Question

Exercise 3: Consider the following discrete model for drug prescription an +1 = an-kan + b, where an is the amount of drug (in mg) in the blood stream after administration of n dosages at regular intervals (e.g. hourly). (a) What do the parameters b and k represent?. (b) Find the fixed points of the model and determine their stability.

Answer 1

Given discrete model for drug perception a_n + 1 = a_n - k_an + b k is proportion of the drug in blood stream that body (or) eliminated the doses hence from above k must be a positive also 'k' values from 0 to 1 i.e. 0 lessthanorequalto k lessthanorequalto 1 as the body cannot be eliminated more already there 'b' is the amount administrated in each dose. Hence 'b' is also the positive fixed points of the model It will occur when a_n + 1 = a_n given model a_n + 1 = a_n - k_an + b k_an = b a_n = b/k for stability when a_n = b/k + C 'C' is small change we see that both more a_n + 1 closer to b/k than a_n Hence it is stable.