Constructing Lyapunov functionals for a delayed viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate

Abstract

For a viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate and distributed delays, we analyze the global asymptotic behavior of its solutions. In this model, the rate of contact between viruses and uninfected target cells and state-dependent removal rate of infected cells depend on general nonlinear functions. The basic reproduction number for the model is discussed. Under certain assumptions, it is shown that if 0 ≤ 1, then the infection-free equilibrium P 0 is globally stable and the viruses are cleared; If 0 > 1, then there is a unique infection equilibrium, which is globally stable implying the infection becomes chronic. The global stability results are achieved by appealing to the direct Lyapunov method.

Global stability of delayed virus infection model including multi-target cells and B-cell impairment

“…A fraction (1 − χ i ) of infected target cells is assumed to be latent infected cells and the remaining χ i becomes active infected cells, where 0 < χ i < 1. Mathematicians have modified multi-target cells models and discussed them in several works (see, e.g., [44,45,47]). We motivated and inspired by the previous works to introduce our virus dynamics model including: (i) multi-target cells, (ii) latent stage of infection, (iii) multiple time delays, (iv) B-cell impairment.…”

Global properties of an age-structured virus model with saturated antibody immune response, multi-target cells and general incidence rate

“…In recent times, several mathematical models have been proposed in order to try to understand the mechanism of virus infections. These models often describe the changes through time in the concentration of infected and uninfected target cells and viral particles in the blood of an infected individual [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Modelling the effect of antibody immune response in the neutralization of virus is a very important topic for research since it can provide useful insights into the dynamics of the infection and offer suggestions for clinical treatment.…”

“…Therefore, we need to incorporate in our virus dynamic models a multi-group component to study virus infection in different populations of cells. Viral infection models dealing with the interaction of virus with more than one class of target cells have been studied in [7][8][9][10][11][12][13] and references cited therein.…”

“…However, there is certain debate that this rate is insufficient to realistically describe the infection process. Some authors have incorporated in their models several types of non-linear incidence functions, including saturated Holling type II incidence βT V /(1 + αV ) [3,5,15], Beddington-DeAngelis functional response βT V /(1 + aT + bV ) [6,7], or even more general functions, e.g., of the forms c(T )f (V ) [16] or h(T, V ) [4,8,9].…”