Bifurcation Analysis of a Mathematical Model of HIV/AIDS Transmission with Treatment Compartments in Rivers State

This study performs a rigorous bifurcation analysis of a mathematical model of HIV/AIDS transmission that incorporates treatment compartments, with parameterisation informed by epidemiological data from Rivers State, South South Nigeria, one of the states with the highest HIV prevalence in the country. Despite the expansion of antiretroviral therapy access under the PEPFAR and Global Fund frameworks, HIV transmission dynamics in Rivers State continue to be influenced by complex interactions among prevention behaviour, treatment coverage, and treatment adherence that require mathematical modelling to disentangle. A deterministic compartmental model partitioning the sexually active population into susceptible, acutely infected, chronically infected untreated, and treated compartments is formulated, with treatment failure and treatment interruption pathways incorporated. The basic reproduction number is derived using the next-generation matrix method, and stability analysis of the disease-free and endemic equilibria is conducted using linearisation and the Centre Manifold Theorem. Backward bifurcation analysis reveals conditions under which the disease-free equilibrium and a stable endemic equilibrium can coexist for values of the basic reproduction number below unity, a finding with significant implications for eradication feasibility. Sensitivity analysis of the basic reproduction number is conducted, and numerical simulations in MATLAB illustrate the bifurcation behaviour under varying treatment coverage and partner change rate parameters. Results highlight the critical role of treatment adherence rate in determining whether backward bifurcation occurs. Keywords: HIV/AIDS, bifurcation analysis, compartmental model, basic reproduction number, Rivers State