The phrase "a slow course" is correct and usable in written English.
It can be used to describe a process, journey, or progression that takes a long time to complete or develop.
Example: "The project is taking a slow course, but we are making steady progress."
Alternatives: "a gradual path" or "a leisurely pace".
As you have noted, the Social Security trust fund is on a slow course to insolvency as the nation's baby boomers reach retirement age.
Doctors have been taught in the past that the cancer usually appeared first in spots on the legs and that the disease took a slow course of up to 10 years.
CV usually runs a slow course, but acute flares with life-threatening manifestations may occur.
Early postnatal changes, including altered cellularity, vascular regression and altered extracellular matrix composition, might set the disc on a slow course towards symptomatic degeneration.
In the second room the bidding took a slower course as shown.
BRUSSELS — In an era when industries are competing to shrink their carbon footprints, shipping has charted a slower course.
Perhaps the most influential advocate of a slower course is William Eskridge Jr., a Yale law professor, copious writer and litigator in support of gay rights, and author of an amicus brief in the Prop 8 case that reads very much like what the appeals court actually decided.
Mr. Obama argued for a slower course, saying, "We are going to want to make sure that we can continue to move towards less emphasis on nuclear weapons," and, he added, to "make sure that our conventional weapons capability is an effective deterrent in all but the most extreme circumstances".
Several lines of evidence have stressed in recent years the importance of HLA class I genotype in predicting progression [34], [35], [36] with certain alleles associated with a slower course of the infection.
Tobacco control has taken a slower course in China than in other countries [5].
This 'deleted'low-copypy' mouse undergoes a slower course of disease, over many months.
