Eczema can not be spread from person to person as it is not a contagious condition. It can, however, be spread on your own body. Sudden changes in temperature, extremely dry skin, scratchy materials, and stress can all cause eczema to be more widely spread around the body.There is also contact dermatitis which flares up from contact with irritants and allergens. The more your body comes in contact with the irritant, the more the eczema will spread.
Sources: WebMD and the National Eczema Society (eczema.org)