A warm welcome to the CameraLabs forums.
In what follows please bear in mind I haven't played with any of the lenses I am about to mention.
Between the Tamron and the Sigma I would likely opt for the Sigma 18-200mm f/3.5-6.3 DC OS, reviewed here
at PhotoZone, simply to take advantage of IS (or OS in Sigma-speak) at the long end where you are probably going to be hand-holding the camera while on safari. If the OS version is out of budget then have a look at Gordon's review of the Sigma 18-200mm F3.5-6.3 DC here
and the Tamron AF 18-200mm F3.5-6.3 XR Di-II LD IF here
. Unfortunately, PhotoZone hasn't tested the EF 28-200mm f/3.5-5.6 USM so it's difficult to make comparisons. I get a sense that the lens performance isn't stunning but probably fairly reflects its price but there is no IS.
I know you stated at the start that you only wanted to take one lens with you. If you already have the EF-S 18-55mm kit lens, which is pretty small, light and easily packed in the case, then you might get much more bang for your buck if you invest in a lens such as the EF 70-300mm f/4-5.6 IS USM, reviewed here
. Optically it seems in a different league to the Sigma, it's cheaper, it benefits from IS and reaches out to 300mm (480mm full-frame equivalent) which is going to be really useful on safari while at the other end of the scale 70mm is likely to be wide enough for closer wildlife. Obviously, with regard to dust, you would have to choose your moments carefully when changing over to and from the kit lens for the big landscape shots. Yet another possibility for a second lens is the cheaper EF-S 55-250mm f4-5.6 IS but no reviews appear to be available for this one yet.