Uninfected Target Cells Research Articles

Mathematical analysis of in-host Ebola virus infection dynamics model with sensitivity analysis

Ebola virus (EBOV) causes a haemorrhagic and lethal Ebola disease disastrous to human beings, which is transmitted by contact of body fluids of infected animals and humans. Presently, there are no therapies for the disease. In this paper, a mathematical model is proposed to investigate the in-vivo dynamics of EBOV infection with sensitivity analysis. A system of five non-linear ordinary differential equations constitutes the model, from which the basic reproduction number, R0 is calculated using the next generation matrix method. The parameter R0 is employed to analyze global stability of disease-free and endemic equilibria. Using the Metzler matrix operator, the results indicate that the disease-free equilibrium point is globally asymptotically stable provided that R0 < 1, which implies that the disease disappears from the host after some period of time. With Lyapunov Stability Theory and LaSalle Invariant Principle, the results indicate that the endemic equilibrium point is globally asymptotically stable provided that R0 > 1, which implies that the disease persists in the host. Sensitivity analysis of the basic reproduction number pertaining to the model parameters is achieved using forward normalized sensitivity index method. The results indicate that the parameters for infection rate, production rate of uninfected target cells and virus replication rate are positively sensitive. On the other hand, the parameters for natural death rate of target cells and natural death rate of the virus are negatively sensitive, implying that the basic reproduction number decreases as the parameters increase and vice versa. Besides, it is shown that the parameter for the infection rate is the most sensitive one while the parameter for the virus reproduction rate is the least sensitive one. Numerical simulations are used to validate the analytical results. The results suggest implementation of deliberate control measures to eradicate EBOV disease by considering sites in the model to which the most sensitive parameters are affiliated.

HIV-1 virological synapse formation enhances infection spread by dysregulating Aurora Kinase B.

HIV-1 spreads efficiently through direct cell-to-cell transmission at virological synapses (VSs) formed by interactions between HIV-1 envelope proteins (Env) on the surface of infected cells and CD4 receptors on uninfected target cells. Env-CD4 interactions bring the infected and uninfected cellular membranes into close proximity and induce transport of viral and cellular factors to the VS for efficient virion assembly and HIV-1 transmission. Using novel, cell-specific stable isotope labeling and quantitative mass spectrometric proteomics, we identified extensive changes in the levels and phosphorylation states of proteins in HIV-1 infected producer cells upon mixing with CD4+ target cells under conditions inducing VS formation. These coculture-induced alterations involved multiple cellular pathways including transcription, TCR signaling and, unexpectedly, cell cycle regulation, and were dominated by Env-dependent responses. We confirmed the proteomic results using inhibitors targeting regulatory kinases and phosphatases in selected pathways identified by our proteomic analysis. Strikingly, inhibiting the key mitotic regulator Aurora kinase B (AURKB) in HIV-1 infected cells significantly increased HIV activity in cell-to-cell fusion and transmission but had little effect on cell-free infection. Consistent with this, we found that AURKB regulates the fusogenic activity of HIV-1 Env. In the Jurkat T cell line and primary T cells, HIV-1 Env:CD4 interaction also dramatically induced cell cycle-independent AURKB relocalization to the centromere, and this signaling required the long (150 aa) cytoplasmic C-terminal domain (CTD) of Env. These results imply that cytoplasmic/plasma membrane AURKB restricts HIV-1 envelope fusion, and that this restriction is overcome by Env CTD-induced AURKB relocalization. Taken together, our data reveal a new signaling pathway regulating HIV-1 cell-to-cell transmission and potential new avenues for therapeutic intervention through targeting the Env CTD and AURKB activity.

A simple transwell-based infection system for obtaining pure populations of VZV-infected cells

Varicella-Zoster virus (VZV) is a human herpesvirus and causes chickenpox and shingles. Research into its molecular virology has been hampered by a lack of methods for generation of high-titre, cell-free infectious virus preparations. VZV propagation and infection in vitro are therefore commonly achieved by co-culture of uninfected ‘target’ cells with infected ‘inoculum’ cells. A major drawback of this approach is that it results in mixed cell populations after infection. To overcome this limitation we developed a transwell-based VZV infection system. Infected inoculum cells and uninfected target cells are spatially separated by a transwell membrane. While cell-cell contact and VZV spread can occur through membrane pores, the two cell populations do not mix. This simple protocol requires no special instrumentation or reagents. We successfully used this system for infection of a range of target cells and obtained pure populations for downstream analyses such as flow cytometry and RT-qPCR. In sum, we developed a broadly applicable approach to study the molecular and cellular biology as well as host-pathogen interactions of VZV.

