Global Stability and Hopf Bifurcation for a Virus Dynamics Model with General Incidence Rate and Delayed CTL Immune Response

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.

Global stability of a delayed virus dynamics model with multi-staged infected progression and humoral immunity

In this paper, we propose a nonlinear virus dynamics model that describes the interac- tions of the virus, uninfected target cells, multiple stages of infected cells and B cells and includes multiple discrete delays. We assume that the incidence rate of infection and removal rate of infected cells are given by general nonlinear functions. The model can be seen as a generalization of several humoral immunity viral infection model presented in the literature. We derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to establish the existence and global stability of the three equilibria of the model. We study the globa! asymptotic stability of the equilibria by using Lyapunov method. We perform some numerical simulations for the model with specific forms of the general functions and show that the numerical results are consistent with the theoretical results.

Numerical Study of Computer Virus Reaction Diffusion Epidemic Model

Reaction–diffusion systems are mathematical models which link to several physical phenomena.The most common is the change in space and time of the meditation of one or more materials.Reaction–diffusion modeling is a substantial role in the modeling of computer propagation like infectious diseases.We investigated the transmission dynamics of the computer virus in which connected to each other through network globally.The current study devoted to the structure-preserving analysis of the computer propagation model.This manuscript is devoted to finding the numerical investigation of the reaction–diffusion computer virus epidemic model with the help of a reliable technique.The designed technique is finite difference scheme which sustains the important physical behavior of continuous model like the positivity of the dependent variables,the stability of the equilibria.The theoretical analysis of the proposed method like the positivity of the approximation,stability,and consistency is discussed in detail.A numerical example of simulations yields the authentication of the theoretical results of the designed technique.

Global dynamics of a viral infection model with full logistic terms and antivirus treatments

In this paper, mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. Though the model is originally to study hepatitis C virus （HCV） dynamics in patients with high baseline viral loads or advanced liver disease, similar models still hold significance for other viral infection, such as hepatitis B virus （HBV） or human immunodeficiency virus （HIV） infection. By means of Volterra-type Lyapunov functions, we know that the basic reproduction number R0 is a sharp threshold para- meter for the outcomes of viral infections. If R0 ~ 1, the virus-free equilibrium is globally asymptotically stable. If R0 ~ 1, the system is uniformly persistent, the unique endemic equilibrium appears and is globally asymptotically stable under a sufficient condition. Other than that, for the global stability of the unique endemic equilibrium, another suffi- cient condition is obtained by Li-Muldowney global-stability criterion. Using numerical simulation techniques, we further find that sustained oscillations can exist and different maximum de novo hepatocyte influx rate can induce different global dynamics along with the change of overall drug effectiveness. Finally, some biological implications of our findings are given.

ELECTRON MICROSCOPIC AUTORADIOGRAPHIC STUDIES ON DYNAMICS AND LOCATION OF DNA SYNTHESIS OF DUCK PLAGUE VIRUS

Electron microscopic autoradiographic studies on the dynamics and location of DNAsynthesis by means of incorporation of ~8H-thymidine during the replication of duck plaguevirus (DPV) revealed that the duration of DNA synthesis of DPV was rather long. The repli-cation of viral DNA occurred simultaneously with the assembly procedure of nucleocapsids, thematuration and release of viruses. DNA synthesis of DPV occurred in the matrix with lowerelectron density in the nucleus. The replicated viral DNA accumulated in the viroplast With highelectron density where the assembly of nucleocapsids occurred. The viroplast with high electrondensity was not the region of viral DNA synthesis.

GLOBAL STABILITY FOR A TWO-STRAIN VIRUS INFECTION MODEL WITH INTRA-CELLULAR DELAY AND IMMUNE RESPONSE

Considering the immune response and intracellular delay, we propose a two-strain virus model and investigate dynamics of this mathematical model. The global dynamics of the model are completely determined by introducing suitable Lyapunov functionals. We show that if the basic reproduction number is less than one, then both strains die out; but when the number is greater than one, at least one of the strains become endemic depending on the parameter values. The theoretical results provide some useful information on the dynamics of the two strains virus.

Dynamical analysis for delayed virus infection models with cell-to-cell transmission and density-dependent diffusion

In this paper,certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated.For the viral model with a single strain,we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number R_(0) and structuring proper Lyapunov functional.Moreover,we found that the infection-free equilibrium is globally asymptotically stable if R_(0)<1,and the infection equilibrium is globally asymptotically stable if R_(0)>1.For the multi-strain model,we found that all viral strains coexist if the corresponding basic reproductive number R^(e)_(j)>1,while virus will extinct if R^(e)_(j)<1.As a result,we found that delay and the density-dependent diffusion does not influence the global stability of the model with cell-to-cell infection and homogeneous Neumann boundary conditions.

Cholesterol modulating the orientation of His17 in hepatitis C virus p7 (5a) viroporin--A molecular dynamic simulation study

Protein p7 of HCV is a 63 amino acid channel forming membrane protein essential for the progression ofviral infection and the sensitivity of this channel to small-molecule inhibitors renders p7 a potentialtarget for novel therapies against HCV infection. Previous biochemical experiments suggested that theHis17 of p7 is a pore-lining residue and solvated-exposed to participate in channel gating. However, arecent NMR structural identification of the p7 hexamer in dodecylphosphocholine （DPC） micellesindicated that the His17 is embedded into the protein matrix. In this work, we performed moleculardynamic simulations to bridge the controversial observations. Our results illustrated that byincorporating the cholesterol into DOPC membranes to mimic an actual membrane-like composition,the orientation of His17 in the hexameric bundles spontaneously access to the central pore region,indicating a versatile property of the p7 viroporin conformation that could be voluntarily influenced byits surrounding environments.

Dynamical behaviors of a general humoral immunity viral infection model with distributed invasion and production

A general nonlinear mathematical model for the viral infection with humoral immunity and two distributed delays is proposed and analyzed. Two bifurcation parameters, the basic reproduction number, R0 and the humoral immunity number, R1 are derived. We established a set of conditions on the general functions which are sufficient to determine the global dynamics of the model. Utilizing Lyapunov functions and LaSalle＇s invariance principle, the global asymptotic stability of all equilibria of the model is obtained. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior.

GLOBAL STABILITY IN A VIRAL INFECTION MODEL

This paper investigates the global stability of a viral infection model with lytic immune response. If the basic reproductive ratio of the virus is less than or equal to one, by the LaSalle＇s invariance principle, the disease-free steady state is globally asymptotically stable. If the basic reproductive ratio of the virus is greater than one but less than or equal to a constant, which is defined by the parameters of the model, then the immune-exhausted steady state is globally asymptotically stable. The endemic steady state is globally asymptotically stable if the inverse is valid.