Lots of good information provided thus far so will only add a little more insight as it relates to other options.
By far using several spotter cameras is the easiest option to assist a PTZ camera to track a person.
The other alternative is to use external mounted sensors that connect to the cameras alarm I/O ports.
These can be PIR, Microwave, Radar, or combination hybrid sensors that incorporate two or more sensors.
Once the zone is tripped it would guide the PTZ to that specific area / zone.
The time and labour to install these sensors and run all the wiring to the cameras / NVR / VMS. May not pencil out for those on a small budget.
Going this route however ensures reliability and low maintenance.
Lastly, there are countless wireless / battery operated sensor options. Given this is intended for health and safety they should not be used or considered!
The odds you, or anyone else, will be diligent enough to change out batteries are slim to none . . .
As an aside you should consider one of those pendants that is worn around the neck. They are dual use such as calling for assistance and boundary detection.
Once the defined boundary is breached all manner of notification can be issued from SMS, email, voice, video.