Question: Data fitting to SIR model

Hey guys

I am currently working on my final project in high school. This project is about mathematical modelling within epidemology, and i am currently working on the mathematical models based on the SIR model.

The basis models for the SIR model were pretty easy, but i cant figure out how to fit data to my models. My first idea was to use the method of Leastsquare and/or Nonlinearfit, but i cant figure out how to do this in maple.

In my worksheet, i have been working with made up data to develop my functions, before fitting real life data. 

In the beginning of my worksheet, i define the "time" and "number of infected" Vectors, the differential equations for s(t), i(t) and r(t), and the initial conditions for my model, where my data is i(t), the number of infected people. Then i solve it numerically with my parameters being: Beta and Alpha. After that i create a procedure according to the method, discussed in this post:

,then followed by a Nonlinear fit.

I am pretty sure that what i have done up until this point is correct, and that the procedure is where the mistake is.  

I sincerely hope someone can help me with this problem!

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