Start with some photos of the real door and the species of the wood. There are several mahoganies.

Thanks RRM1. Does this help?

It looks like there is more figuring in the example door than in yours, but the color should be straight forward. Just do testing on some scrap. I usually spray my stains and mostly blend off-the-shelf stains with pigments and dyes to get what I want. It is also impossible to do from a picture. Every stain maker has its own formulas. Trial and error is the about the only way. It looks like there is a pinkish tint to the wood, so whatever color you choose, you may want to add a little walnut to it to neutralize some of the pink. Walnut will often have a little green in it and that will drive it to more brownish final look. The sample looks reddish, so it may not be necessary. Good luck and come back here, there are knowledgeable people that may help. Looking back at the pic, if the streaking is what you're trying to duplicate, there may be some tricks you can use.
Richard

We just had our Mahogany front doors refinished. The door guy mixed his own colors and the match was perfect.
I don't mean to hijack your thread, but our problem now is to maintain the finish. The doors were only up for 4 years and I would like to have suggestions regarding what I should do to prevent weathering? Should I use some kind of wax?