Hi. Based on your photos, I think fusarium wilt is a good candidate. Most other diseases cause spots or blotches or other similar blemishes on leaves in addition to yellowing (this page from the U. of Maryland has nice comparative photos of tomato diseases), but I’m not seeing that in your photos. Another possibility would be nitrogen deficiency (as noted in this article from Texas A&M University), but that typically won’t kill a plant. Also, it wouldn’t be expected to leave green leaves at the bottom of the plant, since the oldest (lower) leaves are affected first. If you need guidance on fertilization, this article from Ohio State U. includes recommendations for tomatoes. If you aren’t sure, you should get a soil test. Ohio State has a good fact sheet on that here. 

Returning to fusarium wilt, one characteristic is one-sided chlorosis (leaf yellowing), which is evident in the photos you sent. Another is brown streaks in the stem due to the damage to the vascular tissue. This page from Purdue U. has a good example of that if you scroll down to fusarium wilt, as does this fact sheet from the U. of Maryland. I suggest looking for that feature in one of your affected tomato plants. If you see that and fusarium wilt is what you are dealing with, here is what that fact sheet from the U. of Maryland says:

“The best defense is to grow or purchase resistant varieties. If you suspect a fusarium problem, select only varieties with resistance to races 1, 2, and 3 of this disease. However, under severe disease pressure, even plants with resistance to both strains may exhibit symptoms. Rotate tomato plants to another part of the garden or grow plants in containers (keeping infected soil out). Pull up and discard infected plants immediately. If you grow your own plants be sure to sterilize all plant growing equipment and supplies with a 10% chlorine bleach solution and use sterile soil-less growing media. There is no cure for this disease. Plants must be removed and destroyed. When planting, avoid all wet spots and build raised beds if drainage is less than ideal.”

To answer your question about whether this will spread to other tomato plants, it won’t spread directly from plant to plant, but if it is in the soil, it can affect any plant grown in that soil. Your best strategy would be to use fusarium-resistant plants and grow them in a different part of the garden. Crop rotation is a good practice in general, and this fact sheet from Iowa State U. talks more about it.