Global Analysis of a generalized viral infection temporal model with cell-to-cell transmission and absorption effect under therapy

Abstract

In virus dynamics, when a cell is infected, the number of virions outside the cells is reduced by one: this phenomenon is known as absorption effect. Most mathematical in vivo models neglect this phenomenon. Virus-to-cell infection and direct cell-to-cell transmission are two fundamental modes whereby viruses can be propagated and transmitted. In this work, we propose a new virus dynamics model, which incorporates both modes and takes into account the absorption effect and treatment. First we show mathematically and biologically the well-posedness of our model preceded by the result on the existence and the uniqueness of the solutions. Also, an explicit formula for the basic reproduction number R0 of the model is determined. By analyzing the characteristic equations we establish the local stability of the uninfected equilibrium and the infected equilibrium in terms of R0. The global behavior of the model is investigated by constructing an appropriate Lyapunov functional for uninfected equilibrium and by applying a geometric approach to the study of the infected equilibrium. Numerical simulations are carried out, to confirm the obtained theoretical result in a particular case.

A generalized fractional hepatitis B virus infection modelwith both cell-to-cell and virus-to-cell transmissions

“…They sum-up their work by giving some numerical simulations to validate their theoretical results. This recent work and others [19][20][21][22][23] consider only one mode of infection virus-to-cell in their studies, but HBV may generally be spread throughout the body by two within-host routes of infection: the traditional virus-to-cell mode and the cell-to-cell mode [24][25][26][27][28][29][30]. Recently, Yaagoub and Allali [31] studied a fractional HBV model with two modes of transmission cell-to-cell and virus-to-cell and in the presence of adaptive immunity, the authors have used two saturated incidence functions.…”