Open AccessOn viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells
Author(s) -
Alexander S. Bratus,
Svetlana Yu. Kovalenko,
Elena Fimmel
Publication year - 2015
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2015.12.163
Subject(s) - drug , malignant cells , dynamics (music) , cancer , medicine , nonlinear system , drug delivery , drug treatment , pharmacology , physics , chemistry , organic chemistry , quantum mechanics , acoustics
A mathematical spatial cancer model of the interaction between a drug and both malignant and healthy cells is considered. It is assumed that the drug influences negative malignant cells as well as healthy ones. The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. Additionally, we assume some phase constraints for the number of the malignant and the healthy cells and for the total dose of the drug during the whole treatment process. We search through all the courses of treatment switching between an application of the drug with the maximum intensity (intensive therapy phase) and discontinuing administering of the drug (relaxation phase) with the objective of achieving the maximum possible therapy (survival) time. We will call the therapy a viable treatment strategy.