PT-Symmetric Model of Immune Response

Abstract: The study of PT-symmetric physical systems began in 1998 as a complex generalization of conventional quantum mechanics, but beginning in 2007 experiments began to be published in which the predicted PT phase transition was clearly observed in classical rather than in quantum-mechanical systems. This paper examines the PT phase transition in mathematical models of antigen-antibody systems. A surprising conclusion that can be drawn from these models is that a possible way to treat a serious disease in which the antigen concentration is growing out of bounds (and the host will die) is to inject a small dose of a second (different) antigen. In this case there are two possible favorable outcomes. In the unbroken-PT-symmetric phase the disease becomes chronic and is no longer lethal while in the appropriate broken-PT-symmetric phase the concentration of lethal antigen goes to zero and the disease is completely cured.