A Markov model for the effects of virological failure on HIV/AIDS progression in tuberculosis co-infected patients receiving antiretroviral therapy in a rural clinic in northern South Africa

C Shoko, D Chikobvu, P O Bessong


Background. The goal of antiretroviral therapy (ART) is to suppress viral replication to undetectable levels. These low viral load (VL) levels may not be attained in some patients, a situation representing potential virological failure during the course of treatment.

Objectives. To present the results of a Markov model exploring how virological failure and active tuberculosis (TB) affect the progression of HIV in patients on ART.

Methods. A continuous-time non-homogeneous Markov model was used to model the progression of HIV/AIDS in patients on combination ART (cART). We define seven states in our model. The first five states are based on VL levels and the other two are absorbing states: death and withdrawal from the study. The effects of TB co-infection, baseline VL, lactic acidosis and treatment failure on transition intensities were assessed.

Results. The model shows that VL-based transition intensities do not follow a constant rate; rather, there are two different trends in HIV/AIDS progression. The first trend is an increase in the prevalence of state 1 (undetectable VL levels) in the first 0.5 years of treatment. The second trend follows thereafter and shows a slow decrease. Within the first 0.5 years of therapeutic intervention, the undetectable VL state is therefore attainable from any VL state. However, when virological failure occurs, there is an increased risk of death. Developing active TB while on cART increases the risk of viral rebound from undetectable levels to VLs between 50 and 10 000 copies/mL by ~1.03-fold. From a VL between 10 000 and 100 000 copies/mL, developing TB while on cART increases the rate of viral rebound by ~2.5-fold. However, if TB is detected and treated at enrolment, rates of viral rebound from undetectable levels are reduced.

Conclusions. The model confirms that virological failure, coupled with developing active TB while on cART, increases mortality rates irrespective of patient CD4+ count status. It also suggests that while TB at the time of cART initiation does not increase the risk of viral rebound, development of active TB after cART initiation does increase this risk. These findings highlight the importance of strengthening VL monitoring, which should be performed every 2 months, especially in patients with TB, and addressing unsuppressed VLs appropriately if they are detected.


Authors' affiliations

C Shoko, Department of Mathematical Statistics and Actuarial Sciences, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa; Department of Mathematics and Computer Sciences, Faculty of Agriculture and Natural Sciences, Great Zimbabwe University, Zimbabwe

D Chikobvu, Department of Mathematical Statistics and Actuarial Sciences, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa

P O Bessong, HIV/AIDS and Global Health Research Programme, Department of Microbiology, University of Venda, Thohoyandou, South Africa

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Virological failure; Viral rebound; Tuberculosis; Non-homogeneous Markov model; Combination antiretroviral therapy; cART

Cite this article

South African Medical Journal 2020;110(4):313-319. DOI:10.7196/SAMJ.2020.v110i4.13934

Article History

Date submitted: 2020-03-30
Date published: 2020-03-30

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