HSV1716 Infects Multiple Myeloma Cells and Leads to CD138 Downregulation

Multiple myeloma (MM) is a plasma cell malignancy that accounts for approximately 10% of all hematological cancers. MM is classified as incurable due to a high relapse rate after the initial therapy and failure to achieve long-term minimal residual disease (MRD). Therefore, new therapies and combinations are needed. Oncolytic viruses (OVs) are genetically modified viruses that preferentially infect and lyse malignantly transformed cells. HSV1716 is a replication-restricted herpes-simplex virus type I (HSV-1)-based OV (HSV-OV) which has been evaluated in several clinical trials. HSV-OVs have been shown to infect and kill MM cell lines and primary malignant plasma cells. Furthermore, HSV-OV mediated target cell killing was demonstrated to be enhanced by natural killer (NK) cells, an immune cell subset that naturally recognizes malignantly transformed or virally infected cells. The underlying mechanisms behind HSV-OV-enhanced NK-tumor cell killing, however, have not yet been elucidated. Here, we aim to monitor phenotypic changes of MM cells upon HSV1716 infection and thus explore the basis for NK cell recognition of HSV-OV infected target MM cells. The MM cell lines RPMI8226 and MM1S were infected with HSV1716 at various multiplicities of infection (MOIs) over a three-day timecourse. Target cell death and expression of viral glycoproteins were measured at different timepoints by flow cytometry. HSV1716 caused oncolysis of 60% of RPMI8226, and 70% of MM1S cells 48h post-infection (p.i.) at an MOI of 0.5. Under these conditions, the expression of viral glycoprotein E on live cells reached 74% on RPMI8226 cells and 37% on MM1S cells. Primary NK (pNK) cells were isolated from healthy donor peripheral blood mononuclear cells (PBMCs) and co-cultured with infected and uninfected MM cells for 4 hours. CD107a as a marker for NK cell degranulation, as well as the release of IFNγ and TNF were measured on CD3-CD56+ pNK cells by flow cytometry. CD107a expression increased from 15.6% (+/- 0.9%) to 56.2% (+/- 2.4%) following infection of RPMI8226 cells and from 15.6% (+/- 3.4%) to 59.2% (+/- 4.5%) following infection of MM1S cells. Similarly, the expression of IFNγ and TNF increased by four- and three-fold, respectively, as compared to uninfected target cells. To monitor changes in the expression of NK cell ligands on infected MM cells, a 16-color flow cytometry panel was designed. RPMI8226 and MM1S cells were infected at different MOIs, and ligand expression was analyzed at 24h, 48h, and 72h p.i.. Most significantly, an early and progressive downregulation of CD138 expression from 96% on uninfected cells to 79 % (24h MOI 0.5), 70% (48h MOI 0.5), and 22% (72h MOI 0.5) on live RPMI8226 cells and from 99% on uninfected cells to 82% (24h MOI 0.5), 65% (48h MOI 0.5) and 23% (72h MOI 0.5) on live MM1S cells was observed. Of note, the expression of CD38 remained stable at each of these timepoints. While downregulation of HLA class I molecules was observed, the expression of other NK cells ligands on RPMI8226 or MM1S cells did not notably differ between infected and uninfected cells. Together, our data confirm that HSV-OV enhances NK cell-mediated killing of MM cells. While expression of ligands for activating NK cell receptors was not altered on infected versus uninfected RPMI8226 and MM1S cells, a strong downregulation of CD138 with maintained CD38 expression was observed upon HSV1716 infection. The implementation of oncolytic virotherapy as an immunotherapeutic platform for cancer treatment adds a new and promising therapeutic tool for combination therapies to the treatment options of MM.

An exploration of how broadly neutralizing antibodies might induce HIV remission: the 'vaccinal' effect.

