Chimeric Antigen Receptor (CAR) T-cell therapy is an immunotherapy that has recently become highly instrumental in the fight against life-threatening diseases. A variety of modeling and computational simulation efforts have addressed different aspects of CAR T therapy, including Tcell activation, T-and malignant cell population dynamics, therapeutic cost-effectiveness strategies, and patient survival analyses. In this article, we present a systematic review of those efforts, including mathematical, statistical, and stochastic models employing a wide range of algorithms, from differential equations to machine learning. To the best of our knowledge, this is the first review of all such models studying CAR T therapy. In this review, we provide a detailed summary of the strengths, limitations, methodology, data used, and data lacking in current published models. This information may help in designing and building better models for enhanced prediction and assessment of the benefit-risk balance associated with novel CAR T therapies, as well as with the data collection essential for building such models.

Cancer vaccines are an important component of the cancer immunotherapy toolkit enhancing immune response to malignant cells by activating CD4+ and CD8+ T cells. Multiple successful clinical applications of cancer vaccines have shown good safety and efficacy. Despite the notable progress, significant challenges remain in obtaining consistent immune responses across heterogeneous patient populations, as well as various cancers. We present a mechanistic mathematical model describing key interactions of a personalized neoantigen cancer vaccine with an individual patient’s immune system. Specifically, the model considers the vaccine concentration of tumor-specific antigen peptides and adjuvant, the patient’s major histocompatibility complexes I and II copy numbers, tumor size, T cells, and antigen presenting cells. We parametrized the model using patient-specific data from a clinical study in which individualized cancer vaccines were used to treat six melanoma patients. Model simulations predicted both immune responses, represented by T cell counts, to the vaccine as well as clinical outcome (determined as change of tumor size). This model, although complex, can be used to describe, simulate, and predict the behavior of the human immune system to a personalized cancer vaccine.

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