Parameters of a discrete SIR model and Euler’s formulas for SIR model.

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What is the difference between parameters of a discrete SIR model (infection rate and recovery rate), shown below:

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And parameters of Euler formulas shown below if we consider the same data. enter image description here

Can I use the discrete SIR model to estimate parameters of spread of a disease in a specific city and apply those parameters to Euler’s formulas above for the same city?
I thought if the step size = 1 in Euler formulas, then parameters will be the same as discrete SIR model, but I found myself more confused when I decided to research further. Please help.