Authors:Simon Pombili Kashihalwa, Lilian Pazvakawambwa, Josua Mwanyekange Pages: 1 - 13 Abstract: Background: Sojourn time refers to the amount of time a HIV patient spends in each clinical state in a single stay before he/she makes a transition to another state. HIV can be broken down into a number of intermediate states, based on CD4 counts. The four states of the Markov process of HIV are commonly deﬁned as: S1: CD4 count > 500 cells/microlitre of blood; S2: 350 < CD4 count ≤ 500 cells/microlitre of blood; S3: 200 < CD4 count ≤ 350 cells/microlitre of blood; S4: CD4 count ≤ 200 cells/microliter of blood. Aims: The aim of the study was to estimate sojourn and transition between clinical states of patients under ART in Namibia using homogenous semi-Markov processes, on data obtained from MoHSS. Methods: A retrospective study design was used to obtain data on 2422 patients who were observed 11028 times, during 2008 to 2017 follow up period. The four staged semi-Markov model was employed to estimate sojourn times and transition between clinical states. Results: Results indicates that 1637 (67.6%) were female and 785 (32.41%) were male .657(27.13%) patients started ART in state 1, 683(28.19%) patients started ART in state 2, 677(27.95%) patients started ART in state 3 and 405(16.72%) patients started ART in state 4, at treatment commencement (t = 0). As expected, the probabilities of transiting from good to worse states increased with time. After 6 months, the probabilities of transiting from state 1 to 3, and from state 1 to 4 are 0.023 and 0.004 respectively. Whereas after 12 months, the probabilities of transiting from state 1 to 3, and from state 1 to 4 are 0.059 and 0.010 respectively. As time increased the probabilities to remain in the same state is decreasing (probabilities of remaining in state 1 after 6, 12 and 18 months is 0.804, 0.698 and 0.633). Sojourn times for states 1, 2, 3 and 4 were 22, 8, 10 and 15 months respectively. Conclusions: Sojourn time is of interest in HIV modeling, as it gives a signal of how HIV is progressing. Longer sojourn times indicates slow HIV progression and shorter sojourn times indicates rapid HIV progression. As time increases, transition probabilities from good states to worse states increases. PubDate: 2023-03-17 DOI: 10.9734/ajpas/2023/v21i4468 Issue No:Vol. 21, No. 4 (2023)

Authors:Rohit Kumar Verma Pages: 14 - 21 Abstract: Varma [1,2] entropy has attracted attention for a new class of non-linear integer programming problems that arise during the course of discussion. Our focus in this communication is to explore the techniques of dynamic programming. This process requires splitting any optimization event into a finite number of subcomponents for any occurrence of a finite generalized problem. The capacity plan should be partitioned in such a way that the expression can be optimized. PubDate: 2023-03-17 DOI: 10.9734/ajpas/2023/v21i4469 Issue No:Vol. 21, No. 4 (2023)

Authors:A. A. Modhesh, Abdulkareem M. Basheer Pages: 22 - 33 Abstract: Entropy can be mathematically defined as a measure of the uncertainty of random variables that represents the potential quantity of information. This article investigates the behavior of the entropy of random variables which follow a Kumaraswamy distribution using progressively first-failure censored (PFFC) data. In particular, we calculate the maximum likelihood estimation and the confidence interval of entropy by using the observed Fisher information matrix through the asymptotic distribution of the maximum likelihood estimator. Furthermore, we apply the Markov Chain Monte Carlo (MCMC) method which help us to estimates the entropy and to formulation the credible intervals in order to address this problem. Here, a numerical example of real data is presented to illustrate the performance of the proposed method. Finally, we perform Monte Carlo simulations to observe the behavior of the proposed procedure. PubDate: 2023-03-18 DOI: 10.9734/ajpas/2023/v21i4470 Issue No:Vol. 21, No. 4 (2023)