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

Abstract

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. Copyright © 2014 John Wiley & Sons, Ltd.

Optimal chemotherapy and immunotherapy schedules for a cancer‐obesity model with Caputo time fractional derivative

“…and any one of the seven conditions (2)(3)(4)(5)(6)(7)(8) above is satisfied; ie, at least one of m 1 , m 2 , m 3 is positive.…”

“…(i) If D(q) > 0, then the necessary and sufficient condition for the equilibrium point E to be locally asymptotically 3 , then E is locally asymptotically stable.…”

“…Their model includes tumor cells, natural killers, naive and mature cytotoxic T cells, regulatory T cells, naive and mature helper T cells, dendritic cells, and interleukin 2 cytokine. In the study, 3 importance of scheduling immunotherapy is underlined to eradicate and control tumor population. Moreover, immune competition is analyzed in case of tumor population by Brazzoli et al 4 In the work by Robertson-Tessi et al, 5 the effect of chemotherapy and immunotherapy on control of the tumor growth has been presented.…”

Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions

“…Mamat et al [2] proposed a modified model that includes the effect of both IL-2 and INF-α. A model was proposed by Eftimie et al [44] and was modified by Anderson et al [45] and by Hu and Jang [46] to study the effect of CD4 + T cells on the system. CD4 + T cells are helper cells that activate CD8 + T cells to achieve a regulated immune response and protect against tumors.…”

“…CD4 + T cells are helper cells that activate CD8 + T cells to achieve a regulated immune response and protect against tumors. However, CD4 + T cells can play a direct role in killing tumor cells via secretion of cytokines in addition to its traditional helper role [45][46][47][48][49].…”