Broadly neutralizing antibodies (bNAbs) are a potential new therapeutic strategy to treat HIV infection. This review explores possible mechanisms of action of bNAbs and summarizes the current evidence supporting their immunomodulatory properties, which might lead to sustained virological remission - the 'vaccinal effect'. Antiretroviral therapy (ART) is required to confer lasting HIV suppression; stopping ART almost invariably leads to HIV recrudescence from a persistent pool of virally infected cells - the HIV reservoir. HIV-specific broadly neutralizing antibodies (bNAbs) may confer viral control after ART cessation predominantly through blockade of viral entry into uninfected target cells. In some human and animal studies, HIV bNAbs also conferred lasting viral suppression after therapeutic bNAb plasma levels had declined. Immune-modulatory mechanisms have been postulated to underlie this observation - the 'vaccinal effect'. Hypothesized mechanisms include the formation of immune complexes between bNAbs and HIV envelope protein, thereby enhancing antigen presentation and uptake by immune cells, with boosted adaptive immune responses subsequently controlling the HIV reservoir. There is emerging evidence for potent antiviral efficacy of bNAb therapy. Whether bNAbs can induce sustained viral suppression after dropping below therapeutic levels remains controversial. Mechanistic data from on-going and future clinical trials will help answer these questions.

Mathematical modeling of SARS-CoV-2 viral dynamics and treatment with monoclonal antibodies

The novel coronavirus (SARS-CoV-2) affects primarily the respiratory tract, and if left unchecked can cause a spectrum of pathological manifestations such as pneumonia, acute respiratory distress syndrome, myocardial injury, thromboembolism, and acute kidney injury. Medication strategies have involved minimizing the spread of the virus through antiviral medications (monoclonal antibodies or nucleotide reverse transcriptase inhibitors). Here, we develop a mathematical model that simulates viral dynamics in an untreated individual, and the evaluate the impact that a monoclonal antibody can have on slowing viral replication. Drug pharmacokinetics (PK) was informed by a typical two-compartment PK model with parameters typical of a monoclonal antibody, with a third compartment for the lung included as the drug site of action. The viral dynamics were captured using a simplified model describing uninfected target cells, infected target cells, and viral load in the body. The mechanism of action of the simulated antiviral is based on binding to the virus, thereby preventing it from infecting healthy cells. The model is used to project dosages needed to prevent severe disease under a variety of simulated conditions and subject to realistic constraints. The proposed model can capture a variety of scenarios of longitudinal viral dynamics and assess the impact of antiviral therapy on disease severity and duration. The described approach can be easily adapted to rapidly assess the dosages needed to affect duration and outcome of other viral infections and can serve as part of a fast and efficient scientific and modeling response strategy in the future as needed

Viral infection dynamics with mitosis, intracellular delays and immune response.

In this paper, we propose a delayed viral infection model with mitosis of uninfected target cells, two infection modes (virus-to-cell transmission and cell-to-cell transmission), and immune response. The model involves intracellular delays during the processes of viral infection, viral production, and CTLs recruitment. We verify that the threshold dynamics are determined by the basic reproduction number $ R_0 $ for infection and the basic reproduction number $ R_{IM} $ for immune response. The model dynamics become very rich when $ R_{IM} > 1 $. In this case, we use the CTLs recruitment delay $ \tau_3 $ as the bifurcation parameter to obtain stability switches on the positive equilibrium and global Hopf bifurcation diagrams for the model system. This allows us to show that $ \tau_3 $ can lead to multiple stability switches, the coexistence of multiple stable periodic solutions, and even chaos. A brief simulation of two-parameter bifurcation analysis indicates that both the CTLs recruitment delay $ \tau_3 $ and the mitosis rate $ r $ have a strong impact on the viral dynamics, but they do behave differently.

A new high-content screening assay of the entire hepatitis B virus life cycle identifies novel antivirals

