________________________________________ *Corresponding author: Email: skashihalwa@yahoo.com, skashihalwa@nust.na; Asian J. Prob. Stat., vol. 25, no. 1, pp. 141-151, 2023 Asian Journal of Probability and Statistics Volume 25, Issue 1, Page 141-151, 2023; Article no.AJPAS.106181 ISSN: 2582-0230 _______________________________________________________________________________________________________________________________________ An Application of Homogenous Semi- Markov Model for Assessing HIV/AIDS Progression to ART Patients in Namibia Simon Pombili Kashihalwa a* , Josua Mwanyekange a and Lilian Pazvakawambwa b a Department of Mathematics, Statistics and Actuarial Science, Namibia University of Science and Technology, Namibia. b Department of Statistics and Population Studies, University of Namibia, Namibia. Authors’ contributions This work was carried out in collaboration among all authors. All authors read and approved the final manuscript. Article Information DOI: 10.9734/AJPAS/2023/v25i1547 Open Peer Review History: This journal follows the Advanced Open Peer Review policy. Identity of the Reviewers, Editor(s) and additional Reviewers, peer review comments, different versions of the manuscript, comments of the editors, etc are available here: https://www.sdiarticle5.com/review-history/106181 Received: 06/07/2023 Accepted: 13/09/2023 Published: 06/10/2023 __________________________________________________________________________________ Abstract Background: The progression of HIV infection to AIDS and then to death can be considered a stochastic process. Disease progression can be broken down into a finite number of intermediate states, based on CD4 counts. The five states of the Markov process of HIV/AIDS progression are commonly defined as: S1: CD4 count > 500 cells/microliter; S2: 350 < CD4 count ≤ 500 cells/microliter; S3: 200 < CD4 count ≤ 350 cells/microliter; S4: CD4 count ≤ 200 cells/microliter; and D: Death. Objectives: The objective of this study was to model the progression of HIV/AIDS disease of patients under ART follow-up in Namibia using homogenous semi-Markov processes, using the data obtained from Ministry of Health and Social Services. Methods: A retrospective study design was used to obtain data on 2422 patients who were observed 11028 times. The semi-Markov model was employed to estimate the transition probabilities and transition intensity Original Research Article