Parameter Estimation in Recurrent Tumor Evolution with Limited Carrying Capacity

In this work, we study the dynamics of a tumor cell population under pharmacological treatment. While drug treatment initially reduces tumor size, it often fails over time as tumor cells develop resistance, ultimately leading to cancer recurrence. We model this process using a two-type state-dependent branching process, assuming the tumor initially consists of drug-sensitive cells with a small fraction of resistant cells. Drug-sensitive cells may acquire resistance through mutation, accompanied by fitness changes, while the overall tumor burden influences cellular growth rates. Using stochastic differential equation techniques, we establish a functional law of large numbers for the populations of resistant and sensitive cells as well as the initial resistant clone. Additionally, by defining the stochastic time of cancer recurrence—when the tumor regrows to its initial size—we derive law of large number limits for recurrence time, clonal diversity, and the size of the largest clone. These results enable the construction of consistent estimators for key parameters, such as cell growth rate, mutation rate, and the initial fraction of resistant cells.

Parameter Estimation in Recurrent Tumor Evolution with Limited Carrying Capacity

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Xuanming Zhang

"Parameter Estimation in Recurrent Tumor Evolution with Limited Carrying Capacity"

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