Chapter 1 Principles of Virus–Host Interaction This chapter presents a brief overview of basic immunological concepts and ideas necessary for the development of mathematical models of immune processes during virus infections. 1.1 In Brief Immunology as a scientific discipline studies the response of an organism to anti- genic invasion, the recognition of self and non-self, and all the biological, chemical and physical aspects of immune phenomena. To protect the body against pathogens, the immune system has a repertoire of body-wide defense modalities that consist of interacting cells, humoral factors and lymphoid organs (Fig. 1.1). The latter comprise bone marrow, thymus, spleen, lymph nodes and gut that are connected by the vascular systems of blood and lymph allowing the migrating of the immune system compo- nents between the compartments and to the places of pathogenic threat. In the human immune system, there are several hundred cytokines, about 10 20 antibody molecules and 10 13 immuno-competent cells that migrate spatially and interact with each other either competitively or cooperatively. Furthermore, the immuno-competent cells may proliferate, differentiate, mature, age and die. They are derived from stem cells in the bone marrow and develop further in different lymphatic tissues. They function as pathogen-degrading cells (= phagocytes) (i.e. granulocytes and macrophages), antigen-presenting cells (i.e. dendritic cells (DC) and macrophages) and specific effector cells (i.e. T and B lymphocytes). The latter are responsible for cell-mediated elimination of infected cells and antibody production respectively. Pathogens are agents that cause disease. The term is usually used in connection with an infectious microorganism. As this book focuses on the immune responses towards virus infections, only viruses will be considered. However, the principles of antiviral immune mechanisms also apply—at least partially—to other pathogens such as bacteria, helminths or fungi. © Springer International Publishing AG, part of Springer Nature 2018 G. Bocharov et al., Mathematical Immunology of Virus Infections, https://doi.org/10.1007/978-3-319-72317-4_1 1