Problem involving drug delivery and ODE

I am trying to model drug delivery over time using ODE45 to simultaneously solve three differential equations, and it is giving me an exponential decay function, which is what I want. However, I am now trying to model extra doses being applied to the system. For example, I want to increase the concentration of the drug by a set amount at a certain time interval while having the exponential decay still apply. Basically, I want it to look like this:

What can I do to accomplish this?

Answer 1

[Star Strider]

See odeset and particularly the Event Location Property section. An events function will allow you to stop the integration according to specific criteria, change something, then restart the integration.

In your pharmacokinetics application, you can do this either with respect to time or drug concentration.

Answer 2

[Sean de Wolski]

Have you tried using SimBiology?

Perhaps this webinar could get you started.

[Arthur Goldsipe]

Yes, SimBiology is designed just for this sort of problem. You can write your model in terms of reactions instead of ODEs and doses instead of events. If you have access to SimBiology and want to see how to translate this problem into a SimBiology model, please post another question on MATLAB Answers. It should just be a few lines of code.