Abstract
In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium E*0, CTL-inactivated infection equilibrium E*1 and CTL-activated infection equilibrium E*2. We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters R0 and R1, if R0 ≤ 1, E*0 is globally asymptotically stable, if R1 ≤ 1 R0, E*1 is globally asymptotically stable and if R1 >1, E*2 is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at E*2 changes completely, although R1 > 1, a Hopf bifurcation at E*2 is established. In the end, we present some numerical simulations.
Highlights
Immunity can be broadly categorized into adaptive immunity and innate immunity
We have considered a virus dynamics model with a general incidence rate and three delays τ1,τ 2 and τ3
This general incidence represents a variety of possible incidence functions that could be used in virus dynamics models
Summary
Immunity can be broadly categorized into adaptive immunity and innate immunity. Adaptive immunity is mediated by clonally B-cells and T-cells are called lymphocytes, humoral and cellular immunity is characterized by specificity and memory. We introduced the standard viral infection model with CTL immune response considered by Nowak and Bangham [16] as follows: dx (t ) = s − dx (t ) − β x (t ) v (t ), dt dy (= t ) β x (t )v (t ) − δ y (t ) − py (t ) z (t ), dt dv (t ). In [10], Yuan et al have presented a model HIV-1 with an incidence rate of the form β x (t ) f (v (t )) This incidence rate considered in this paper generalized many forms of commonly used incidence rate, including simple mass action, saturation incidence rate, Beddington-DeAngelis functional response form and the Crowly-Martin functional response form introduced by Crowly-Martin (see [20]).
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