Illinois work comp law is pretty worker friendly, but not every injury that happens while you are working is a case. For example, if you are walking down the hallway and your leg buckles for no reason or if you faint, it's typically not a claim because nothing about the job increased your risk of having an accident.
In the same way, if you get stung by a bee at work, unless you are a bee keeper or in some other job that requires you to be around a lot of bees. But if you are sitting at your desk or working in a factory and a bee flies in and stings you, you will probably not have a case.
With a bee sting or a snake bite, you can pin point where and when it happened. With something like a mosquito bite, which could happen anywhere, you would have a hard time proving for certain that it happened while working.
You might be thinking that a mosquito bite isn't a big deal and you are usually going to be right. But a recent caller to my office had a spouse who is a landscaper and has been in the hospital with West Nile Virus. There is no way to 100% say for certain he was bit at work, but because his job requires him to work in an area with lots of mosquitoes, a really good argument can be made that he most likely did get the disease because of his job. And since his job puts him at a highly increased risk of getting bitten, it's most likely a case.
Of course you can expect that the insurance company will fight him because whenever they have a possible defense that is their strategy. But it seems like a very winnable case and given how big the injuries are, it's worth taking a shot at it. You don't have to prove 100% for certain that you were bit at work. Testifying (truthfully) that you are around mosquitoes all the time at work and don't recall being bitten outside of work should be enough to make the case a winner unless there is some other evidence against you.
Big picture, this isn't a common issue, but there are tons of unique injuries every year that don't fall in to the common, every day type of case. That doesn't mean it's not a case though and you should certainly talk to an attorney to see if you have any options.