Abstract
In this work an HIV-1 infection model with nonlinear incidence rate and distributed intracellular delays and with humoral immunity is investigated. The disease transmission function is assumed to be governed by general incidence rate f(T, V)V. The intracellular delays describe the time between viral entry into a target cell and the production of new virus particles and the time between infection of a cell and the emission of viral particle. Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected equilibrium without B cells response, and infected equilibrium with B cells response. The results obtained show that the global dynamics of the system depend on both the properties of the general incidence function and the value of certain threshold parameters R 0 and R 1 which depends on the delays.
Highlights
Immunity can be broadly categorized into adaptive immunity and innate immunity
We have studied an HIV-1 infection model with humoral immune response and intracellular distributed delays and general incidence rate
This general incidence represents a variety of possible incidence functions that could be used in virus dynamics model as well as epidemic models
Summary
Immunity can be broadly categorized into adaptive immunity and innate immunity. Adaptive immunity is mediated by clonally distributed T and B lymphocytes, namely, humoral and cellular immunity, and is characterized by specificity and memory. Many studies have been done to improve the model (1) by introducing delays and changing the incidence rate according to different practical background. In the present paper, motivated by the works of [1, 5, 13], we propose the following model with a general incidence rate and distributed delays and humoral immunity: f (T. where the parameters in system (2) have the same meanings as in system (1). F(T, V)V is the general incidence rate It is assumed in (2) that the uninfected cells that are contacted by the virus particles at time t − τ become infected cells at time t, where τ is distributed according to P1(τ) over the interval [0, h1], where h1 is the limit superior of this delay. A brief discussion is given in the last section to conclude this paper
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