Effect of humoral immunity on HIV-1 dynamics with virus-to-target and infected-to-target infections

Abstract

We consider an HIV-1 dynamics model by incorporating (i) two routes of infection via, respectively, binding of a virus to a receptor on the surface of a target cell to start genetic reactions (virus-to-target infection), and the direct transmission from infected cells to uninfected cells through the concept of virological synapse in vivo (infected-to-target infection); (ii) two types of distributed-time delays to describe the time between the virus or infected cell contacts an uninfected CD4+ T cell and the emission of new active viruses; (iii) humoral immune response, where the HIV-1 particles are attacked by the antibodies that are produced from the B lymphocytes. The existence and stability of all steady states are completely established by two bifurcation parameters, R0 (the basic reproduction number) and R1 (the viral reproduction number at the chronic-infection steady state without humoral immune response). By constructing Lyapunov functionals and using LaSalle’s invariance principle, we have proven that, if R0≤1, then the infection-free steady state is globally asymptotically stable, if R1≤1<R0, then the chronic-infection steady state without humoral immune response is globally asymptotically stable, and if R1>1, then the chronic-infection steady state with humoral immune response is globally asymptotically stable. We have performed numerical simulations to confirm our theoretical results.

Modeling the Adaptive Immunity and Both Modes of Transmission in HIV Infection

“…Our model can be adapted for HBV infection, and the above result can also explain the dysfunction of the adaptive immune response in patients infected with HBV, which is still largely incomplete [33]. Furthermore, the model and the results presented in this study improve and generalize the models and the corresponding results in more recent papers with only cellular immunity [5], with only humoral immunity [6][7][8][9], and with both arms of immunity [15,17].…”

“…In 2016, Wang et al [5] improved the model given by Equation (2) by considering the role of cellular immune response. In the same year, Elaiw et al [6] improved the model given by Equation (2) by considering only the role of humoral immune response and infinite distributed delay in virus production. In 2017, Lin et al [7] improved the models of Wang and Zou [8] and Murase et al [9] by incorporating both modes of transmission, intracellular delay and humoral immunity.…”

Stability of delayed pathogen dynamics models with latency and two routes of infection

“…However, in these works the antibody immune response was neglected. In very recent works [34,35], and [36], both pathogen-to-susceptible and infected-to-susceptible transmissions were incorporated in the pathogen dynamics models with antibody immune response. However, the latently infected cells were neglected in these models.…”

Stability of general virus dynamics models with both cellular and viral infections and delays

“…All the aforementioned works assume that the uninfected cells becomes infected because of virus contacts. Recently, it has been reported that the uninfected cells can also become infected because of direct contact with infected cells . The viral infection model with cell‐to‐cell transmission and distributed time delay has been proposed in as a nonlinear system with integral delay terms: where T ( t ), T ∗ ( t ), and V ( t ) are the concentrations (the number of cells or viruses per unit volume) of the uninfected uninfected cells, infected cells, and free virus particles at time t , respectively.…”