Open AccessViral dynamics of a latent HIV infection model with Beddington-DeAngelis incidence function, B-cell immune response and multiple delays
Author(s) -
Yan Wang,
Minmin Lu,
Daqing Jiang
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021014
Subject(s) - basic reproduction number , immune system , hopf bifurcation , lyapunov function , stability (learning theory) , stability theory , latency (audio) , mathematics , control theory (sociology) , exponential stability , dynamics (music) , function (biology) , bifurcation , immunology , biology , computer science , physics , microbiology and biotechnology , nonlinear system , medicine , telecommunications , population , environmental health , control (management) , quantum mechanics , machine learning , artificial intelligence , acoustics
In this paper, an HIV infection model with latent infection, Beddington-DeAngelis infection function, B-cell immune response and four time delays is formulated. The well-posedness of the model solution is rigorously derived, and the basic reproduction number $\mathcal{R}_0$ and the B-cell immune response reproduction number $\mathcal{R}_1$ are also obtained. By analyzing the modulus of the characteristic equation and constructing suitable Lyapunov functions, we establish the global asymptotic stability of the uninfected and the B-cell-inactivated equilibria for the four time delays, respectively. Hopf bifurcation occurs at the B-cell-activated equilibrium when the model includes the immune delay, and the B-cell-activated equilibrium is globally asymptotically stable if the model does not include it. Numerical simulations indicate that the increase of the latency delay, the cell infection delay and the virus maturation delay can cause the B-cell-activated equilibrium stabilize, while the increase of the immune delay can cause it destabilize.