Mathematical modeling of T cell exhaustion in the tumor microenvironment

T cell exhaustion (TCE), a hallmark of chronic infections and cancer, is characterized by progressive loss of effector function, sustained expression of inhibitory receptors, and stable transcriptional/epigenetic reprogramming. Within the tumor microenvironment (TME), exhausted CD8⁺ T cells fail to eliminate malignant cells, contributing to immune evasion and resistance to immunotherapy. Although checkpoint blockade has provided clinical benefit, outcomes remain variable, underscoring the need to better understand the temporal and mechanistic basis of exhaustion. Current modeling efforts have yielded valuable insights; however, they often focus on isolated aspects of tumor-immune interactions. Deterministic models such as ordinary, partial, and delay differential equations capture population dynamics, but omit stochastic variation and single-cell heterogeneity. Stochastic and agent-based models address randomness and spatial structure at a greater computational cost. Hybrid and multiscale approaches increasingly integrate these methods, but few explicitly capture the progressive, time-series nature of TCE as revealed by recent epigenetic and transcriptomics studies. This review analyzes various mathematical and computational frameworks including deterministic, stochastic, and hybrid approaches that have been applied to study TCE in viral and cancer contexts. We distinguish between TCE-specific models that directly represent exhaustion dynamics and TCE-relevant frameworks that model tumor-immune interactions, spatial tumor microenvironment features, and pharmacological interventions that could be adapted to optimize future TCE models. By comparing strengths and limitations across frameworks, we identify key gaps including limited integration of temporal resolution, lack of multiscale intracellular regulation, and scarce validation with longitudinal experimental data. We also highlight how TCE-relevant models can support pharmacological and translational questions, including dose optimization, pharmacokinetic /pharmacodynamic (PK/PD) integration, and mechanisms of immunotherapy failure. Future models that adopt hybrid, time-resolved, and multiscale designs linking intracellular regulatory networks, population-level signaling, and spatially heterogeneous TME features, calibrated with time-series omics data, would be invaluable in addressing these gaps. Such frameworks would provide mechanistic insights into exhaustion trajectories, supporting advances in immunotherapy design and clinical outcomes.