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IOSR Journal of Engineering (IOSRJEN) ISSN (e): 2250-3021, ISSN (p): 2278-8719 Vol. 04, Issue 06 (June. 2014), ||V4|| PP 45-49

www.iosrjen.org

A Mathematical Model ForProlactin Levels In Olanzapine Treatment Of Schizophrenia Patients 1, 1,

S.Lakshmi , and 2,M.Goperundevi

Principal and Research Advisor, Govt. Arts and Science College,Peravurani – 614 804, Thanjavur- District, Tamilnadu. 2, Research Scholar, P.G & Research Dept. of Mathematics,K.N.Govt. Arts College for Women (Autonomous), Thanjavur – 613 007.

ABSTRACT: Elevated prolactin levels may play important roles, both direct and indirect in various pathologic states, including breast cancer, oesteoporosis, cardiovascular disorders, sexual disturbances and schizophrenia. In our previous paper[7]a two– step strategy for modeling degradation for elevated prolactin levels in patients with Schizophrenia with an initiation period is proposed. As a result we can identify which location parameter needs to be increased in order to improve the overall reliability. Here, in the application part the study was designed to investigate the relationship between the treatment effect of olanzapine and the serum prolactin level in schizophrenia and to investigate the factors that may act as predictors of response for olanzapine treatment. As a result the curves for the availability function and the failure rate density function are obtained for the corresponding medical curve given in the application part.

KEYWORDS: Schizophrenia, Olanzapine, Prolactin, Antipsychotics, Availability Functions. Mathematical Subject Classification:

I.

60 Gxx

MATHEMATICAL MODEL

Assumptions: 1. The time till failure has an exponential distribution đ??¸(đ?›˝) 2. The time till repair has an exponential distribution đ??¸(đ?›ž). 1 1 Let đ?œ† = đ?›˝ and đ?œ‡ = đ?›ž . Accordingly, 0, đ?‘Ąâ‰¤0 đ?‘“ đ?‘Ą = −đ?œ†đ?‘Ą đ?œ†đ?‘’ , đ?‘Ą>0 And 0, đ?‘Ąâ‰¤0 đ?‘” đ?‘Ą = đ?œ‡đ?‘’ −đ?œ‡đ?‘Ą , đ?‘Ą>0 The corresponding Laplace transforms are đ?‘“ ∗ đ?‘ = đ?œ† (đ?œ† + đ?‘ ) and đ?‘” ∗ đ?‘ = đ?œ‡ (đ?œ‡ + đ?‘ ), respectively. According to the equation đ?‘“ ∗ đ?‘ đ?‘”∗ đ?‘ đ?‘Łâˆ— đ?‘ = 0 < đ?‘ < ∞ ‌ ‌ ‌ ‌ ‌ (1.1) 1 − đ?‘“ ∗ đ?‘ đ?‘”∗ đ?‘ the Laplace transform of the renewal density is đ?œ†đ?œ‡ đ?œ†đ?œ‡ 1 1 đ?‘Łâˆ— đ?‘ = 2 = − ‌ ‌ ‌ ‌ ‌ (1.2) đ?‘ + đ?œ†+đ?œ‡ đ?‘ đ?œ†+đ?œ‡ đ?‘ đ?‘ +đ?œ†+đ?œ‡ ∗ Every Laplace transform đ?‘“ đ?‘ on (0,∞) has a unique inverse f(t) on (0,∞). The inverse transform of (1.2) can be easily checked as đ?œ†đ?œ‡ đ?œ†đ?œ‡ đ?‘Ł đ?‘Ą = − đ?‘’ −đ?‘Ą(đ?œ†+đ?œ‡ ) , 0 < đ?‘Ą < ∞ ‌ ‌ ‌ ‌ ‌ (1.3) đ?œ†+đ?œ‡ đ?œ†+đ?œ‡ In a similar fashion we obtain the failure density đ?œ†đ?œ‡ đ?œ†2 đ?‘¤ đ?‘Ą = + đ?‘’ −đ?‘Ą(đ?œ† +đ?œ‡ ) , 0 < đ?‘Ą < ∞ ‌ ‌ ‌ ‌ ‌ (1.4) đ?œ†+đ?œ‡ đ?œ†+đ?œ‡ Integrating (2.2) and (2.3) we obtain, for 0 < đ?‘Ą < ∞ đ?œ†đ?œ‡ đ?œ†đ?œ‡ đ?‘‰ đ?‘Ą = đ?‘Ąâˆ’ 1 − đ?‘’ −đ?‘Ą(đ?œ†+đ?œ‡ ) , ‌ ‌ ‌ ‌ ‌ (1.5) đ?œ†+đ?œ‡ đ?œ†+đ?œ‡ 2 And đ?œ†đ?œ‡ đ?œ†2 đ?‘Š đ?‘Ą = đ?‘Ą+ 1 − đ?‘’ −đ?‘Ą(đ?œ†+đ?œ‡ ) , ‌ ‌ ‌ ‌ ‌ (1.6) đ?œ†+đ?œ‡ đ?œ†+đ?œ‡ 2 International organization of Scientific Research

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