Bridging the treatment gap: Modelling the impact of ART access for immigrants on HIV/AIDS transmission in Botswana

The Human Immunodeficiency virus (HIV) remains a major public health concern in Botswana, with significant strides made in treatment coverage among citizens. However, for many years, the immigrant population (which comprised about 7% of the population in 2016) was excluded from accessing antiretroviral therapy (ART), raising concerns about their role in sustaining HIV transmission. This study formulates and analyses a deterministic compartmental model that incorporates both citizens and immigrants, stratifying infected individuals by treatment and viral suppression status. The model includes key features such as ART adherence, viral suppression dynamics, and Acquired Immunodeficiency Syndrome (AIDS) progression. A core component of the model is the introduction of a policy intervention that grants ART access to immigrants, as implemented by the Botswana government in 2019. The model steady states are determined and analysed in terms of the basic reproduction number, $\left(R_0^{pre}\right)$. It is observed that the model has two unique steady states, the disease-free steady state and an endemic equilibrium point. The disease-free equilibrium point is globally asymptotically stable if $R_0^{pre}<1$, while the endemic equilibrium point is globally asymptotically stable if $R_0^{pre}>1$. Comparing pre-policy and post-policy scenarios, we find that the reproduction number is significantly higher before the policy change, indicating that excluding immigrants from treatment increases overall HIV transmission. Numerical simulations are carried out to determine the impact of the immigrant population on the incidence of HIV/AIDS dynamics. Our results suggest that extending ART access to immigrants significantly reduces the overall HIV burden and can accelerate progress towards epidemic control.