A Stochastic Cancer Model for Investigating the Dynamical Effects of a Viral Injection Therapy”

Abstract

This paper presents a stochastic model for tumor-viral-immune interactions, focusing on uninfected tumor cells, virus-infected cells, and cytotoxic T lymphocytes (CTLs) under environmental uncertainties. It incorporates logistic tumor growth, viral infection saturation, and immune-mediated clearance through stochastic differential equations, ensuring positive solutions and trajectory non-explosion. Lyapunov functions confirm boundedness and biological feasibility. The model highlights the importance of the interaction between viral infection and immune activation in tumor control, where effective immune stimulation limits tumor growth, while decay mechanisms promote persistence. Randomness affects population dynamics and therapeutic outcomes, reinforcing the model's relevance in cancer virotherapy and paving the way for future studies on stability, extinction criteria, and treatment strategies.