Backward bifurcation on HIV/AIDS SEI₁I₂TAR model with multiple interactions between sub-populations

Abstract

The HIV/AIDS model was dynamically analyzed in this study. The model has seven compartments: the uneducated, the educated, the HIV-positive who take antiretroviral therapy (ART), the HIV-positive who do not take ART, people receiving ART treatment, people with AIDS who do not receive any treatment (full-blown AIDS), and the recovered. This model takes into account the analysis of the multiple interactions between the uneducated and the educated subpopulations, the HIV-positive who take and who do not take ART. The free-disease and endemic equilibrium points, as well as the basic reproduction number $(R_0)$ as a limit condition for infection-free and endemic occurrence, were produced by a mathematical analysis. The center-manifold hypothesis was used to prove that a backward bifurcation exists. The free-disease and endemic equilibrium points coexist when $R_0<1.$ This means that HIV/AIDS is still spreading. A basic reproduction number below one is insufficient to constitute a free-disease condition. In order to determine essential parameters that significantly contribute to HIV/AIDS transmission, we computed sensitivity index values using a sensitivity analysis. The HIV/AIDS model and bifurcation parameter both identified the rate of HIV transmission from uneducated individuals to HIV-positive individuals who do not receive ART as the most crucial parameter. A numerical simulation supports the dynamical analysis.

Keywords:

• HIV/AIDS model
• dynamical system
• multiple interactions
• backward bifurcation

Acknowledgments

The authors would like to thank Brawijaya University for giving support through Hibah Doktor 2021, No: 1629/UN10.F09/PN/2021.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Universitas Brawijaya.