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Volume 11,     Number 3,     Fall 2003

 

A REACTION-DIFFUSION MODEL OF LEUKEMIA TREATMENT BY CHEMOTHERAPY
WENXIANG LIU AND H. I. FREEDMAN

Abstract. A model of leukemia treatment by chemotherapy techniques is proposed utilizing a system of reaction diffusion equations representing the change in densities of normal cells, competing cancer cells, and chemotherapy in a given organ or area. We view the interactions between normal and cancer cells as being competitive for available resources, and we think of the chemotherapy agent as a predator on both normal and leukemia cells. The existence, uniqueness, and boundedness of the solutions are established by means of a comparison principle and a monotonicity method. We analyze the constant solutions and their stabilities. The main method used in studying the stability is the spectral analysis of the linearized operators. Persistence criteria for the normal cells and cancer cells are also derived. The analysis is carried out both analytically and numerically.

 

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