Bartlett Formulation

The Bartlett formulation reveals discrepancies caused by early extinction of the wild-type lineage that deterministic wild-type models cannot represent. With death, the full Bartlett PDE can be solved numerically only for small replication capacities. With no death, the limited Bartlett model has 2^k minus 1 total wild-type divisions. The Bartlett formulation treats both wild-type cells and mutants as stochastic birth-death processes. In the Bartlett formulation, capacities x_0 through x_k and mutants are all stochastic variables. A joint probability generating function is derived for the Bartlett formulation from Kolmogorov forward equations.