Dynamic analysis of a degenerated temporal-spatial acquired immunodeficiency syndrome model with voluntary counseling and testing awareness and antiretroviral therapy treatment

Source abstract

To study the joint effects of periodic antiretroviral therapy (ART), voluntary counseling and testing (VCT) awareness, and spatial heterogeneity on the transmission of Human Immunodeficiency Virus (HIV)/Acquired Immunodeficiency Syndrome (AIDS), in this paper, we formulate a degenerated temporal-spatial HIV/AIDS model with VCT awareness and ART treatment. To overcome the difficulty in lacking compactness of the semiflow, instead of using the non-compactness measures under the framework of nonlinear semigroups, we apply the global exponential attractor theories of non-autonomous dissipative evolution equations. Firstly, we study the well-posedness of the model, and then the existence of the principal eigenvalue λ* of the corresponding linear system is discussed by the Krein–Rutman theorem. Secondly, we establish the existence of the global attractor for the system. Further, the long-term threshold dynamics of the system in terms of λ* are obtained: the disease-free steady-state is globally asymptotically stable when λ* < 0, and the system is uniformly persistent when λ* > 0. Finally, some numerical simulations indicate that increasing the VCT awareness, ART treatment rate and treatment level can play an important role in controlling the spread of HIV/AIDS.