Hi Carlton
I'm sorry you're unsure of where your brother might be, have you a last address for him and do you know if he had any family of his own, children or grandchildren? Very often contacting neighbours is a good start, just checking for other residents in the same street can work, using 192.com and the electoral roll maybe. I take it you are not able to get any discharge info from the hospotal, what about trying the local GP's surgeries and explaining the situation, it's a long shot as they probably will not be able to give any info out, but they could perhaps put yopu in touch with maybe a care home where he may have been transferred.
You could always try calling care homes in the bournemouth area if you think he had no way of caring for himself at home and would have had to be given accomodation in a care home or nursing home.
that's as much as i can come up with at the moment, unless you do actually feel the worst has happened and then a call to bournemouth register office would certainly eliminate a death for him in the area. you only need to give his name and date of birth and they can probably tell you if they have a death registration for him, I hope that's not the case and he has just found himself a plac to rest and recouperate in a specialist home. good luck, i'll help if i can.
regards
dot