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The phrase "a slow and persistent" is correct and usable in written English.
It can be used to describe something that occurs gradually and consistently over time, often in a context related to behavior, processes, or changes.
Example: "The disease progressed at a slow and persistent rate, making it difficult to detect in its early stages."
Alternatives: "gradual and steady" or "steady and relentless".
Exact(2)
On the other hand, neurodegenerative conditions like MS and ALS owe their prolonged progression to a slow and persistent increase in proinflammatory cytokines.
In high-Na+ media, however, the osmotic fragility curves showed a slow and persistent right shift, eventually leading to the lysis of many RBCs.
Similar(58)
This rapid and transient kinetic of mRNA accumulation is characteristic of regulatory components and differs from that showed by, for example, transcripts encoding for defense components (e.g., protease inhibitors) which is characterized by a slower and more persistent rate of mRNA accumulation, reaching maximum levels after hours to days [ 8].
The slow and persistent nature of the changes in AMPAR surface expression is suggestive of a gene-mediated pathway involving nuclear receptors.
In contrast to the rapid and transient nature of canonical NF-κB signaling, the noncanonical NF-κB signaling pathway is characteristically slow and persistent [ 13].
The simple moral of the tortoise and the hare, for example, is, "After that, Hare always reminded himself, "Don't brag about your lightning pace, for slow and steady won the race!" It encapsulates both the mistake--being lazy and arrogant from over-confidence--and the lesson to be learned--that slow and persistent will win over quick and careless.
A few months ago Security firm RSA's SecurID systems were the victim of "an advanced persistent threat, a slow and consistent attack used by hackers to obtain specific information".
Use of microspheres allows a slow, persistent and long-term release of rotenone.
Throughout this period from 1998 to 2008, the CD incidence rates in children aged 3 6.9, 7 10.9, and 11 14.9 years were about the same and were characterized by a slow but persistent increase over time.
The Fed has cut rates 13 times since the beginning of 2001, first in a failed effort to prevent a recession and more recently in hopes of halting a period of slow growth and persistent layoffs.
The demise of the hedge funds began a slow but persistent loss of market confidence in the bank.
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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