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To perform numerical calculation, p 1 can be obtained from the given data. [5]
As S 1 , T and W 1 (cost per medical treatment) are selected values, hence equation (8) will clearly specify the optimal control u(t) as a function of time.
Thus one can select u(t) graphically which signifies clearly how the control u(t) is to be applied to achieve the goal (estimated) S 2 with the time period t (say) by equation (8). Where Ø(t)can be obtained from equation (7) with the help of equation (6).
Conclusion
It is of note from equation (8) that u(t) decreases as the time increases and approaches to T. Thus at the initial stage, the cost of medical treatment will be higher and this cost decreases accordingly; This is expected because as time increases the infected TB elderly persons will be decreased due to application of medical treatment which significantly decrease the transmission of TB among the elderly population.
Numerical calculation can well simply be performed which can be carried out to reveal clearly a pilot project for achieving the purpose. It is to note further that as T (fixed estimated time) increases, u(t) decreases slowly. This is plausible because increase of T will give a greater opportunity and liberty to bring down infection to S 2 and thus the cost of treatment will slowly decrease. Thus greater T will give more liberty to the government / NGO regarding cost and activities, if situation does permit, otherwise, the utilization of medical treatment as a function of time is to be performed with much higher degree of progress.
However, in further cause of study, we will perform several numerical graphs on different selected values of S 2 , S 1 , T 1 , W 1 and Ø 1
Some other optional control problems can be investigated in this respect with the aid of [3, 4].
References
- Recent trends in geriatrics and gerontological studies; Proc. of state level conference on geriatrics and gerontological studies in West Bengal , December, 16-17, 2004
- Pontrayagin, L.S. et al: The Mathematical theory of optimal process (1962).
- Butkovokiy, A.G : The distributed Control systems, American Elesvier publishing company (1964)
- Golub, N. N : optimal control of linear and non-linear system, translated from Autometika Telmekhanika, No. 9, 16-28 _1964)
- Health on the March 2005-06 published by, State Bureau of Health service, Directorate of Health Services, Government of West Bengal.
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