Conventional models in mathematical immunology consist of ordinary or delay differential equations for the concentrations of different cells participating in the immune response and for the concentration of pathogen. Their spatial distribution in the tissue or cell culture, or their dependence on the genotype is described by reaction-diffusion equations with time delay characterizing clonal expansion of lymphocytes and with nonlocal terms taking into account cross reaction in the immune response. In this presentation we will study some mathematical properties of such models and their biomedical applications.