Food allergies to eggs and cow's milk are common during infancy but often undergo desensitization during childhood. To investigate the age dependence of food allergies, we develop a simple mathematical model focusing on T helper 2 cells (Th2) causing allergies and induced regulatory T cells (iTreg) suppressing them. We assume as follows: Both types of cells differentiate from naïve T cells reactive to specific food allergens, with the rate of supply from the thymus decreasing with age. Naïve T cells are activated by allergens in peripheral tissues, differentiating into both Th2 and iTreg cells. The activation rate of Th2 cells is reduced by iTreg cells. Th2 cells promote allergies while iTreg cells help mitigate them. Analyses show that food allergies may develop at one age and resolve at a later age. Negative selection in the thymus reduces the number of naïve T cells that react to proteins resembling components of the body. As a result, allergies to these substances tend to start and resolve earlier in life than those to dissimilar materials. Food allergy starting at an older age tends to have a longer duration if the rate of naïve T cell supply decreases according to a hyperbolic (instead of exponential) function of age.