Background & AimsChronic hepatitis B is an incurable disease. Addressing the unmet medical need for therapies has been hampered by a lack of suitable cell culture models to investigate the HBV life cycle in a single experimental setup. We sought to develop a platform suitable to investigate all aspects of the entire HBV life cycle. MethodsHepG2-NTCPsec+ cells were inoculated with HBV. Supernatants of infected cells were transferred to naïve cells. Inhibition of infection was determined in primary and secondary infected cells by high-content imaging of viral and cellular factors. Novel antivirals were triaged in cells infected with cell culture- or patient-derived HBV and in stably virus replicating cells. HBV internalisation and target-based receptor binding assays were conducted. ResultsWe developed an HBV platform, screened 2,102 drugs and bioactives, and identified 3 early and 38 late novel HBV life cycle inhibitors using infectious HBV genotype D. Two early inhibitors, pranlukast (EC50 4.3 μM; 50% cytotoxic concentration [CC50] >50 μM) and cytochalasin D (EC50 0.07 μM; CC50 >50 μM), and 2 late inhibitors, fludarabine (EC50 0.1 μM; CC50 13.4 μM) and dexmedetomidine (EC50 6.2 μM; CC50 >50 μM), were further investigated. Pranlukast inhibited HBV preS1 binding, whereas cytochalasin D prevented the internalisation of HBV. Fludarabine inhibited the secretion of HBV progeny DNA, whereas dexmedetomidine interfered with the infectivity of HBV progeny. Patient-derived HBV genotype C was efficiently inhibited by fludarabine (EC50 0.08 μM) and dexmedetomidine (EC50 8.7 μM). ConclusionsThe newly developed high-content assay is suitable to screen large-scale drug libraries, enables monitoring of the entire HBV life cycle, and discriminates between inhibition of early and late viral life cycle events. Lay summaryHBV infection is an incurable, chronic disease with few available treatments. Addressing this unmet medical need has been hampered by a lack of suitable cell culture models to study the entire viral life cycle in a single experimental setup. We developed an image-based approach suitable to screen large numbers of drugs, using a cell line that can be infected by HBV and produces large amounts of virus particles. By transferring viral supernatants from these infected cells to uninfected target cells, we could monitor the entire viral life cycle. We used this system to screen drug libraries and identified novel anti-HBV inhibitors that potently inhibit HBV in various phases of its life cycle. This assay will be an important new tool to study the HBV life cycle and accelerate the development of novel therapeutic strategies.

Cell-to-Cell Transmission of Turkey Herpesvirus in Chicken Embryo Cells via Tunneling Nanotubes.

Marek's disease virus (MDV) is an oncogenic alphaherpesvirus that causes immunosuppression, T cell lymphomas, and neuropathic disease in infected chickens. To protect chickens from MDV infection, an avirulent live vaccine of turkey herpesvirus (HVT) has been successfully used in chickens worldwide. Many vaccine manufacturers have used chicken embryo fibroblast (CEF) cells to produce the HVT vaccine. Generally, it has been suggested that HVT is a highly cell-associated herpesvirus that spread via cell-to-cell contact, but it is unclear how HVT is transmitted from infected cells to uninfected target cells. Here, we show via immunofluorescence analysis that nanotubes containing the actin cytoskeleton and HVT antigens from infected CEF cells were observed to contact neighboring cells. When the infected cells were treated with inhibitors for actin polymerization or depolymerization, the formation and extension of the nanotubes from infected cells were greatly inhibited and the intercellular contact was abolished, leading to a drastic reduction in plaque formation and viral titers of the cell-associated virus. Our data indicate that cell-to-cell contacts via nanotubes composed of actin filaments are essential for efficient viral spreading and replication. This finding might contribute to the further improvement of efficient HVT vaccine production.

Threshold dynamics of a general delayed within-host viral infection model with humoral immunity and two modes of virus transmission

In this paper, a general viral infection model with humoral immunity is investigated. The model describes the interaction of uninfected target cells, infected cells, free viruses and humoral immune response, incorporating two virus transmission modes and intracellular delay. Some reasonable hypothesises are made for the general incidence rates. Through stability analysis of equilibria under these hypothesises, the model exhibits threshold dynamics with respect to the immune-inactivated reproduction rate \begin{document}$ \mathfrak{R}_0 $\end{document} and the immune-activated reproduction rate \begin{document}$ \mathfrak{R}_1 $\end{document} . The theoretical results and corresponding numerical simulations show that the intracellular latency, both of virus-to-cell infection and cell-to-cell infection have direct effects on the global dynamics of the general viral infection model. Our results improve and generalize some known results on within-host virus dynamics.

