Supplementation with 30 mg of zinc a day increased immune cell number by 29% & function by around 45% in elderly.
www.sciencedaily.com
Around 30% of nursing home residents have low zinc levels and this was associated with a significantly higher incidence of pneumonia and morbidity from it. It is important to keep in mind that too much supplemental zinc (I think above 30 mg/day) can be toxic.