Application of Multi-State Semi-Markov Models on HIV/AIDS Disease Progression

Solomon Kalayu Mengesha*, Gebregewergis Alemu Gebremedhn**, Tilahun Ferede***, Cheru Atsmegiorgis ****
*-**Lecturer, Adigrat University, Tigray, Ethiopia.
***-****Hawassa University, Awassa, Ethiopia.
Periodicity:July - September'2018
DOI : https://doi.org/10.26634/jmat.7.3.14988

Abstract

Although remarkable progress has been made in the control of the global Human Immunodeficiency Virus (HIV/AIDS) epidemic, the burden of HIV has reached contemporary at the shocking level in Sub-Saharan Africa. Understanding the cycle of HIV/AIDS disease progression can have great value on the effectiveness of the therapy. The purpose of this study is to determine factors affecting the progression between different stages of the disease and to model the progression of HIV/AIDS disease of an HIV infected patients under ART follow-up using multistate Semi-Markov model. A cohort of 526 HIV infected patients has been sampled from a Hawassa University Referral Hospital, Hawassa, Ethiopia, who have been under ART follow up from September 2012 to August 2017. States of the Markovian process are defined by the seriousness of the sickness based on the CD4 counts in cells/microliter. The five states of HIV/AIDS disease progression considered in the multi-state Semi-Markov model were defined based on of the following CD4 cell counts. State I, State II, State III, State IV and Death state. The major transiently prognostic factors between different states of HIV/AIDS disease were sex, age, ART adherence level, TB status, functional status, opportunistic infections , and body weight of patients. Hence, the progression of HIV/AIDS was significantly accelerated with poor ART adherence, patient's co-infection with TB, older patients, and patients being bedridden. The conditional probabilities of patients from any good states to worst state are increasing over time. Weibull sojourn time distribution is the appropriate and is preferably used as sojourn time distribution under multistate models. As time elapsed, the transition probability of patients is more likely to be in worse state than to be in better one. This shows that patients should aware the need to initiate therapy at early stages of the virus.

Keywords

Multistate, Semi-Markov, Progression, Transition Probability.

How to Cite this Article?

Mengesha, S. K., Gebremedhn, G. A., Tilahun, F., & Atsmegiorgis, C. (2018). Application of Multi-State Semi-Markov Models on HIV/AIDS Disease Progression, i-manager's Journal on Mathematics, 7(3), 30-41. https://doi.org/10.26634/jmat.7.3.14988

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