Figure 6.6. Increasing variation in rates of transition reduces acceleration.

Figure 6.6

Increasing variation in rates of transition reduces acceleration. In this example, there are n = 10 steps. The first and last steps are the slowest; the middle steps are the fastest. In particular, ui = un-1-i = u*ki for i = 0,...,4, with u values chosen so that m/L = 10−8. Larger values of k cause greater variation in rates. Greater rate variation reduces acceleration by concentrating the limiting transitions onto fewer steps. Here, for the curves from top to bottom, the values are k = 2 and u* = 2.245 × 10−3, 2.715 × 10−4, 6.85 × 10−5, 2.66 × 10−5. The values of accelerations for ages less than 15 were erratic because of the numerical calculations. At t = 0 the acceleration is n − 1 = 9.

From: Chapter 6, Theory I

Cover of Dynamics of Cancer
Dynamics of Cancer: Incidence, Inheritance, and Evolution.
Frank SA.
Princeton (NJ): Princeton University Press; 2007.
Copyright © 2007, Steven A Frank.

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