A mathematical model for drug administration by using the phagocytosis of red blood cells |
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Authors: | Edoardo Beretta Fortunata Solimano Yasuhiro Takeuchi |
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Institution: | (1) Istituto di Biomatematica, Universita di Urbino, I-61029 Urbino, Italy, IT;(2) Department of Applied Mathematics, Faculty of Engineering, Shizuoka University, 432 Hamamatsu, Japan, JP |
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Abstract: | A mathematical model for the delivery of drug directly to the macrophages by using the phagocytosis of senescent red blood
cells is proposed. The model is based on the following assumption: At time t=0 a preassigned red blood cell population n(0, a)=φ(a), a>0, loaded by the drug, is injected in the blood circulation. Among the cells of that population only those with an age a≧ā (ā=120 days) will be phagocytosed by macrophages. Of course, the lifetime of the drug must be higher than ā. Within the
red blood cells it cannot be metabolized, neither can it diffuse through their membranes. The emphasis of the paper is on
the mathematical properties and on the formulation of the control problem.
Received 15 December 1994; received in revised form 20 July 1995 |
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Keywords: | : Delay differential equations Stability Control |
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