6,473 research outputs found

    Global dynamics of cell mediated immunity in viral infection models with distributed delays

    Get PDF
    In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in \textit{vivo}. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection R0R_{0} and for CTL response R1R_{1} such that R1<R0R_{1}<R_{0}. It is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of Lyapunov functional. More specifically, the uninfected equilibrium is globally asymptotically stable if R01R_{0}\leq1, an infected equilibrium without immune response is globally asymptotically stable if R11<R0R_{1}\leq1<R_{0} and an infected equilibrium with immune response is globally asymptotically stable if R1>1R_{1}>1. The immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if R1>1R_{1}>1.Comment: 16 pages, accepted by Journal of Mathematical Analysis and Application

    A stochastic model for internal HIV dynamics

    Get PDF
    In this paper we analyse a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. We also carry out analysis on the asymptotic behaviour of the model. We approximate one of the variables by a mean reverting process and nd out the mean and variance of this process. Numerical simulations conclude the paper

    Impact of delay on HIV-1 dynamics of fighting a virus with another virus

    Full text link
    In this paper, we propose a mathematical model for HIV-1 infection with intracellular delay. The model examines a viral-therapy for controlling infections through recombining HIV-1 virus with a genetically modified virus. For this model, the basic reproduction number R0\mathcal{R}_0 are identified and its threshold properties are discussed. When R0<1\mathcal{R}_0 < 1, the infection-free equilibrium E0E_0 is globally asymptotically stable. When R0>1\mathcal{R}_0 > 1, E0E_0 becomes unstable and there occurs the single-infection equilibrium EsE_s, and E0E_0 and EsE_s exchange their stability at the transcritical point R0=1\mathcal{R}_0 =1. If 1<R0<R11< \mathcal{R}_0 < R_1, where R1R_1 is a positive constant explicitly depending on the model parameters, EsE_s is globally asymptotically stable, while when R0>R1\mathcal{R}_0 > R_1, EsE_s loses its stability to the double-infection equilibrium EdE_d. There exist a constant R2R_2 such that EdE_d is asymptotically stable if R1<R0<R2R_1<\mathcal R_0 < R_2, and EsE_s and EdE_d exchange their stability at the transcritical point R0=R1\mathcal{R}_0 =R_1. We use one numerical example to determine the largest range of R0\mathcal R_0 for the local stability of EdE_d and existence of Hopf bifurcation. Some simulations are performed to support the theoretical results. These results show that the delay plays an important role in determining the dynamic behaviour of the system. In the normal range of values, the delay may change the dynamic behaviour quantitatively, such as greatly reducing the amplitudes of oscillations, or even qualitatively changes the dynamical behaviour such as revoking oscillating solutions to equilibrium solutions. This suggests that the delay is a very important fact which should not be missed in HIV-1 modelling

    Novel decay dynamics revealed for virus-mediated drug activation in cytomegalovirus infection

    Get PDF
    Human cytomegalovirus (CMV) infection is a substantial cause of morbidity and mortality in immunocompromised hosts and globally is one of the most important congenital infections. The nucleoside analogue ganciclovir (GCV), which requires initial phosphorylation by the viral UL97 kinase, is the mainstay for treatment. To date, CMV decay kinetics during GCV therapy have not been extensively investigated and its clinical implications not fully appreciated. We measured CMV DNA levels in the blood of 92 solid organ transplant recipients with CMV disease over the initial 21 days of ganciclovir therapy and identified four distinct decay patterns, including a new pattern exhibiting a transient viral rebound (Hump) following initial decline. Since current viral dynamics models were unable to account for this Hump profile, we developed a novel multi-level model, which includes the intracellular role of UL97 in the continued activation of ganciclovir, that successfully described all the decline patterns observed. Fitting the data allowed us to estimate ganciclovir effectiveness in vivo (mean 92%), infected cell half-life (mean 0.7 days), and other viral dynamics parameters that determine which of the four kinetic patterns will ensue. An important clinical implication of our results is that the virological efficacy of GCV operates over a broad dose range. The model also raises the possibility that GCV can drive replication to a new lower steady state but ultimately cannot fully eradicate it. This model is likely to be generalizable to other anti-CMV nucleoside analogs that require activation by viral enzymes such as UL97 or its homologues

    The effects of distributed life cycles on the dynamics of viral infections

    Full text link
    We explore the role of cellular life cycles for viruses and host cells in an infection process. For this purpose, we derive a generalized version of the basic model of virus dynamics (Nowak, M.A., Bangham, C.R.M., 1996. Population dynamics of immune responses to persistent viruses. Science 272, 74-79) from a mesoscopic description. In its final form the model can be written as a set of Volterra integrodifferential equations. We consider the role of age-distributed delays for death times and the intracellular (eclipse) phase. These processes are implemented by means of probability distribution functions. The basic reproductive ratio R0R_0 of the infection is properly defined in terms of such distributions by using an analysis of the equilibrium states and their stability. It is concluded that the introduction of distributed delays can strongly modify both the value of R0R_0 and the predictions for the virus loads, so the effects on the infection dynamics are of major importance. We also show how the model presented here can be applied to some simple situations where direct comparison with experiments is possible. Specifically, phage-bacteria interactions are analysed. The dynamics of the eclipse phase for phages is characterized analytically, which allows us to compare the performance of three different fittings proposed before for the one-step growth curve

    Mathematical modelling of internal HIV dynamics

    Get PDF
    We study a mathematical model for the viral dynamics of HIV in an infected individual in the presence of HAART. The paper starts with a literature review and then formulates the basic mathematical model. An expression for R0, the basic reproduction number of the virus under steady state application of HAART, is derived followed by an equilibrium and stability analysis. There is always a disease-free equilibrium (DFE) which is globally asymptotically stable for R0 1 then some simulations will die out whereas others will not. Stochastic simulations suggest that if R0 > 1 those which do not die out approach a stochastic quasi-equilibrium consisting of random uctuations about the non-trivial deterministic equilibrium levels, but the amplitude of these uctuations is so small that practically the system is at the non-trivial equilibrium. A brief discussion concludes the paper

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

    Full text link
    Some viruses, such as human immunodeficiency virus, can infect several types of cell populations. The age of infection can also affect the dynamics of infected cells and production of viral particles. In this work, we study a virus model with infection-age and different types of target cells which takes into account the saturation effect in antibody immune response and a general non-linear infection rate. We construct suitable Lyapunov functionals to show that the global dynamics of the model is completely determined by two critical values: the basic reproduction number of virus and the reproductive number of antibody response
    corecore