I would like to know this patent just for US market or Worldwide.
I noticed the patent owner has not paid the fee since 2011.
Does it mean the patent is now expried(invalid) ?
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There is no such thing as a "worldwide patent" rather, each jurisdiction has self control over patents covering its territorial region. Thus, a US patent offers exclusive rights to the covered invention within the US while a European patent offers exclusive rights to the invention in Europe, etc. Someone with a valuable invention can get patent protection in each jurisdiction, but that involves a step-by-step approach of seeking protection in each place.
Once a patent issues, the patentee must continue to pay regular "maintenance" or "renewal" fees in order to keep the patent enforceable. This is something like a property tax. The patent will be deemed abandoned and unenforceable if the maintenance fees are unpaid.
According to the USPTO records, the patent you referenced (US6558681) has been abandoned for failure and therefore it is no longer infringement for someone to use the invention in the US without the patentee's permission. One important caveat here is the patentee can revive an abandoned patent fairly easily if it has been abandoned less than 24-months. This patent was abandoned back in 2011 (more than 24-months ago) and therefore can be revived only if the patentee proves that its delay was "unavoidable" despite "reasonable care." That turns out to be a difficult standard to meet.
I also looked up the worldwide patent family and found that there are a number of corresponding patents throughout Europe (including the UK) and Canada. I did not do a comprehensive search, but I did find that the Renewal fees are current in the UK (UKIPO Records). This means that the patent is still in force in the UK and perhaps throughout Europe as well.
Bottom Line: The US patent is expired; The corresponding UK patent is still in force; and Other European and Canadian versions may also still be in force.