Modelling dynamics of undetectable disease in leukemia concerning therapy

Abstract

The recent developments in antibody-based immunotherapy are believed to be promising against B cell leukemia, the most commonly diagnosed blood cancer. This disease has a peculiar tendency to reappear and lacks a quantitative understanding of post-treatment residual disease, which may have a role in the relapse. The need to predict the relapse, and reduce the adverse toxic effect of current standard, chemotherapy, demands a quantitative effort. We formulate a stochastic model that captures not only the deterministic behavior but also the fluctuations taking place in the residual disease. We also use first-passage analysis techniques developed for random walks to predict the long-term effects of fluctuations. The immunotherapy model predicts the containment of tumors for an adequate response of the immune system. We propose a sequential chemotherapy-immunotherapy strategy that may provide better outcomes. The mathematical workflow developed here sheds light on an equivalent formulation of master equations, that provides remarkable speed up for numerical computations. All in all, we provide a cell-population based stochastic model, to understand contemporary leukemia treatments, that can be used to test strategies as well as their outcomes.