A Stochastic Framework for Evaluation of Prostate Cancer Progression and Treatment Dynamics

Prostate cancer progression is inherently heterogeneous, driven by complex interactions among tumor biology, patient-specific factors, and treatment response. Existing deterministic models inadequately capture this variability, limiting their ability to represent the stochastic nature of disease evolution and to support reliable prediction in clinical settings. This study introduces a probabilistic framework for modeling prostate cancer progression based on the Fokker–Planck equation, which governs the temporal evolution of the probability density of a latent disease state. The latent state, associated with tumor burden and prostate-specific antigen (PSA) dynamics, evolves under the combined influence of deterministic and stochastic processes. The drift term characterizes tumor growth and therapeutic effects, while the diffusion term captures intrinsic biological variability arising from genetic mutations, microenvironmental conditions, and inter-patient heterogeneity. Numerical simulations demonstrate the evolution of disease-state distributions under varying treatment scenarios, highlighting the ability of the proposed framework to capture a spectrum of plausible trajectories rather than a single deterministic outcome. This enables a more realistic representation of disease progression and treatment response at both individual and population levels. The proposed approach provides a principled foundation for integrating stochastic tumor dynamics with clinical biomarkers and therapeutic interventions. By moving beyond deterministic assumptions, it supports the development of predictive, patient-specific models and advances the application of probabilistic reasoning in oncology and health informatics.