While the referenced article is not written with CLL patients in mind, I'm certain that this is a common question, given illnesses can be more frequent and longer lasting for us.
Toby Mündel, Senior Lecturer, School of Sport and Exercise at Massey University, New Zealand explains how exercise affects the immune system:
Of particular note is the plot of Risk of infection vs Exercise amount and intensity plus these excerpts:
"...when repeated regularly, and with sufficient rest in between, each bout of exercise improves immune function that accumulatively leads to a 20-60% reduced risk of infection.
While you may have seen adverts claiming that supplement X can improve your immune function and protect against infection (think probiotics, green tea or berry extract), none appear to provide the same benefit as a healthy, well-fed and active individual."
If your symptoms are above the neck, you’ll still be able to manage a lighter-than-normal workout.
"When should I not exercise?
Well, you should probably swap your training for some R&R if your symptoms are below the neck (chest congestion, cough, stomach problems such as vomiting or diarrhoea) or you have a fever, muscle aches or widespread fatigue."
and in a reply to a comment:
"Good advice to avoid areas with large numbers of people if you're sick, presumably start by not going into work, though. As Matthew points out, exercise needn't just be at the gym - there are plenty alternatives that mean you still get your kick but don't unnecessarily spread your germs. Germs are all around us, so being considerate to others should start with good hygiene (e.g. washing and drying hands properly)..."
From personal experience, I can't stress enough how important it is to maintain some level of exercise, fatigue permitting, in order to maintain your overall health.
Photo: Sunset looking North along the farm access track. Evening is my favourite time of the day to go for a walk, particularly in summer, when the worst of the heat is usually gone. Kangaroos are more likely to be active too.