Abstract
TB remains one of the leading causes of mortality among HIV-infected individuals. Existing
models frequently fail to capture the complex dynamic relationship between TB and
HIV, making it challenging to implement targeted public health policies and allocate resources
efficiently. In this work, we explore the complex interactions between TB and HIV
co-infection using topological data analysis (TDA), machine learning (ML) and mathematical
modelling. ART status at initiation of TB treatment was used as the target variable.
Variables included as predictors were demographics, clinical, microbiologic, diagnostic,
and treatment characteristics. TDA revealed distinct clusters separating ART and non-ART
patients and a history of TB infection. The Mapper graph information is an additional
feature for machine learning models. TB history added an extra layer to the network.
CD4 count, gender, TB case status, and time between initiating TB treatment and being
down-referred were identified as key predictors of ART initiation. The results show
that integrating TDA Mapper features significantly enhanced the performance of machine
learning models on the TB-HIV co-infection. The mathematical model development was
derived from the features extracted from the TDA results. The model consists of six compartments,
and a system of non-linear ordinary differential equations was formulated and
solved. The control reproduction number (Rc) was calculated using the next-generation
matrix approach. The Global stability of the equilibrium point was determined using the
Lyapunov function. Numerical simulation results showed that effective epidemic control
depends on simultaneous increases of TB and HIV treatment, reduction of transmission
rates, and reduction of the induced mortality rate among treated populations.