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Global properties of virus dynamics models with multitarget cells and discrete-time delays. (English) Zbl 1233.92059
Summary: We propose a class of virus dynamics models with multitarget cells and multiple intracellular delays and study their global properties. The first model is a 5-dimensional system of nonlinear delay differential equations (DDEs) that describes the interaction of the virus with two classes of target cells. The second model is a $\left(2n+1\right)$-dimensional system of nonlinear DDEs that describes the dynamics of the virus, $n$ classes of uninfected target cells, and $n$ classes of infected target cells. The third model generalizes the second one by assuming that the incidence rate of infection is given by saturation functional response. Two types of discrete time delays are incorporated into these models to describe (i) the latent period between the time the target cell is contacted by the virus particle and the time the virus enters the cell, (ii) the latent period between the time the virus has penetrated into a cell and the time of the emission of infectious (mature) virus particles. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of these models. We have proven that if the basic reproduction number ${R}_{0}$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if ${R}_{0}>1$ (or if the infected steady state exists), then the infected steady state is globally asymptotically stable.
##### MSC:
 92C60 Medical epidemiology 34K20 Stability theory of functional-differential equations 34K60 Qualitative investigation and simulation of models 37N25 Dynamical systems in biology 92D30 Epidemiology