Treatment of melanoma with dendritic cell vaccines and immune checkpoint inhibitors: A mathematical modeling study

Ling Xue, Hongyu Zhang, Xiaoming Zheng, Wei Sun, Jinzhi Lei

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Dendritic cell (DC) vaccines and immune checkpoint inhibitors (ICIs) play critical roles in shaping the immune responses of tumor cells (TCs) and are widely used in cancer immunotherapies. Quantitatively evaluating the effectiveness of these therapies are essential for the optimization of treatment strategies. Here, based on the combined therapy of melanoma with DC vaccines and ICIs, we formulated a mathematical model to investigate the dynamic interactions between TCs and the immune system and understand the underlying mechanisms of immunotherapy. First, we obtained a threshold parameter for the growth of TCs, which is given by the ratio of spontaneous proliferation to immune inhibition. Next, we proved the existence and locally asymptotic stability of steady states of tumor-free, tumor-dominant, and tumor-immune coexistent equilibria, and identified the existence of Hopf bifurcation of the proposed model. Furthermore, global sensitivity analysis showed that the growth of TCs strongly correlates with the injection rate of DC vaccines, the activation rate of CTLs, and the killing rate of TCs. Finally, we tested the efficacy of multiple monotherapies and combined therapies with model simulations. Our results indicate that DC vaccines can decelerate the growth of TCs, and ICIs can inhibit the growth of TCs. Besides, both therapies can prolong the lifetime of patients, and the combined therapy of DC vaccines and ICIs can effectively eradicate TCs.

Original languageEnglish
Article number111489
JournalJournal of Theoretical Biology
StatePublished - Jul 7 2023


  • Combined therapy
  • Dendritic cell vaccines
  • Hopf bifurcation
  • Immune checkpoint inhibitors
  • Melanoma
  • Tumor-immune system


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