Additives in the foods, and especially tBHQ (tert-butylhydroquinone), hamper the immune response so it can't fight the cells that have been infected. As the immune system is supposed to work hand-in-glove with the vaccine, the additives make the vaccine itself less effective.
The additives are commonly found in processed and fast foods, such as chips and crackers, and in frozen foods. There's no legal requirement for manufacturers to list tBHQs on the packaging so there's no way of knowing for sure if the food contains them.
Researchers from Michigan State University tested two flu strains, H1N1 and H3N2, on laboratory mice, some of whom were also fed tBHQs, and then monitored their immune responses.
The additive affected the immune system's T cells, which are mainly responsible for fighting infections. It slowed the activation of T cells and reduced their ability to fight infections sooner. It also affected the immune system's ability to 'remember' how to respond to the virus, especially when a new strain was introduced later.