When you create/sell your prison, you must turn on events for this to occur. Several prisoners come down with a highly contagious virus. The virus will spread to nearby inmates, so try to isolate them (e.g. by putting them into solitary/lockdown). Prisoners suffering from this virus will look sickly, move slowly and vomit a lot. Some will fall unconscious. Prisoners will also have a Sick status effect in their mouse-over bio. Extreme cases can cause prisoners to die if not treated. 

Your guards will try to take confirmed cases to the infirmary for cure. Some inmates will go to the infirmary themselves, but only when they are let out their cells. It is recommended to call for paramedics because they will walk around the prison healing the infected.

A good strategy to counteract sick prisoners is to immediately place your 'patient Zeros' into 24 hour lockdown, and bring paramedics/Doctors to treat them. Once treated, they will display in large Green Letters 'Treated', and will require sometime to get fully better. Be cautious, as being treated does not mean the virus cannot be spread from that prisoner again. Identifying prisoners can be done easily by using the Bangup option, and after identifying all carrier, lockdown them as I said before and let all healthy prisoners out. Guards should bring all prisoners in lockdown food, so need of food should not be greatly affected.