1. The pathogenic disease in "Contagion" was called Nipah. It was a combination of a flue and a virus, which caused respiratory disease and inflammation of the brain.
2. Cheever's statement is valid because flus/viruses can spread/caught by not taking care of your body (aka poor nutrition), and people who are in a lower socioeconomic class may not have the resources to prevent or fight off these sicknesses with proper vaccinations and medicine.
3. Cheever's statement is ironic because in the movie, shaking hands became a way of spreading Nipah. He's referring to biological warfare.