A fractional mathematical model of breast cancer competition model
Author links open overlay panelJ.E.Solís-PérezaJ.F.Gómez-Aguilar
bA.Atanganac

a
    Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México

b
    CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México

c
    Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa



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.