Chapter

New Challenges for Cancer Systems Biomedicine

Part of the series SIMAI Springer Series pp 249-266

On the Dynamics of Tumor-Immune System Interactions and Combined Chemo- and Immunotherapy

  • Alberto d’OnofrioAffiliated withDepartment of Experimental Oncology, European Institute of Oncology
  • , Urszula LedzewiczAffiliated withDepartment of Mathematics and Statistics, Southern Illinois University Edwardsville Email author 
  • , Heinz SchättlerAffiliated withDepartment of Electrical and Systems Engineering, Washington University

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Abstract

Tumor-immune system interplay is extremely complex, and, as such, it represents a big challenge for mathematical oncology. Here we investigate a simple general family of models for this important interplay by considering both the delivery of a cytotoxic chemotherapy and of immunotherapy. Then methods of geometrical optimal control are applied to a special case (the Stepanova model) in order to infer (under suitable constraints) the best combination of drugs scheduling to transfer — through therapy —the system from an initial condition in the malignant region of the state space into a benign region. Our findings suggest that chemotherapy is always needed first to reduce a large tumor volume before the immune system can become effective.