Project description:Mufudza2012 - Estrogen effect on the dynamics
of breast cancer
This deterministic model shows the
dynamics of breast cancer with immune response. The effects of
estrogen are incorporated to study its effects as a risk factor for
the disease.
This model is described in the article:
Assessing the effects of
estrogen on the dynamics of breast cancer.
Mufudza C, Sorofa W, Chiyaka
ET.
Comput Math Methods Med 2012; 2012:
473572
Abstract:
Worldwide, breast cancer has become the second most common
cancer in women. The disease has currently been named the most
deadly cancer in women but little is known on what causes the
disease. We present the effects of estrogen as a risk factor on
the dynamics of breast cancer. We develop a deterministic
mathematical model showing general dynamics of breast cancer
with immune response. This is a four-population model that
includes tumor cells, host cells, immune cells, and estrogen.
The effects of estrogen are then incorporated in the model. The
results show that the presence of extra estrogen increases the
risk of developing breast cancer.
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and identified by:
BIOMD0000000642.
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Project description: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.
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