Modeling Pancreatic Cancer Dynamics with Immunotherapy

Bull Math Biol. 2019 Jun;81(6):1885-1915. doi: 10.1007/s11538-019-00591-3. Epub 2019 Mar 6.


We develop a mathematical model of pancreatic cancer that includes pancreatic cancer cells, pancreatic stellate cells, effector cells and tumor-promoting and tumor-suppressing cytokines to investigate the effects of immunotherapies on patient survival. The model is first validated using the survival data of two clinical trials. Local sensitivity analysis of the parameters indicates there exists a critical activation rate of pro-tumor cytokines beyond which the cancer can be eradicated if four adoptive transfers of immune cells are applied. Optimal control theory is explored as a potential tool for searching the best adoptive cellular immunotherapies. Combined immunotherapies between adoptive ex vivo expanded immune cells and TGF-[Formula: see text] inhibition by siRNA treatments are investigated. This study concludes that mono-immunotherapy is unlikely to control the pancreatic cancer and combined immunotherapies between anti-TGF-[Formula: see text] and adoptive transfers of immune cells can prolong patient survival. We show through numerical explorations that how these two types of immunotherapies are scheduled is important to survival. Applying TGF-[Formula: see text] inhibition first followed by adoptive immune cell transfers can yield better survival outcomes.

Keywords: Cytokine; Immunotherapy; Ordinary differential equations; Pancreatic cancer.

Publication types

  • Validation Study

MeSH terms

  • CD8-Positive T-Lymphocytes / immunology
  • Combined Modality Therapy
  • Computer Simulation
  • Cytokines / immunology
  • Humans
  • Immunotherapy, Adoptive / methods*
  • Immunotherapy, Adoptive / statistics & numerical data
  • Killer Cells, Natural / immunology
  • Mathematical Concepts
  • Models, Immunological*
  • Nonlinear Dynamics
  • Pancreatic Neoplasms / immunology
  • Pancreatic Neoplasms / pathology
  • Pancreatic Neoplasms / therapy*
  • RNA, Small Interfering / genetics
  • RNA, Small Interfering / therapeutic use
  • Transforming Growth Factor beta / antagonists & inhibitors
  • Transforming Growth Factor beta / biosynthesis
  • Transforming Growth Factor beta / genetics


  • Cytokines
  • RNA, Small Interfering
  • Transforming Growth Factor beta