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"apply the model to" is correct and usable in written English.
You can use this expression whenever you want to discuss using a model in order to better understand or analyze a subject. For example, "We need to apply the model to our current process in order to evaluate its effectiveness."
Exact(60)
We apply the model to health services projections in the Netherlands between 2010 and 2050.
We apply the model to the Willamette Basin, Oregon, USA.
We apply the model to light water at room temperature.
Next, we apply the model to empirical data to demonstrate feasibility.
Then we apply the model to a specific model that is currently operating.
We apply the model to the dehydrogenation of ethane over pure transition metal catalysts.
We apply the model to the case of runway capacity expansion at Haneda Airport.
We apply the model to analyze stochastic stability in 2×2 coordination games.
Therefore, we can apply the model to optimize the design of customized power systems.
Finally, we apply the model to study p53-induced cellular responses to DNA damage.
Subsequently, the proposed algorithm is employed to apply the model to a case study.
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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