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A Study on TB Infected Aged Population :
An Optimal Control Theoretic Approach
Dr. Dilip Kumar Chakrabory
Teacher – In – Charge, Netaji Nagar Day College
Piyanka Dhar
Netaji Nagar College Computer Centre, Kolkata
In this paper we have studied an optimal control problem of aged persons infected in Tuberculosis (TB) by applying the proper medical treatment as control, by considering a certain weighing function, that is, the cost per medical treatment, the total cost of the medical treatment has been investigated. The whole problem has been considered in the viewpoint of achieving a certain goal under the minimization of cost within a stipulated period.
It can obviously be felt very commonly that the elderly persons generally loose significantly their power of resistance to certain diseases like TB. It can be presumed that due to the lack of nutrition, the loss of vitality is greatly seen in the rural areas. So the problem to control the transmission of TB infected aged persons optimally should be considered from the mathematical standpoint with the aid of available statistical data. Statement of the problem
The problem is to find optimally the medical treatment (Control) u(t) so that within a short stipulated period T, the number of aged person (aged 55 years onwards) affected by Tuberculosis (TB) can be brought down to a certain estimated level under minimization of the cost of the treatment. This can be termed as the “minimum cost optimal control problem”.
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