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The phrase "a second model" is correct and usable in written English.
You can use it when referring to an additional or alternative model in a discussion or comparison.
Example: "After analyzing the first model, we decided to implement a second model to improve our results."
Alternatives: "an alternative model" or "a different model".
Exact(60)
A second model lasted six weeks.
We construct a second model of a hardware deployment.
The model was linked to a second model, from which it drew vital information.
The same concepts are then applied to Mexico as a second model system.
Demand for a greater variety of fonts led to a second model in 1878.
A second model, the Bose QC20i, has an in-line remote intended for Apple iOS devices.
A second model was made, and exhibited at the International Exhibition of Decorative and Industrial Arts in Paris in 1925.
A second model screens cash flow statements, balance sheets and other financial data, looking for securities that may be mispriced.
In order to simplify the model, a second model of ANN was proposed without curvature ratio.
A second model of leadership is not so much leading by directing as leading by serving.
A second model will appear in only 3,000 Wal-Mart stores later in June.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com