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Global dynamics of reaction-diffusion oncolytic M1 virotherapy with immune response

Author

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  • Elaiw, A.M.
  • Hobiny, A.D.
  • Al Agha, A.D.

Abstract

Oncolytic virotherapy is a promising cancer treatment that uses replication-competent viruses to target and kill tumor cells. Oncolytic alphavirus M1 is a naturally occurring virus which showed high selectivity and potent efficacy in human cancers. Our purpose in this paper is to propose and analyze a model of oncolytic M1 virotherapy with spatial effects and anti-tumor immune response. We investigate the non-negativity and boundedness of solutions for the modified model. We calculate all possible equilibrium points and determine the threshold conditions needed for their existence. One of the equilibria represents the success of the treatment, while the others represent a partial success or a complete fail. We study the global stability of the corresponding equilibrium points by constructing suitable Lyapunov functionals. We also provide the instability conditions of the equilibrium points. We perform some numerical simulations in order to verify the effect of the immune response on oncolytic virotherapy. Our results indicate that the immune response may weaken the effectiveness of oncolytic virotherapy and control the tumor.

Suggested Citation

  • Elaiw, A.M. & Hobiny, A.D. & Al Agha, A.D., 2020. "Global dynamics of reaction-diffusion oncolytic M1 virotherapy with immune response," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    • Handle: RePEc:eee:apmaco:v:367:y:2020:i:c:s0096300319307507
    DOI: 10.1016/j.amc.2019.124758
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    References listed on IDEAS

    as
    1. Kim, Kwang Su & Kim, Sangil & Jung, Il Hyo, 2018. "Hopf bifurcation analysis and optimal control of Treatment in a delayed oncolytic virus dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 1-16.
    2. Elaiw, A.M. & Almuallem, N.A., 2015. "Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1067-1089.
    3. Elzbieta Ratajczyk & Urszula Ledzewicz & Heinz Schättler, 2018. "Optimal Control for a Mathematical Model of Glioma Treatment with Oncolytic Therapy and TNF- $$\alpha $$ α Inhibitors," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 456-477, February.
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    Citations

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    Cited by:

    1. Elaiw, A.M. & Alshaikh, M.A., 2020. "Stability preserving NSFD scheme for a general virus dynamics model with antibody and cell-mediated responses," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Elaiw, A.M. & Al Agha, A.D., 2021. "Global dynamics of SARS-CoV-2/cancer model with immune responses," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    3. Ahmed Elaiw & Afnan Al Agha, 2020. "Global Analysis of a Reaction-Diffusion Within-Host Malaria Infection Model with Adaptive Immune Response," Mathematics, MDPI, vol. 8(4), pages 1-32, April.
    4. Mittal, R.C. & Goel, Rohit & Ahlawat, Neha, 2021. "An Efficient Numerical Simulation of a Reaction-Diffusion Malaria Infection Model using B-splines Collocation," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Younoussi, Majda El & Hajhouji, Zakaria & Hattaf, Khalid & Yousfi, Noura, 2022. "Dynamics of a reaction-diffusion fractional-order model for M1 oncolytic virotherapy with CTL immune response," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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    More about this item

    Keywords

    Oncolytic; Virotherapy; M1 virus; Immune response; Diffusion; Global stability;
    All these keywords.

    JEL classification:

    • M1 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration

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