The Stochastic Analysis of a Diabetic Person's Blood Glucose Levels During Treatment

This paper assumes a diabetic person with n stages and the absorption stage is a controlled stage. Blood glucose level of a patient with a damaged pancreas may pass through the fair control stage, poor control stage, and very poor control stage several times before it reaches the controlled stage during the treatment. Blood glucose level can identify from any one of the n stages and it can be moved to other stages easily. This may form number of cycles of fair control stage to poor control stage to fair control stage based on the changes in the blood glucose level of the patient. This paper provides two types of models. In model 1, r to s to r cycle, and in model 2 u to v to w to u cycle. This paper obtains the probability generating function of the number of cycles before the glucose level is controlled and their numerical illustrations are provided. Introduction: In model 1,Blood glucose level of a patient with damaged pancreas may pass through fair control level (say stage r) and poor control level (say stage s) several times, between them before the glucose level reaches controlled level due to the treatment. This may form number of cycles of fair control level to poor control level to fair control level based on the changes in the blood glucose level of the patient. This is taken as one r-s-r cycle. In model 2, Blood glucose level of a patient with damaged pancreas may pass through fair control level (say stage u) ,poor control level (say stage v)and very poor control level (say stage w) several times, between them before the glucose level reaches controlled level due to the treatment. This may form number of cycles of fair control level to poor control level to very poor control level to fair control level based on the changes in the blood glucose level of the patient. This is taken as one u-v-w-u cycle. For more details on such deficiency and disorder, one may refer to [3], [4], [5]. Using the Mathematical approach given in [1], [8], [9], and [10], we study the case of a diabetic person. Results: The results of model 1 in section 2 and model 2 in section 3. In this sections are derive the probability generating function, mean and variance of number of cycles occur in our model during treatment time. Conclusions: In Model 1, if a diabetic person start the treatment in fair control stage then the person can reduce the expected value of number of r-s-r cycle. In Model 2, when the transition probability of controlled blood glucose level (absorption stage) is high, the expected value of r-s-r cycle is decrease