• 2019-07
  • 2019-08
  • 2019-09
  • 2019-10
  • 2019-11
  • 2020-03
  • 2020-07
  • 2020-08
  • 2021-03
  • Filipin III br Substituting the parameters described in into


    Substituting the parameters described in (56) into the model
    dt D
    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-
    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–
    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
    Declaration of Competing Interest
    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
    [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.