Some good advice there.
I have Crohns disease and am on immune suppressants; therefore I have a compromised immune system and get sick a lot. I take a few supplements which seem to help, and if I do get sick now it doesn't seem to last as long and I bounce back quicker.
I take Vitamin C and zinc supplements, probiotics, which are really good if you have had a gut infection, they put the good bacteria back in - if you have had a bad infection, your good bacteria and enzymes may be depleted and you may not be absorbing enough from your food - I use Optibac, sea kelp and spirulina which provide calcium and minerals, and also L-glutamine, which helps with tissue repair.
You could also consider cutting out some of the known "gut irritants" for a while - irritation and inflammation in the gut promotes malabsorption of vitamins and minerals from food. The worst culprits are gluten and dairy, but it might be worth cutting down on sugar as a sugary diet, even fruit, can feed the bad bacteria/yeasts etc in the gut. Legumes like beans and lentils also contain a starch called raffinose, which is hard for the gut to break down if it is compromised. It is not uncommon to develop intolerances or allergies to certain foods after a bad infection.
It might sound a bit "cranky" but after making some of these adjustments to my diet I experienced a massive reduction in bad gut symptoms, and get sick much less.