### Abstract

Aim: development of a mathematical model for non-invasive mammary duct tumor. Methods: the model was developed using the apparatus technique of ordinary differential equations and partial differential equations. The gland duct is represented by a hollow cylindrical tube inside which the afunctional tissue growth occurs. Results: initial boundary value problems were set for differential equations; stability limits of stationary solutions were determined; an option of the mathematical model for treatment was proposed; conditions for the existence of autowave solutions were found, and numerical solutions were constructed. Conclusion: on the basis of the developed model, an estimate of the tumor growth rate was given; a treatment option was proposed, and an explanation of the reasons for a possible recurrence of the disease was given.

Original language | English |
---|---|

Pages (from-to) | 1554-1558 |

Journal | Drug Invention Today |

Volume | 12 |

Issue number | 7 |

Publication status | Published - 1 Jul 2019 |

### Fingerprint

### Scopus subject areas

- Drug Discovery

### Cite this

*Drug Invention Today*,

*12*(7), 1554-1558.

}

*Drug Invention Today*, vol. 12, no. 7, pp. 1554-1558.

**Mathematical model of the blocked breast duct.** / Kolpak, Eugeny P.; Frantsuzova, Inna S.; Evmenova, Elizaveta O.

Research output

TY - JOUR

T1 - Mathematical model of the blocked breast duct

AU - Kolpak, Eugeny P.

AU - Frantsuzova, Inna S.

AU - Evmenova, Elizaveta O.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Aim: development of a mathematical model for non-invasive mammary duct tumor. Methods: the model was developed using the apparatus technique of ordinary differential equations and partial differential equations. The gland duct is represented by a hollow cylindrical tube inside which the afunctional tissue growth occurs. Results: initial boundary value problems were set for differential equations; stability limits of stationary solutions were determined; an option of the mathematical model for treatment was proposed; conditions for the existence of autowave solutions were found, and numerical solutions were constructed. Conclusion: on the basis of the developed model, an estimate of the tumor growth rate was given; a treatment option was proposed, and an explanation of the reasons for a possible recurrence of the disease was given.

AB - Aim: development of a mathematical model for non-invasive mammary duct tumor. Methods: the model was developed using the apparatus technique of ordinary differential equations and partial differential equations. The gland duct is represented by a hollow cylindrical tube inside which the afunctional tissue growth occurs. Results: initial boundary value problems were set for differential equations; stability limits of stationary solutions were determined; an option of the mathematical model for treatment was proposed; conditions for the existence of autowave solutions were found, and numerical solutions were constructed. Conclusion: on the basis of the developed model, an estimate of the tumor growth rate was given; a treatment option was proposed, and an explanation of the reasons for a possible recurrence of the disease was given.

KW - Differential equations

KW - Mathematical model

KW - Numerical methods

KW - Stability

KW - Tumor

UR - http://www.scopus.com/inward/record.url?scp=85071078095&partnerID=8YFLogxK

UR - https://pdfs.semanticscholar.org/6d7c/1da0922e5bae968880bc13d23251729b4277.pdf

M3 - Article

AN - SCOPUS:85071078095

VL - 12

SP - 1554

EP - 1558

JO - Drug Invention Today

JF - Drug Invention Today

SN - 0975-7619

IS - 7

ER -