A BIVARIATE MATHEMATICAL MODEL FOR THE EFFECT OF MELATONIN PRODUCTION ON SAMPLINGS Dr. S. Lakshmi 1 and Akanksha A. Desai 2 I. INTRODUCTION Melatonin: Melatonin is a hormone made by the Pineal gland, a small gland in the brain. Melatonin helps control our sleep and wake cycles. Very small amount of it are found in foods such as meats, grains, fruits, vegetables. Our body has its own internal clock that controls our natural cycle of waking & sleeping hours.Melatonin levels begin to rise from mid to late evening, remain high for the night and then drop in the early morning hours. Uses of Melatonin: Melatonin supplements are sometimes used to treat jet lag or sleep problems (insomnia). Scientists are also looking at other good uses for melatonin, such as:  Treating seasonal affective disorder (SAD).  Helping to control sleep patterns for people who work night shifts.  Preventing or reducing problems with sleeping and confusion after surgery.  Reducing chronic cluster headaches Synthesis: Melatonin synthesis from the pineal gland is regulated by the circadian pacemaker located in the suprachiasmatic nuclei and by ocular light exposure. Melatonin has a circadian rhythm that peaks 1 Department of Mathematics,Kunthavai Nachiyaar Government College, Thanjavur/ Bharathidasan University Trichy, Tamilnadu,India 2 Bharathidasan University, Trichy, Tamilnadu, India International Journal of Latest Trends in Engineering and Technology Vol.(7)Issue(4), pp.299-304 DOI: http://dx.doi.org/10.21172/1.74.041 e-ISSN:2278-621X Abstract: To provide guidelines for collecting and analyzing urinary, salivary, and plasma melatonin, thereby assisting clinicians and researchers in determining which method of measuring melatonin is most appropriate for their particular needs and facilitating the comparison of data between laboratories. The benefits and disadvantages of current methods of collecting and analyzing melatonin are summarized. Although a single method of analysis would be the most effective way to compare studies, limitations of current methods preclude this possibility. Given that the best analysis method for use under multiple conditions is not established, it is recommended to include, in any published report, one of the established low threshold measures of dim light melatonin onset to facilitate comparison between studies. Administration of melatonin with time of day and midnight are fitted with bivariate normal distribution and the probability density function, marginal distributions and corresponding expectations are obtained using stochastic model. Here we suggest that saliva sampling is a good method to measure. Keywords: Plasma melatonin, salivary melatonin