Type 1 diabetes is a disease characterized by progressive loss of beta-cell function due to an autoimmune reaction affecting the islets of Langerhans. It is now generally accepted that cytokines are implicated in the pathogenesis of autoimmune diseases. Animal studies have shown that interleukin-1beta, tumor necrosis factor-alpha, and interferon-gamma affect type 1 diabetes development profoundly. It has been suggested that beta-cells are destroyed by cytokine-induced free radical formation before cytotoxic T-helper (Th)-lymphocytes and/or autoantibody-mediated cytolysis. This hypothesis is known as the "Copenhagen model." We introduce a mathematical model encompassing the various processes within this framework. The model is expressed in rate equations describing the changes in numbers of beta-cells, macrophages, and Th-lymphocytes. Being concerned with the earliest events, we explore the conditions necessary to maintain self-sustained beta-cell elimination based on the feedback between immune cells and insulin-producing cells. The motivation for this type of analysis becomes clear when we consider the multifactorial and complicated nature of the disease. Indeed, recent research has provided detailed information about the different factors that contribute to the development of the disease, stressing the importance of incorporating these findings into a more general picture. A mathematical formalism allows for a more comprehensive description of the biological problem and can reveal nonintuitive properties of the dynamics. Despite the rather complicated structure of the equations, our main conclusion is simple: onset of type 1 diabetes is due to a collective, dynamical instability, rather than being caused by a single etiological factor.