I think you should calculate the z-transform of the e^(-44s) part. It will become a discrete transport delay in simulink. That means you are adding 22 poles to z-domain plot.
Look at these equations:
z = e^(sT)
T = 1/F
Check out the books where it is written laplace to z-transform and you will understand how a complex number s is.
And your first part of the equation is a first order simple continuous transfer function.
Summary: Use a 1st order continuous transfer function and a transport delay blocks in simulink library.
It will look like somethin like this: