Suppose that a drug is administered once every 4 hours, where the drug moves from the gastrointestinal tract into the circulatory system. Denote by c(t) the dosage at time t and by a and b the rates at which the drug is consumed in the gastrointestinal tract (GT) and the circulatory system (CS) respectively. Initially, neither the GT nor the CS contain the drug, so that the situation can be modelled as
, (0) 0
( ) , (0) 0
ax by y
dt
dy
c t ax x
dt
dx
Suppose that , ( 4) ( )
0 1 4
0 1
( ) 0 c t c