Thomas Ryan ("Statistical Methods for Quality Improvement", Wiley, 1989) describes several procedures. He tends to try to reduce all control charting to the Normal case, so his procedures are not as creative as they could be, but he claims they work pretty well. One is to treat the values as Binomial data and use the ArcSin transformation, then run standard CUSUM charts. Another is to view the values as Poisson data and use the square root transformation, then again run a CUSUM chart. For these approaches, which are intended for process quality control, you're supposed to know the number of potentially exposed individuals during each period. If you don't, you probably have to go with the Poisson model. Given that the infections are rare, the square root transformation sets your upper control limit a tiny bit above (u/2)^2 where typically u = 3 (corresponding to the usual 3-SD UCL in a Normal chart), whence any count of Ceiling((3/2)^2) = 3 or greater would trigger an out-of-control condition.
One wonders whether control charting is the correct conceptual model for your problem, though. You're not really running any kind of quality control process here: you probably know, on scientific grounds, when the infection rate is alarming. You might know, as a hypothetical example, that fewer than ten infections over a week-long period is rarely a harbinger of an outbreak. Why not set your upper limit on this kind of basis rather than employing an almost useless statistical limit?