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The Listeria bacillus is not airborne. Any contamination would be due to direct contact with the uncooked meat or meat juices. Keeping the thawing meat in the bottom drawer is adequate to keep from accidentally contaminating other foods by dripping meat juices. For extra safety, you can put the meat into a sealed container. A ziplock plastic bag inside another container (eg, bowl) will provide extra safety and ease of handling to avoid spilling anything.
To prevent infection with Listeria, or any other the food borne pathogens there are simple steps you should make routine:
--Thoroughly cook all meats
--Thoroughly wash all vegetables especially when you are going to eat them raw
--Keep meat and vegetables stored separately.
--Only use pasteurized dairy products
--Thoroughly clean all utensils and cutting boards after use, and between meats and vegetables; and use separate cutting boards for meat and other foods. Take special care that your cutting board and utensils used to handle foods to be eaten raw are clean before use.
--Clean your refrigerator once a week.
--Wash your hands frequently when preparing foods: before, during (between handling of different raw foods), and after you are finished.
Food storage and safety is an important issue, especially when you have a family. Here is a link to a site that has more tips about food storage and safety: