Mumps
Mumps is considered most contagious in the five days after the onset of symptoms, and isolation is recommended during this period. In someone who has been admitted to the hospital, standard and droplet precautions are needed. People who work in healthcare cannot work for five days.
Transmission (medicine)
"Airborne transmission refers to infectious agents that are spread via droplet nuclei (residue from evaporated droplets) containing infective microorganisms. These organisms can survive outside the body and remain suspended in the air for long periods of time. They infect others via the upper and lower respiratory tracts." Diseases that are commonly spread by coughing or sneezing include bacterial meningitis, chickenpox, common cold, influenza, mumps, strep throat, tuberculosis, measles, rubella, whooping cough, SARS and leprosy. 
"Droplet transmission occurs when respiratory droplets generated via coughing, sneezing or talking contact susceptible mucosal surfaces, such as the eyes, nose or mouth. Transmission may also occur indirectly via contact with contaminated formites with hands and then mucosal surfaces. Respiratory droplets are large and are not able to remain suspended in the air thus they are usually dispersed over short distances."