Qualitative behavior of systems of tumor-CD4+-cytokine interactions with treatments

Luke Anderson, Sophia Jang, Jui Ling Yu

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Immunotherapies are important methods for controlling and curing malignant tumors. Based on recent observations that many tumors have been immuno-selected to evade recognition by the traditional cytotoxic T lymphocytes, we propose mathematical models of tumor-CD4+-cytokine interactions to investigate the role of CD4+ on tumor regression. Treatments of either CD4+ or cytokine are applied to study their effectiveness. It is found that doses of treatments are critical in determining the fate of the tumor, and tumor cells can be eliminated completely if doses of cytokine are large. Bistability is observed in models with either of the treatment strategies, which signifies that a careful planning of the treatment strategy is necessary for achieving a satisfactory outcome.

Original languageEnglish
Pages (from-to)4330-4344
Number of pages15
JournalMathematical Methods in the Applied Sciences
Issue number17
StatePublished - Nov 30 2015


  • bistability
  • cytokine
  • global stability
  • ordinary differential equations
  • tumor


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