Solutions of DifferentialDifference Equations Arising from Mathematical Models of Granulocytopoiesis
The closed form solutions of differentialdifference equations arising from mathematical models of granulocytopoiesis, both with and without maturing cells, are presented. The model with maturing cells, which we call model I, is considered first. The solution technique consists of a Laplace transform approach that converts each of the two differentialdifference equations to a difference equation in the transform domain, and subsequent Laplace transform inversion of the solution to express it in the time domain. The model without maturing cells, which we call model II, is next considered and is solved by a method similar to that for model I. From these solutions, useful information and properties, like average number of active and maturing cells, and the transient growth and half-life periods of cells in each stage, can be obtained analytically. This information can play a very crucial role in the treatment of granulocytopoiesis. Further, the numerical solution of another model, which we call model III, for describing the dynamics of imatinib (drug used to treat certain types of cancer)-treated chronic myelogenous leukemia is discussed using a wavelet adaptive computational approach.
differentialdifference equation granulocytopoiesis closed form solution laplace transform wavelets