we again obtain a Riccati equation,

but now it contains a time-dependent coefficient. If we substitute the value of y(t) at t = 0, y = 1, we will get the solution

For the saturated value of y(t), y(t) = D/L, we obtain x{t) = 1 - (L - D)ut, (L - D)t < 1, (3.44)

This gives us bounds for P2 = 1 — x(t). In general, we can solve equation (3.43) numerically. For a particular set of parameters, the function Pz(t) is presented in Figure 3.2.

3.4 Overview

In this chapter we developed the main ideas of the stochastic formalism for two-hit models of carcinogenesis. In the next chapters we will see how these ideas can be applied to studying some of the most intriguing questions of cancer initiation and progression.

Chapter 4

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