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.

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.

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.

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.