Abstract
A mathematical model of the system of clinical medicine is proposed. The model is composed of 3 vector variables, which represent inner state of an organism, symptom and treatment as functions of time and of their interrelationships.
The inner state is governed by an inner mechanism of the organism and assumed to be unobservable in itself. However, it reveals itself transformed into symptoms which are observable by medical means. An inference of the inner state derived from the symptom is called a diagnosis. A medical means which is applied to the organism to bring the inner state of disease to that of health is called a treatment.
The model is restricted to a linear dynamical system with a discrete time variable for the sake of simplicity. Especially a stationary system in which the structure of the system does not vary with time is considered in detail along the line developed in the theory of linear dynamical system.
Several concepts such as diagnosability, treatability, simulation of a system and optimal treatment are introduced and their mathematical properties are investigated in some detail.
The correspondence between the present model and the actual case is discussed, bearing upon further development of the model.
