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  • Filipin III br Substituting the parameters described in into

    2019-10-07

    
    Substituting the parameters described in (56) into the model
    dt
    D
    dt D
    E
    dt
    F
    dt
    The numerical results given in Fig. 4a–d shows numerical simu-lations of the special solution of our model as function of time for different values of αn for n ∈ [1; 5].
    5. Conclusions
    The solution of the model (57) can be obtained applying the
    Adams-Bashforth method [34]. The Numerical scheme is given by In this paper, we study a fractional breast cancer model. The
    mathematical model is built using a Liouville–Caputo and Caputo–
    Fabrizio–Caputo fractional derivatives. We consider the integer or-
    D
    der malaria transmission model proposed in [4] and modify it Filipin III to
    become a fractional order model. Special solutions using an iter-
    ative scheme via Laplace transform were obtained and the fixed
    point theorem is discussed to prove the existence and uniqueness
    of the coupled-solutions. Furthermore, we obtain numerical solu-
    tions considering the Atangana–Toufik numerical scheme. We can
    observe that the results obtained by using the Caputo–Fabrizio–
    D
    Caputo fractional derivative are different to those obtained by the
    derivative of Liouville–Caputo type, for the first fractional deriva-
    tive the memory effect is more evident. The numerical solutions
    showed that the dynamical behaviour of the breast cancer model
    depends on the fractional derivative. Also new behaviors have been
    T
    n
    D
    E
    Declaration of Competing Interest
    None.
    C
    T
    Acknowledgments
    E
    Jesús Emmanuel Solís Pérez acknowledges the support pro-
    KTn−1 (tn−1 )En−1 (tn−1 ) , vided by CONACyT through the assignment doctoral fellowship.
    by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014
    and the support provided by SNI-CONACyT.
    n F n
    References
    [2] Mufudza C, Sorofa W, Chiyaka ET. Assessing the effects of estrogen on the dy-namics of breast cancer. Comput Math Methods Med 2012;1:1–14.
    [4] Abernathy K, Abernathy Z, Baxter A, Stevens M. Global dynamics of a breast cancer competition model. Differ Equations Dyn Syst 2017;1:1–15.
    [5] Chen C, Baumann WT, Xing J, Xu L, Clarke R, Tyson JJ. Mathematical models of the transitions between endocrine therapy responsive and resistant states in breast cancer. J R Soc Interface 2014;11(96):1–11.
    [6] Wang Z, Butner JD, Kerketta R, Cristini V, Deisboeck TS. Simulating cancer growth with multiscale agent-based modeling. In: Seminars in cancer biology., vol. 30. Academic Press.; 2015. p. 70–8.
    [7] Paine I, Chauviere A, Landua J, Sreekumar A, Cristini V, Rosen J, Lewis MT. A geometrically-constrained mathematical model of mammary gland ductal elongation reveals novel cellular dynamics within the terminal end bud. PLoS Comput Biol 2016;12(4):1–23.
    [9] Jenner AL, Yun CO, Kim PS, Coster AC. Mathematical modelling of the interac-tion between cancer cells and an oncolytic virus: insights into the effects of treatment protocols. Bull Math Biol 2018;1:1–15.
    [10] Weis JA, Miga MI, Yankeelov TE. Three-dimensional image-based mechanical modeling for predicting the response of breast cancer to neoadjuvant therapy. Comput Methods Appl MechEng 2017;314:494–512.
    [11] Lee AJ, Cunningham AP, Kuchenbaecker KB, Mavaddat N, Easton DF, Anto-niou AC. BOADICEA breast cancer risk prediction model: updates to cancer in-cidences, tumour pathology and web interface. Br J Cancer 2014;110(2):1–11.
    [12] Owolabi KM. Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems. Chaos Solitons Fractals 2016;93:89–98.