Mathematical Modeling on the Transmission Dynamics of HIV and Hepatitis B (HBV) Co-Infection in the United States

Abstract

Human immunodeficiency virus (HIV) and hepatitis B virus (HBV) are major public health concern worldwide, contributing to significant morbidity and mortality. Managing co-infection between HIV and HBV presents additional challenges in clinical treatment and patient outcomes. In this article, we developed a comprehensive co-infection model to explore the complex transmission dynamics between HIV and HBV in the United States. Our model incorporates crucial factors such as infection through birth or migration, HBV vaccination, and the possibility of reinfection following HBV recovery. Our mathematical analysis started with the analysis of the two non-co-infection submodels, that is, for HIV-only and HBV-only models. We derived the basic reproduction number for each submodel and appliedthe Routh-Hurwitz criterion to assess the local stability of their respective disease-free equilibrium points. Our investigation revealed that the HIV-only submodel is globally asymptotically stable when its basic reproduction number remains below one. Conversely, the HBV-only submodel exhibits a backward bifurcation, meaning that both disease-free and endemic equilibrium states can coexist even when the reproduction number falls below one. This phenomenon complicates HBV control strategies under such conditions. However, in the absence of reinfection, the HBV-only model reaches global stability at the disease-free equilibrium whenever its reproduction number is below one. Using center manifold theory, we further demonstrated that the full HIV-HBV co-infection model also undergoes backward bifurcation. A sensitivity analysis was conducted on the basic reproduction numbers of HIV and HBV to identify critical parameters influencing the transmission dynamics of both infections. Our results indicate a positive correlation between the spread of one infection and the prevalence of the other. Additionally, we validated the model by fitting it to annual cumulative data on new HIV cases and reported acute HBV infections in the United States. Numerical simulations suggest that increasing condom use adherence, enhancing treatment coverage for both infections, and boosting HBV vaccination rates can substantially reduce the prevalence of HIV, HBV, and their co-infection.