Revealing uninfected and infected target cell dynamics from peripheral blood data in highly and less pathogenic simian/human immunodeficiency virus infected Rhesus macaque

Since chimeric simian and human immunodeficiency viruses (SHIVs) used here, that is, SHIV-#64 and -KS661 utilize both CCR5 and CXCR4 chemokine receptors, they have broad target cell properties. A highly pathogenic SHIV strain, SHIV-KS661, causes an infection that systemically depletes the CD4+ T cells of Rhesus macaques, while a less pathogenic strain, SHIV-#64, does not cause severe symptoms in the macaques. In our previous studies, we established in vitro quantification system for virus infection dynamics, and concluded that SHIV-KS661 effectively produces infectious virions compared with SHIV-#64 in the HSC-F cell culture. However, in vivo dynamics of SHIV infection have not been well understood. To quantify SHIV-#64 and -KS661 infection dynamics in Rhesus macaques, we developed a novel approach and analyzed total CD4+ T cells and viral load in peripheral blood, and reproduced the expected dynamics for the uninfected and infected CD4+ T cells in silico. Using our previous cell culture experimental datasets, we revealed that an infection rate constant is different between SHIV-#64 and -KS661, but the viral production rate and the death rate are similar for the both strains. Thus, here, we assumed these relations in our in vivo data and carried out the data fitting. We performed Bayesian estimation for the whole dataset using MCMC sampling, and simultaneously fitted our novel model to total CD4+ T cells and viral load of SHIV-#64 and -KS661 infection. Our analyses explained that the Malthusian parameter (i.e., fitness of virus infection) and the basic reproduction number (i.e., potential of virus infection) for SHIV-KS661 are significantly higher than those of SHIV-#64. In addition, we demonstrated that the number of uninfected CD4+ T cells in SHIV-KS661 infected Rhesus macaques decreases to the significantly lower value than that before the inoculation several days earlier compared with SHIV-#64 infection. Taken together, the differences between SHIV-#64 and -KS661 infection before the peak viral load might determine the subsequent destiny, that is, whether the systemic CD4+ T cell depletion occurs or the host immune response develop.

Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays

This paper deals with the study of an HIV dynamics model with two target cells, macrophages and CD4 + T cells and three categories of infected cells, short-lived, long-lived and latent in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). The model is incorporated with distributed time delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The effect of antibody on HIV infection is analyzed. The production and removal rates of the ten compartments of the model are given by general nonlinear functions which satisfy reasonable conditions. Nonnegativity and ultimately boundedness of the solutions are proven. Using the Lyapunov method, the global stability of the equilibria of the model is proven. Numerical simulations of the system are provided to confirm the theoretical results. We have shown that the antibodies can play a significant role in controlling the HIV infection, but it cannot clear the HIV particles from the plasma. Moreover, we have demonstrated that the intracellular time delay plays a similar role as the Highly Active Antiretroviral Therapies (HAAT) drugs in eliminating the HIV particles.

Stability of delayed HIV dynamics models with two latent reservoirs and immune impairment

The purpose of this paper is to investigate the qualitative behavior of HIV dynamics models with immune impairment. The HIV particles infect both CD4+ T cells and macrophages. Both latently and actively infected cells are incorporated into the models. The models consider multiple discrete or distributed delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The existence and global stability of the steady states are determined by the basic reproduction number. The global stability analysis of the steady states is performed using Lyapunov method. We solve the system of delay differential equations numerically to support the theoretical results.

Dynamics of two time delays differential equation model to HIV latent infection

In this paper, we studied a HIV latent infection model with two time delays, where one delay is the time between viral entry into a cell and establishment of HIV latency and the other delay is the time between cell infection and viral production. The infection usually considered is linear, but in this article we consider that the infection rate of modeling HIV infection is nonlinear, where the rate of infection is βTV1+bV, and logistic growth of the uninfected target cells T. We defined the basic reproductive number and showed the local and global stability of the disease-free equilibrium and the permanence of the infected equilibrium. Furthermore, we discussed the dynamics of system under the three conditions: (1) τ1=τ2=0, (2) τ1=0,τ2>0, (3) τ1>0,τ2∈[0,τ2∗).

Global dynamics of delayed CHIKV infection model with multitarget cells

We propose a latent chikungunya viral infection model with multitarget cells and saturated incidence rate. The model is an $$(3n+2)$$ -dimensional system of nonlinear delay differential equations (DDEs) that describes the population dynamics of CHIKV, n categories of uninfected target cells, n categories of infected cells and antibodies. The model is incorporated by intracellular discrete or distributed time delays. The qualitative behavior of the model is studied. We investigate the global stability of the equilibria of the models by using direct Lyapunov method. The effect of the time delay on the stability of the equilibria has also been illustrated by numerical simulations.

