A model of HIV/AIDS population dynamics including ARV treatment and pre-exposure prophylaxis

Abstract

Antiretroviral treatment (ART) and oral pre-exposure prophylaxis (PrEP) have recently been used efficiently in management of HIV infection. Pre-exposure prophylaxis consists in the use of an antiretroviral medication to prevent the acquisition of HIV infection by uninfected individuals. We propose a new model for the transmission of HIV/AIDS including ART and PrEP. Our model can be used to test the effects of ART and of the uptake of PrEP in a given population, as we demonstrate through simulations. The model can also be used to estimate future projections of HIV prevalence. We prove global stability of the disease-free equilibrium. We also prove global stability of the endemic equilibrium for the most general case of the model, i.e., which allows for PrEP individuals to default. We include insightful simulations based on recently published South-African data. MSC: 92D30; 34K20

An SEIR model with infected immigrants and recovered emigrants

“…The proof by contradiction that we use towards Theorem 2.2 has been popularly used, for instance, in [ 12 ] and [ 14 ].…”

Forecasting the Effect of Pre-Exposure Prophylaxis (PrEP) on HIV Propagation with a System of Differential–Difference Equations with Delay

“…Their numerical simulations showed that the epidemic spread could be controlled thanks to vaccination, even if the basic reproduction number remains above 1. In [7,8], an explicit PrEP compartment was included in the SICA model. The parameters in [8] were adjusted with clinical data and PrEP's effectiveness mathematically proven.…”

Extinction and positive recurrence of a regime‐switching HIV/AIDS model with treatment and standard incidence

“…HIV slowly deprives the immune function and increases the risk of infection with a variety of other diseases. Despite new scientific progress and a series of public health interventions, AIDS remains one of the most devastating diseases in human history 2 . Globally, 37.9 million people were living with HIV at the end of 2018 and 770,000 people died of HIV‐related illnesses worldwide in 2018 3 .…”

“…Despite new scientific progress and a series of public health interventions, AIDS remains one of the most devastating diseases in human history. 2 Globally, 37.9 million people were living with HIV at the end of 2018 and 770,000 people died of HIV-related illnesses worldwide in 2018. 3 There is still a lack of effective drugs to eradicate HIV infection worldwide.…”