This model is based on the publication:
"CAR T cell therapy in B-cell acute lymphoblastic leukaemia: Insights from mathematical models".
Odelaisy León-Triana, Soukaina Sabir, Gabriel F. Calvo, Juan Belmonte-Beitia, Salvador Chulián, Álvaro Martínez-Rubio, María Rosa, Antonio Pérez-Martínez, Manuel Ramirez-Orellana, Víctor M. Pérez-García
doi: 10.1016/j.cnsns.2020.105570 

Comment:
This model is based on equations (4a)-(4c).

Abstract: 
Immunotherapies use components of the patient immune system to selectively target can- cer cells. The use of chimeric antigenic receptor (CAR) T cells to treat B-cell malignancies –leukaemias and lymphomas–is one of the most successful examples, with many patients experiencing long-lasting full responses to this therapy. This treatment works by extract- ing the patient’s T cells and transducing them with the CAR, enabling them to recognize and target cells carrying the antigen CD19 + , which is expressed in these haematological cancers. Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T cells. The model accounts for mature and progenitor B-cells, leukaemic cells, CAR T cells and side effects by including the main biological processes involved. The model explains the early post-injection dynamics of the different compart- ments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that gives the maximum CAR T cell ex- pansion in vivo and the severity of side effects. Our mathematical model captures other known features of the response to this immunotherapy. It also predicts that CD19 + cancer relapses could be the result of competition between leukaemic and CAR T cells, analogous to predator-prey dynamics. We discuss this in the light of the available evidence and the possibility of controlling relapses by early re-challenging of the leukaemia cells with stored CAR T cells.