Variable Effect of HIV Superinfection on Clinical Status: Insights From Mathematical Modeling.

HIV superinfection (infection of an HIV positive individual with another strain of the virus) has been shown to result in a deterioration of clinical status in multiple case studies. However, superinfection with no (or positive) clinical outcome might easily go unnoticed, and the typical effect of superinfection is unknown. We analyzed mathematical models of HIV dynamics to assess the effect of superinfection under various assumptions. We extended the basic model of virus dynamics to explore systematically a set of model variants incorporating various details of HIV infection (homeostatic target cell dynamics, bystander killing, interference competition between viral clones, multiple target cell types, virus-induced activation of target cells). In each model, we identified the conditions for superinfection, and investigated whether and how successful invasion by a second viral strain affects the level of uninfected target cells. In the basic model, and in some of its extensions, the criteria for invasion necessarily entail a decrease in the equilibrium abundance of uninfected target cells. However, we identified three novel scenarios where superinfection can substantially increase the uninfected cell count: (i) if the rate of new infections saturates at high infectious titers (due to interference competition or cell-autonomous innate immunity); or when the invading strain is more efficient at infecting activated target cells, but less efficient at (ii) activating quiescent cells or (iii) inducing bystander killing of these cells. In addition, multiple target cell types also allow for modest increases in the total target cell count. We thus conclude that the effect of HIV superinfection on clinical status might be variable, complicated by factors that are independent of the invasion fitness of the second viral strain.

Dynamical analysis of a delayed reaction-diffusion virus infection model with logistic growth and humoral immune impairment

In this paper, the dynamical analysis of a delayed reaction-diffusion virus infection model with logistic growth and chemotaxis for the uninfected target cells and humoral immune impairment is studied. By analyzing corresponding characteristic equations, the local stability of the infection-free equilibrium is established. The stability properties and Turing instability of the antibody-free equilibrium and antibody-present infection equilibrium have been extensively discussed. The existence of Hopf bifurcation with antibody response delay as a bifurcation parameter at the antibody-present infection equilibrium is established. The numerical simulations are carried out in order to illustrate the dynamical behavior of the model.

Impacts of the Cell-Free and Cell-to-Cell Infection Modes on Viral Dynamics

Virus can disseminate between uninfected target cells via two modes, namely, the diffusion-limited cell-free viral spread and the direct cell-to-cell transfer using virological synapses. To examine how these two viral infection modes impact the viral dynamics, in this paper, we propose and analyze a general viral infection model that incorporates these two viral infection modes. The model also includes nonlinear target-cell dynamics, infinitely distributed intracellular delays, nonlinear incidences, and concentration-dependent clearance rates. It is shown that the numbers of secondly infected cells through the cell-free infection mode and the cell-to-cell infection mode both contribute to the basic reproduction number. Under some reasonable assumptions, the model exhibits a global threshold dynamics: the infection is cleared out if the basic reproduction number is less than one and the infection persists if the basic reproduction number is larger than one. Two specific examples are provided to illustrate that our theoretical results cover and improve some existing ones. When the underlying assumptions are not satisfied, oscillations via global Hopf bifurcation can be observed. A brief simulation of two-parameter bifurcation analysis is given to explore the joint impacts on viral dynamics for the interplay between nonlinear target-cell dynamics and intracellular delays.

GLOBAL STABILITY OF A GENERAL VIRUS DYNAMICS MODEL WITH MULTI-STAGED INFECTED PROGRESSION AND HUMORAL IMMUNITY

In this paper, we propose an [Formula: see text]-dimensional nonlinear virus dynamics model that describes the interactions of the virus, uninfected target cells, [Formula: see text]-stages of infected cells and B cells. We assume that the incidence rate of infection, the generation and removal rates of all compartments are given by general nonlinear functions. We derive two threshold parameters, the basic reproduction number, [Formula: see text] and the humoral immunity number, [Formula: see text] and establish 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 steady states of the model is proved. Numerical simulations are conducted for specific forms of the general functions in order to illustrate the dynamical behavior.

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 interactions 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 global 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.