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A basic mathematical model for IL-2-based cancer immunotherapy is proposed and studied. Our analysis shows that the outcome of therapy is mainly determined by three parameters, the relative death rate of CD4 + T cells, the relative death rate of CD8 + T cells, and the dose of IL-2 treatment. Minimal equilibrium tumor size can be reached with a large dose of IL-2 in the case that CD4 + T cells die out. However, in cases where CD4 + and CD8 + T cells persist, the final tumor size is independent of the IL-2 dose and is given by the relative death rate of CD4 + T cells. Two groups of in silico clinical trials show some short-term behaviors of IL-2 treatment. IL-2 administration can slow the proliferation of CD4 + T cells, while high doses for a short period of time over several days transiently increase the population of CD8 + T cells during treatment before it recedes to its equilibrium. IL-2 administration for a short period of time over many days suppresses the tumor population for a longer time before approaching its steady-state levels. This implies that intermittent administration of IL-2 may be a good strategy for controlling tumor size., Competing Interests: Declaration of competing interest On behalf of all coauthors, I state that: There is non-financial interest in this research., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy., Competing Interests: Declaration of competing interest There is non-financial interest in this research., (Copyright © 2024 Elsevier Inc. All rights reserved.)