TY - JOUR
T1 - Fractional order delay differential model of a tumor-immune system with vaccine efficacy
T2 - Stability, bifurcation and control
AU - Rihan, Fathalla A.
AU - Udhayakumar, K.
N1 - Funding Information:
This work has been supported by the UAE University (UAE) , fund # 12S005-UPAR-2020 .
Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/8
Y1 - 2023/8
N2 - The aim of this paper is to present a mathematical model of tumor vaccine efficacy in the context of immunotherapy treatment. The model is governed by fractional-order delay differential equations with a control variable. Transforming growth factor beta (TGF-β) inhibition alone gives limited clinical advantages, but when combined with a tumor vaccine, it can dramatically increase the immune system's anti-tumor response. The mathematical model takes into account tumor growth dynamics, TGF-β concentrations, cytotoxic effector cells, and regulatory T-cells. The non-negativity of the solutions to such a model has been examined. The steady-state stability and Hopf bifurcation of tumor time delays τ are investigated. An optimal fractional-order control problem is derived and analyzed in the presence of immunotherapy treatments. Using Adams–Bashforth–Moulton predictor–corrector algorithms, we illustrate numerical examples that confirm the analytical findings. The optimal control treatment method reduces the load of tumor cells while increasing the effector cells.
AB - The aim of this paper is to present a mathematical model of tumor vaccine efficacy in the context of immunotherapy treatment. The model is governed by fractional-order delay differential equations with a control variable. Transforming growth factor beta (TGF-β) inhibition alone gives limited clinical advantages, but when combined with a tumor vaccine, it can dramatically increase the immune system's anti-tumor response. The mathematical model takes into account tumor growth dynamics, TGF-β concentrations, cytotoxic effector cells, and regulatory T-cells. The non-negativity of the solutions to such a model has been examined. The steady-state stability and Hopf bifurcation of tumor time delays τ are investigated. An optimal fractional-order control problem is derived and analyzed in the presence of immunotherapy treatments. Using Adams–Bashforth–Moulton predictor–corrector algorithms, we illustrate numerical examples that confirm the analytical findings. The optimal control treatment method reduces the load of tumor cells while increasing the effector cells.
KW - Bifurcation
KW - Control
KW - Stability
KW - Time delay
KW - Tumor-immune interaction
KW - Vaccine
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U2 - 10.1016/j.chaos.2023.113670
DO - 10.1016/j.chaos.2023.113670
M3 - Article
AN - SCOPUS:85162186477
SN - 0960-0779
VL - 173
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 113670
ER -