An Optimization Model of Tuberculosis Epidemiology

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Abstract
The problems of management of tuberculosis in developing nations are studied utilizing the tools of systems analysis. The tuberculosis system consists of interacting components which are the “states of nature” of the disease. The interaction of these components determine the future state of the disease. Controls in the form of therapy, vaccinations or prophylaxis may be superimposed on the natural processes, thus altering the future course of the disease. A descriptive mathematical model describing the flows between the various categories is used to predict the trends both with and without intervention. An optimization model is derived from the descriptive model under the assumption that a program of reduction of active cases has been specified. The optimization model selects the forms of control which achieve the specified reduction program at least cost. Optimization is accomplished via linear programming. The model is general in that the parameters, costs and initial conditions may be varied for different situations. The descriptive mathematical model and the optimization model which determines the most efficient controls are intended to improve decision-making in public health management of tuberculosis.

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