Adequate protein is essential for immune system function as well as all other functions in the body. There were some trials using vegan diets with HIV patients and they found that they did not respond well to this diet, they found it required too much energy for the body to make the proteins from non animal sources. I knew someone who went into cachexia (muscle wasting) using this diet while he was sick. The body will scavenge proteins from the muscles if not given enough dietary protein.
B12 has to be supplemented with these diets since it is primarily supplied via animal protein. It along with other b vits are critical for protein metabolism.
With the immune system working hard, it is important to make sure your food is void of additional pathogens. I knew someone who used unpasteurized milk and cheese and became incredibly ill. Any fresh dairy should be avoided since infections create a secondary lactase deficiency which creates more inflammatory immune reactions. (low lactase diary is ok such as aged cheeses) Make sure your raw fruits and vegetables are adequately sanitized.
Watch for any food sensitivities since the immune system is already skewed from the infection. These sensitivities will create more stress on the body.