Modeling the Dual‐Edged Dynamics of Adenovirus Transmission and Oncolytic Therapy With Optimal Control in Cancer‐Vulnerable Populations

Adenovirus presents a unique public health and clinical challenge because it acts both as a contagious respiratory pathogen capable of causing widespread outbreaks and as a promising oncolytic agent for cancer therapy. This dual role creates a critical need for integrated management strategies, yet existing models typically address either transmission or treatment in isolation, ignoring the complex interplay between infection spread and therapeutic benefit. To bridge this gap, we develop a novel integer‐order compartmental model that unifies adenovirus transmission dynamics, including an asymptomatic carrier compartment, with its oncolytic potential against cancer. The model considers six distinct population groups: healthy susceptible, cancer susceptible, symptomatic infected, asymptomatic carriers, recovered, and cancer patients in virus‐induced remission. We emphasize that the infected compartments I and C are total populations containing both healthy and cancer‐infected individuals. The model uses effective parameters to represent population‐level averages, which is mathematically equivalent to a more detailed model with separate infected compartments for healthy and cancer patients. The study establishes the existence, uniqueness, positivity, and boundedness of solutions; derives the disease‐free equilibrium; and computes the basic reproduction number via the next‐generation matrix method. Stability analysis reveals that the system exhibits a backward bifurcation, meaning that reducing below unity may be insufficient for disease eradication when asymptomatic carriers and vulnerable cancer patients are present. We provide a rigorous center manifold analysis to establish this bifurcation result mathematically. Local and global sensitivity analyses (using normalized forward sensitivity indices and partial rank correlation coefficients) identify the transmission rate, cancer patient susceptibility, and recovery rates as the most influential parameters driving . We then formulate and solve a weighted single‐objective optimal control problem incorporating multiple competing objectives with three time‐dependent interventions: prevention ( u ₁ ), enhanced virotherapy ( u ₂ ), and immunotherapy ( u ₃ ). We provide detailed biological justifications for each model assumption and control selection, including explicit discussion of the distinction between natural infection and engineered virotherapy, and clarify that the therapeutic remission term is explicitly included in the objective functional to capture the dual objective of disease control and therapeutic benefit. Applying Pontryagin’s maximum principle, we characterize the optimal control strategies and solve the coupled state‐adjoint system numerically using the forward–backward sweep method with fourth‐order Runge–Kutta integration, with rigorous convergence and stability verification. We provide quantitative definitions of synergistic effects and show that combining all three controls achieves an 84% reduction in infection burden and a 187% increase in therapeutic remissions, outperforming any single or double intervention. These findings provide a quantitative foundation for integrated public health policies that simultaneously mitigate adenovirus transmission and maximize its cancer‐fighting potential, offering actionable insights for clinicians and policymakers navigating the complex trade‐offs between infection risk and therapeutic opportunity.