This ordinary differential equation model of the cellular kinetics and pharmacodynamics of CAR-T cell therapy is described in the publication:
Chaudhury, A., Zhu, X., Chu, L., Goliaei, A., June, C., Kearns, J. and Stein, A., 2020. Chimeric Antigen Receptor T Cell Therapies: A Review of Cellular Kinetic‐Pharmacodynamic Modeling Approaches. The Journal of Clinical Pharmacology, 60(S1).
DOI: 10.1002/jcph.1691

Comment:
This model is based on equations 4-5 from the manuscript.
Abstract:
Chimeric antigen receptor T cell (CAR-T cell) therapies have shown significant efficacy in CD19+ leukemias and lymphomas. There remain many challenges and questions for improving next-generation CAR-T cell therapies, and mathematical modeling of CAR-T cells may play a role in supporting further development. In this review, we introduce a mathematical modeling taxonomy for a set of relatively simple cellular kinetic-pharmacodynamic models that describe the in vivo dynamics of CAR-T cell and their interactions with cancer cells. We then discuss potential extensions of this model to include target binding, tumor distribution, cytokine-release syndrome, immunophenotype differentiation, and genotypic heterogeneity.