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Modeling the dynamics of glioma-immune surveillance

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  • Khajanchi, Subhas

Abstract

The proposed mathematical model describes how glioma cells evolve and survive the brief encounter with the immune system mediated by macrophages and the tumor specific CD8+T cells. We characterize the dynamics of the system by observing biologically realistic singular points and their stability analysis. The global asymptotic stability of the interior equilibrium point is studied with the help of Lyapunov method and we prove the uniform persistence by using the method of average Lyapunov function. The numerical simulation demonstrates that the model, with the parameter assumptions and values we used, is capable of reproducing glioma escape from immune surveillance in a biologically realistic time frame. We investigate the conditions under which the macrophages can be infiltrated, and identify the parameter values for which the inhibition of the gliomas proliferation is acquired.

Suggested Citation

  • Khajanchi, Subhas, 2018. "Modeling the dynamics of glioma-immune surveillance," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 108-118.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:108-118
    DOI: 10.1016/j.chaos.2018.06.028
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    References listed on IDEAS

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    1. Khajanchi, Subhas, 2015. "Bifurcation analysis of a delayed mathematical model for tumor growth," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 264-276.
    2. Álvaro G López & Jesús M Seoane & Miguel A F Sanjuán, 2016. "Decay Dynamics of Tumors," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-15, June.
    3. Khajanchi, Subhas & Ghosh, Dibakar, 2015. "The combined effects of optimal control in cancer remission," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 375-388.
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    1. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "The impact of the media awareness and optimal strategy on the prevalence of tuberculosis," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    2. Khajanchi, Subhas & Nieto, Juan J., 2019. "Mathematical modeling of tumor-immune competitive system, considering the role of time delay," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 180-205.
    3. Khajanchi, Subhas, 2021. "The impact of immunotherapy on a glioma immune interaction model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Khajanchi, Subhas & Bera, Sovan & Roy, Tapan Kumar, 2021. "Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 354-378.
    5. Li, Qian & Xiao, Yanni, 2019. "Bifurcation analyses and hormetic effects of a discrete-time tumor model," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    6. Sardar, Mrinmoy & Biswas, Santosh & Khajanchi, Subhas, 2021. "The impact of distributed time delay in a tumor-immune interaction system," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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