, USA.
authors.forename: Anne
authors.initials: A
authors.lastname: Talkington
authors.affiliation: Departments of Chemistry and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
authors.forename: Claudia
authors.initials: C
authors.lastname: Dantoin
authors.affiliation: Department of Mathematics, Duke University, Durham, NC, USA. rtd@math.duke.edu.
authors.forename: Rick
authors.initials: R
authors.lastname: Durrett
mesh_terms: D018941:Antigens, CD19 / Q000378:metabolism; D006801:Humans; D016219:Immunotherapy, Adoptive / Q000379:methods / Q000706:statistics & numerical data; D055641:Mathematical Concepts; D018448:Models, Immunological; D054198:Precursor Cell Lymphoblastic Leukemia-Lymphoma / Q000276:immunology / Q000628:therapy; D013601:T-Lymphocytes / Q000276:immunology / Q000637:transplantation
chemical_list: D018941:Antigens, CD19; C000604811:CD19 molecule, human
keywords: Acute lymphoblastic leukemia; Chimeric antigen receptor T cells; ODE models; Saturating response; Stability analysis