Solved: Metastasis of malignant tumors Metastasis is the process by which cancer cells

Chapter 10, Problem 5

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Metastasis of malignant tumors Metastasis is the process by which cancer cells spread throughout the body and initiate tumors in various organs. This sometimes happens via the bloodstream, where cancer cells become lodged in capillaries of organs and then move across the capillary wall into the organ. Using C to denote the number of cells lodged in a capillary and I for the number that have invaded the organ, we can model this as C9 2C 2 C I9 C 2 I 1 I where all constants are positive, is the rate of movement across the capillary wall, is the rate of dislodgment from the capillary, is the rate at which cancer cells in the organ die, and is their growth rate. (a) Find the general solution. (b) Classify the equilibrium at the origin when . and when , . (c) What is the solution to the initial-value problem if Cs0d C0 and Is0d 0? (d) Use your result from part (c) to show that the tumor will grow in the long term if and only if . .