Biomathematical models of schizophrenia.

This paper summarizes the work of developing and analyzing a mathematical model of schizophrenia. First the psychological and physiological studies of patients with periodic catatonia made by R. R. Gjessing are briefly described. Then a mathematical model, which is based on Gjessing's work and consists of a set of nonlinear ordinary differential equations, is derived. Gjessing showed that there was a periodic change in the basal metabolic rate associated with a periodic change in the symptoms of catatonia. This suggests a study of the thyroid control system, and since the thyroid control system is a negative feedback system, previous engineering studies are followed and a system of ordinary differential equations is used as a model. The first such model was due to Danziger and Elmergreen, and their model and improvements of their model are described. Then the models are analyzed qualitatively and the mathematical results are interpreted medically. Solutions of the system of differential equations corresponding to a stable set of symptoms in the schizophrenic patients, solutions corresponding to periodic patterns of symptoms (periodic catatonia), and solutions corresponding to random or unpredictable patterns of symptoms are obtained. The model suggests that since certain parameters are varied, various types of solutions and hence various patterns of symptoms are obtained. There are a number of unresolved questions in this study, and these problems are discussed in detail as they arise.