When my husband was diagnosed with cancer in December 2016, it meant that he had to go to daily radiation in the city. Obviously he was not well enough to drive himself in and out. Once a week after his radiation, he had a meeting with his oncologist and we found that he wasn't taking information in as well as he normally would and so I needed to go with him for that.
Clearly I couldn't close my day home for several weeks because parents don't get that much time off and I was concerned if they went elsewhere, they would not want to then come back and have another adjustment for their child.
Our son drove him in and out but knowing that once a week I needed to go with him, we found someone to provide back up care.
Since you clearly know you have the potential for sick days, and since your client's clearly didn't get that message even if you tried to forewarn them at interview, perhaps you also need a plan B.
Find someone who you trust. Pay for their police checks if they don't have them. Get the children used to that person. And add a clause into your contracts that in the event of illness, you have a back up carer, that parents will be notified if you are ill and that carer will be in your place. Then all you have to do is isolate yourself out of the day care space or any common spaces.
It required a huge amount of cleaning and sanitizing to make sure that with a compromised immune system my husband didn't catch anything from the day care children. The same amount of cleaning will be required for you to ensure you don't pass anything to the children. Same situation, different people at risk of being passed sickness.
This might sound harsh - but when you know that you will likely have more time off sick than the average person, or your availability might be compromised more than other provider's, then you plan for that. And yes, it does mean paying for someone to cover your business but the alternative of losing your business due to being unreliable is worth the expense.
All in all, my husband was in treatment for 6 weeks so 6 days I paid for cover for the day home. Yes, it meant paying more than I earned those days but that's the way it goes. He still has regular checks and in time, if nothing more is found the frequency of those will reduce but for now, we keep the same back up carer, inform client's as soon as we have an appointment and we bring in the back up carer. We also bring her in every couple of weeks anyway just so the children can maintain a relationship with her for the time being.
I can relate - I just don't compromise on my reputation of being a reliable provider with a quality program.

