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A fractional mathematical model of breast cancer competition model

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  • Solís-Pérez, J.E.
  • Gómez-Aguilar, J.F.
  • Atangana, A.

Abstract

In this paper, a mathematical model which considers population dynamics among cancer stem cells, tumor cells, healthy cells, the effects of excess estrogen and the body’s natural immune response on the cell populations was considered. Fractional derivatives with power law and exponential decay law in Liouville–Caputo sense were considered. Special solutions using an iterative scheme via Laplace transform were obtained. Furthermore, numerical simulations of the model considering both derivatives were obtained using the Atangana–Toufik numerical method. Also, random model described by a system of random differential equations was presented. The use of fractional derivatives provides more useful information about the complexity of the dynamics of the breast cancer competition model.

Suggested Citation

  • Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2019. "A fractional mathematical model of breast cancer competition model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 38-54.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:38-54
    DOI: 10.1016/j.chaos.2019.06.027
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    References listed on IDEAS

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    1. Ingrid Paine & Arnaud Chauviere & John Landua & Amulya Sreekumar & Vittorio Cristini & Jeffrey Rosen & Michael T Lewis, 2016. "A Geometrically-Constrained Mathematical Model of Mammary Gland Ductal Elongation Reveals Novel Cellular Dynamics within the Terminal End Bud," PLOS Computational Biology, Public Library of Science, vol. 12(4), pages 1-23, April.
    2. Owolabi, Kolade M., 2016. "Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 89-98.
    3. Atangana, Abdon & Jain, Sonal, 2018. "The role of power decay, exponential decay and Mittag-Leffler function’s waiting time distribution: Application of cancer spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 330-351.
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    Cited by:

    1. Ahmed, Najma & Shah, Nehad Ali & Taherifar, Somaye & Zaman, F.D., 2021. "Memory effects and of the killing rate on the tumor cells concentration for a one-dimensional cancer model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Shaw, Pawan Kumar & Kumar, Sunil & Momani, Shaher & Hadid, Samir, 2022. "Dynamical analysis of fractional plant disease model with curative and preventive treatments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Gao, Wei & Baskonus, Haci Mehmet, 2022. "Deeper investigation of modified epidemiological computer virus model containing the Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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