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The phrase "a persistent level of" is correct and usable in written English.
It can be used to describe a continuous or ongoing degree of something, often in contexts related to performance, behavior, or conditions.
Example: "The team has maintained a persistent level of excellence throughout the season."
Alternatives: "an ongoing degree of" or "a continual amount of".
Exact(9)
These maintain a persistent level of inflammation that is enhanced further by the movement of immune cells – such as white blood cells, which wrongly assume the inflammation is a sign of injury or infection – into the fat tissue.
But if you look at the last 60 years in particular, we still witnessed a persistent level of violence in our politics, particularly when it comes to race.
In this study we address the question of whether expertise can be gained in a triple-conjunction (color, spatial frequency, and orientation) search task when both the features and spatial location of the target are changed from trial to trial while maintaining a persistent level of bottom up uncertainty in the Shanon entropy sense.
However, national surveillance data demonstrated a persistent level of reported cases in recent years.
Of the questionnaires which were returned, 66% reported a reduction of subjectively perceived care burden, 29% reported a persistent level of burden and 5% reported an increased burden in the time during their treatment in the DSC.
Walsh et al. (2008) found a persistent level of PABP during the infection cycle of vaccinia virus, but did not provide any evidence that PABP is in fact produced during the viral infection cycle.
Similar(51)
In 1 of our patients, an 8-month-old girl for whom no acute-phase sample was available, the virus was detected at day 23 of illness, an unusually persistent level of viremia.
There is a low but persistent level of verbal abuse of identifiably Jewish people on the street.
In validation 2 set, CD was defined as having a very high and persistent level of transglutaminase auto-antibodies or confirmed by biopsy, so we refer to this group as having CD autoimmunity.
The most pronounced example is an exceptionally high and persistent level of child malnutrition (46% in 2005 6).
It is generally accepted now that chronic heart failure is accompanied by low, but persistent, level of cordiomyocyte death [19].
More suggestions(15)
a great level of
a persistent surplus of
a crazy level of
a persistent nag of
a degraded level of
a comfortable level of
a mixed level of
a persistent kind of
a persistent mingling of
a persistent set of
a sufficient level of
a persistent region of
a persistent exposer of
a commendable level of
a persistent cloud of
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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