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Chaos and optimal control of cancer self-remission and tumor system steady states

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  • El-Gohary, Awad

Abstract

This paper is devoted to study the problem of optimal control of cancer self-remission and tumor unstable steady-states. The stability analysis of the biologically feasible equilibrium states is presented using a local stability approach. The system appears exhibit a chaotic behavior for some ranges of the system parameters. The necessary optimal control inputs for the asymptotic stability of the positive equilibrium states and minimizes the require performance measure are obtained as nonlinear function of the system densities. Analysis and extensive numerical examples of the uncontrolled and controlled systems were carried out for various parameters values and different initial densities.

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  • El-Gohary, Awad, 2008. "Chaos and optimal control of cancer self-remission and tumor system steady states," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1305-1316.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:5:p:1305-1316
    DOI: 10.1016/j.chaos.2006.10.060
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    Cited by:

    1. El-Gohary, Awad, 2009. "Chaos and optimal control of equilibrium states of tumor system with drug," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 425-435.
    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. Das, Parthasakha & Das, Samhita & Upadhyay, Ranjit Kumar & Das, Pritha, 2020. "Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Llanos-Pérez, J.A. & Betancourt-Mar, J.A. & Cocho, G. & Mansilla, R. & Nieto-Villar, José Manuel, 2016. "Phase transitions in tumor growth: III vascular and metastasis behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 560-568.
    5. Pham, Tuan D., 2014. "The butterfly effect in ER dynamics and ER-mitochondrial contacts," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 5-19.
    6. Mohammad Shahzad, 2016. "Chaos Control in Three Dimensional Cancer Model by State Space Exact Linearization Based on Lie Algebra," Mathematics, MDPI, vol. 4(2), pages 1-11, May.
    7. Dehingia, Kaushik & Das, Parthasakha & Upadhyay, Ranjit Kumar & Misra, Arvind Kumar & Rihan, Fathalla A. & Hosseini, Kamyar, 2023. "Modelling and analysis of delayed tumour–immune system with hunting T-cells," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 669-684.
    8. El-Gohary, Awad & Alwasel, I.A., 2009. "The chaos and optimal control of cancer model with complete unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2865-2874.

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