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According to Global Statistics, there were approximately 37,9 million people across the globe with HIV/Aids in 2018. They also state that in 2018, an estimated 1,7 million individuals worldwide became newly infected with HIV. 

In the city of Masvingo, Zimbabwe, Claris Shoko is a Statistics lecturer at the Great Zimbabwe University. In her PhD thesis at the University of the Free State (UFS) in the Department of Mathematical Statistics and Actuarial Sciences, she presented the argument that the inclusion of both the CD4 cell count and the viral-load counts in the monitoring and management of HIV+ patients on antiretroviral therapy (ART), is helping in reducing mortality rates, leading to improved life expectancy for HIV/Aids patients. 

She received her doctoral degree at the December UFS Graduation Ceremonies, with her thesis: Continuous-time Markov modelling of the effects of treatment regimens on HIV/Aids immunology and virology. 

CD4 cell count and viral-load count

Dr Shoko explains: “When the human immunodeficiency virus (HIV) enters the human body, the virus attacks the CD4 cells in their blood. This process damages CD4 cells, causing the number of white blood cells in the body to drop, making it difficult to fight infections.”

“Clinical markers such as CD4 cell count and viral-load count (number of HIV particles in a ml of blood) provide information about the progression of HIV/Aids in infected individuals. These markers fully define the immunology and the virology of HIV-infected individuals, thereby giving us a clear picture of how HIV/Aids evolve within an individual.”

Dr Shoko continues: “The development of highly active antiretroviral therapy (HAART) has helped substantially to reduce the death rate from HIV. HAART reduces viral load-count levels, blocking replication of HIV particles in the blood, resulting in an increase of CD4 cell counts and the life expectancy of individuals infected with HIV. This has made CD4 cell counts and viral-load counts the fundamental laboratory markers that are regularly used for patient management, in addition to predicting HIV/Aids disease progression or treatment outcomes.”

In the treatment of HIV/Aids, medical practitioners prescribe combination therapy to attack the virus at different stages of its life cycle, and medication to treat the opportunistic infections that may occur. “The introduction of combined antiretroviral therapy (cART) has led to the dramatic reduction in morbidity and mortality at both individual level and population level,” states Dr Shoko.

Once HIV-positive patients are put on cART, the effectiveness of treatment is monitored after the first three months and a further follow-up is done every six months thereafter. During the monitoring stages, CD4 cell count and viral load is measured. Patients are also screened for any tuberculosis (TB) co-infection and checked for any signs of drug resistance. These variables determine whether or not there is a need for treatment change. 

She continues: “Previous studies on HIV modelling could not include both CD4 cell count and viral load in one model, because of the collinearity between the two variables. In this study, the principal component approach for the treatment of collinearity between variables is used. Both variables were then included in one model, resulting in a better prediction of mortality than when only one of the variables is used.”

“Viral-load monitoring helps in checking for any possibilities of virologic failure or viral rebound, which increases the rate of mortality if not managed properly. CD4 cell count then comes in to monitor the potential development of opportunistic infections such as TB. TB is extremely fatal, but once detected and treated, the survival of HIV/Aids patients is assured,” Dr Shoko explains.

Markov model

She applied the Markov model in her study. The model, named after the Russian mathematician Andrey Markov, represents a general category of stochastic processes, characterised by six basic attributes: states, stages, actions, rewards, transitions, and constraints. 

According to Dr Shoko, Markov models assume that a patient is always in one of a finite number of discrete states, called Markov states. All events are modelled as transitions from one state to another. Each state is assigned a utility, and the contribution of this utility to the overall prognosis depends on the length of time spent in each state. For example, for a patient who is HIV positive, these states could be HIV+ (CD4 cell count above 200 cells/mm3), Aids (CD4 cell count below 200 cells/mm3) and Dead.

“Markov models are ideal for use in HIV/Aids studies, because they estimate the rate of transition between multiple-disease states while allowing for the possible reversibility of some states,” says Dr Shoko, quoting Hubbard and Zhou.

“Relatively fewer HIV modelling studies include a detailed description of the dynamics of HIV viral load count during stages of HIV disease progression. This could be due to the unavailability of data on viral load, particularly from low- and middle-income countries that have historically relied on monitoring CD4 cell counts for patients on ART because of higher costs of viral load-count testing,” Dr Shoko concludes