Fractional Discrete-Time Modeling and Analysis of Oncolytic Adenovirus Therapy with Tumor-Specific Immune Response (European Journal of Pure and Applied Mathematics, 2025)
Oncolytic viruses (OVs) are garnering increasing attention for their ability to directly target malignant cells while simultaneously stimulating the immune response against cancer. This study presents a novel discrete-time fractional-order mathematical framework to investigate the dynamics of oncolytic adenovirus therapy in conjunction with tumor-specific immune responses. The model captures the intricate interactions between viral infection processes and the immune system's role in modulating tumor progression. To assess the effectiveness of oncolytic viral therapy, local stability and bifurcation analyses are conducted at the model’s equilibrium points. A set of local bifurcations is examined, and the necessary and sufficient conditions for detecting these bifurcations are derived using an algebraic criterion method. Numerical simulations support the theoretical results, indicating that increasing the viral infection rate and carefully managing time steps with immune response can achieve stable and tumor-suppressive outcomes. Given the limitations of achieving complete tumor eradication through genetically modified adenovirus therapy alone, this study explores the application of chaos control strategies to maintain the stability of the system dynamics.
Keywords: fractional derivatives; differential equations; fractional differential equations; antiperiodic; nonlocal boundary conditions; existence.