Periodic Dosing with Exponential Decay

This page allows you to analyze a model for drug delivery. Assume that we use uniform dosage and that the administration of a dose immediately results in the recipients concentration of the drug increasing by co units. N doses are administered at uniform interval of T time units. Furthermore, the body eliminates the drug according to an exponential decay model where 1/e is removed in τ time units. In a given dosage interval, let c(t) be the concentration and let t = 0 when dosed, then the concentration obeys the differential equation     dc/dt = - c(t)/τ     with the initial condition     c(0) = co. This initial-value problem has the unique solution     c(t) = co e-t/τ.


co =
T =
N =
τ =

References:

Jones, D.S. and B.D. Sleeman Differential Equations & Mathematical Biology. Chapman & Hall/CRC, Boca Raton, FL, 2002.

Mazumdar, J. An Introduction to Mathematical Physiology & Biology. Cambridge University Press, Cambridge, UK, 1999.