Analysis of an Age-Structured Model of Chemotherapy-Induced Neutropenia

Neutropenia is a blood disorder characterized by low levels of neutrophils and is a common side effect of chemotherapy. Administration of granulocyte-colony stimulating factor (G-CSF) is a typical treatment that helps stabilize the level of neutrophils. However, it is not known if changes to the frequency and dosage of administered G-CSF will lead to better treatment. We analyze a nonlinear hyperbolic system of coupled integro-differential equations aimed at quantifying the effect of treatment plans on patients with chemotherapy-induced neutropenia. We show how this age-structured model can be decoupled for short time. We then investigate the equivalence of an integral equation with a related nonlinear PDE and prove existence and uniqueness of solutions of the integral equation. This is used to finally demonstrate existence and uniqueness of solutions to the full PDE system.