Dynamics of tumor–CD4+–cytokine–host cells interactions with treatments

Xiaochuan Hu, Sophia R.J. Jang

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Mathematical models of interactions between tumor cells, CD4+ T cells, cytokines, and host cells are proposed to investigate the role of CD4+ on tumor regression. Our results suggest that host cells along with the mechanism of production of CD4+ T cells play important roles in driving tumor dynamics. Cancer cells can be eradicated if the tumor has a small growth rate and is also not competitive. Treatments by either CD4+, cytokines, or a combination of the two are applied to study their effectiveness. It is concluded that doses of treatments along with the tumor size are critical in determining the fate of the tumor. Tumor cells can be eliminated completely if doses of treatments by cytokine are large. The treatments are in general more effective if the tumor size is smaller. Bistability is observed in all of the models with or without the treatment strategies indicating that there is a window of opportunity for clearing off the tumor cells.

Original languageEnglish
Pages (from-to)1339-1351
Number of pages13
JournalApplied Mathematics and Computation
StatePublished - Mar 15 2018


  • Bistability
  • Cytokine
  • Global stability
  • Immunotherapy
  • Ordinary differential equations
  • Tumor


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