A As someone who has survived meningitis during my professional career, I have more than passing knowledge about this subject. It’s highly unlikely that any employee diagnosed with meningitis would have the capacity to “come to HR” to tell you she has meningitis and ask for a leave of absence. Given the seriousness and potentially life-threatening nature of the illness, it’s more likely the employee would have been sent straight to a hospital without having the time to tell you anything. So the first thing you should do is send your employee or her healthcare provider the Family and Medical Leave Act (FMLA) medical certification form to be completed and returned within the time allowed to confirm whether she does in fact have meningitis.
In the meantime, I wouldn’t be too concerned about any obligations to notify other employees and risking unnecessary widespread panic. According to my medical references, although meningitis is contagious, it isn’t as contagious as either the common cold or the flu, and it cannot be transmitted simply by breathing the air where a person with meningitis has been.