A MATHEMATICAL-MODEL FOR DRUG ADMINISTRATION BY USING THE PHAGOCYTOSIS OF RED-BLOOD-CELLS

A mathematical model for the delivery of drug directly to the macropha ges by using the phagocytosis of senescent red blood cells is proposed . The model is based on the following assumption: At time t = 0 a prea ssigned red blood cell population n(0, a) = phi(a), a > 0, loaded by t he drug, is injected in the blood circulation. Among the cells of that population only those with an age a greater than or equal to (a) over bar ((a) over bar = 120 days) will be phagocytosed by macrophages. Of course, the lifetime of the drug must be higher than (a) over bar. Wi thin the red blood cells it cannot be metabolized, neither can it diff use through their membranes: The emphasis of the paper is on the mathe matical properties and on the formulation of the control problem.