Differential Model of the Interaction Between Tumor Population and Neutrons in Capture Therapy

Neutron capture therapy combines selective uptake of capture agents with neutron irradiation in orderto enhance tumor cell killing. In this work, a simplified differential model is proposed for the interactionbetween tumor population and neutron density. Tumor growth is represented by a logistic law, whileneutron-mediated cell destruction is introduced through a bilinear interaction term. A second equationmodels neutron production and absorption in the irradiated medium. Analytical properties, equilibriumstates, effective growth reduction, and cumulative neutron exposure are discussed. The model providesan introductory mathematical framework for understanding how neutron presence may affect tumorevolution in capture-based therapies.