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In this paper, a dynamic HIV model with cell-to-cell transmission, two immune responses, and induced apoptosis is proposed and studied. First, the non-negativity and boundedness of the solutions of the model are given, and then the exact expression of the basic reproduction number R0 is obtained by using the next generation matrix method. Second, criteria are obtained for the local stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses. Furthermore, the threshold conditions are also derived for the global asymptotic stability of the disease-free equilibrium, immune responsefree equilibrium, and the infected equilibrium with both humoral and cellular immune responses by constructing the suitable Lyapunov function. Finally, some numerical simulations are conducted to verify the theoretical results; the numerical simulation results show that the increase of apoptosis rate had a positive role in the control of viral infection. [ABSTRACT FROM AUTHOR]

In this paper, we construct a general four-dimensional delayed HIV infection model with virus-to-cell infection, cell-to-cell transmission, CTL immune response and parameter perturbations. By substitution, the four-dimensional delayed stochastic differential equations can be transformed into a degenerate eight-dimensional stochastic differential equations. The existence of the global positive solution of the system is obtained rigorously. By constructing appropriate Lyapunov functions, the existence of a stationary Markov process is derived when the stochastic reproduction number R 0 s is greater than one. Finally, we investigate the effects of noise level and the cell-to-cell transmission on the dynamic behavior of the model. Our model is a general model of the existing stochastic virus infection model, and the theoretical results improve and generalize the existing conclusion. [ABSTRACT FROM AUTHOR]

This paper develops a mathematical model to investigate the Human Immunodeficiency Virus (HIV) infection dynamics. The model includes two transmission modes (cell-to-cell and cell-free), two adaptive immune responses (cytotoxic T-lymphocyte (CTL) and antibody), a saturated CTL immune response, and latent HIV infection. The existence and local stability of equilibria are fully characterized by four reproduction numbers. Through sensitivity analyses, we assess the partial rank correlation coefficients of these reproduction numbers and identify that the infection rate via cell-to-cell transmission, the number of new viruses produced by each infected cell during its life cycle, the clearance rate of free virions, and immune parameters have the greatest impact on the reproduction numbers. Additionally, we compare the effects of immune stimulation and cell-to-cell spread on the model's dynamics. The findings highlight the significance of adaptive immune responses in increasing the population of uninfected cells and reducing the numbers of latent cells, infected cells, and viruses. Furthermore, cell-to-cell transmission is identified as a facilitator of HIV transmission. The analytical and numerical results presented in this study contribute to a better understanding of HIV dynamics and can potentially aid in improving HIV management strategies. [ABSTRACT FROM AUTHOR]

In this paper, we propose an HIV model with latent reservoir, delayed CTL immune response and immune impairment in which both virus-to-cell infection and cell-to-cell viral transmission are considered. By using Lyapunov functionals and LaSalle's invariance principle, it is verified that when time delay is equal to zero, the global threshold dynamics of the model is determined by the basic reproduction ratio. With the help of uniform persistence theory for infinite dimensional systems, we obtain the uniform persistence when the basic reproduction ratio is greater than unity. By choosing time delay as a bifurcation parameter and analyzing the corresponding characteristic equation of the system, we establish the existence of Hopf bifurcation at the chronic-infection equilibrium. Numerical simulations are carried out to illustrate the corresponding theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we proposed and studied a delayed HIV pathogenesis model with saturation incidence, both virus-tocell and cell-to-cell transmission. We address the basic reproduction number R0, the characteristic equations, and local stability of feasible equilibria are established. Where the delay incorporates both virus-to-cell and cell-to-cell transmission. Moreover, we discuss the existence of Hopf Bifurcation when a delay is used as a bifurcation parameter. Numerical simulations are performed to satisfy our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a reaction–diffusion viral infection model with nonlinear incidences, cell-to-cell transmission, and a time delay. We impose the homogeneous Neumann boundary condition. For the case where the domain is bounded, we first study the well-posedness. Then we analyze the local stability of homogeneous steady states. We establish a threshold dynamics which is completely characterized by the basic reproduction number. For the case where the domain is the whole Euclidean space, we consider the existence of traveling wave solutions by using the cross-iteration method and Schauder's fixed point theorem. Finally, we study how the speed of spread in space affects the spread of cells and viruses. We obtain the existence of the wave speed, which is dependent on the diffusion coefficient. [ABSTRACT FROM AUTHOR]

In this paper, we consider an HIV infection model with virus-to-cell infection, cell-to-cell transmission, intracellular delay and mitosis of uninfected cells. The basic reproduction number is calculated by using the method of the next generation matrix. By comparison arguments, it is proved that when the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. When the basic reproduction number is greater than unity, the existence of Hopf bifurcation and stability switch at the chronic-infection equilibrium of the model with or without intracellular delay is established. Further, by constructing Lyapunov functionals, sufficient conditions are obtained for the global asymptotic stability of the chronic-infection equilibrium when the cell-to-cell transmission is negligible. Numerical simulations are carried out to illustrate the main theoretical results. The normal form is calculated to determine the bifurcation direction and stability, as well as amplitude and period of bifurcating periodic solutions when the intracellular delay is absent. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors for multiple delayed latent virus model with virus-to-cell infection and cell-to-cell transmissions and humoral immunity are investigated. The virus-to-cell and cell-to-cell incidence rates are modeled by general nonlinear functions. The basic reproduction number R 0 and the humoral immune response number R 1 are calculated and proved to be threshold conditions determining the local and global properties of the virus model. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is presented, and the effects of some key parameters on viral dynamics are revealed by numerical simulations. [ABSTRACT FROM AUTHOR]

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 R0 and the immune-activated reproduction rate R1. 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. [ABSTRACT FROM AUTHOR]

Recent researches show that virus‐to‐cell infection and cell‐to‐cell transmission are two HIV infection modes. In this paper, we propose a delayed HIV infection model including both virus‐to‐cell infection and cell‐to‐cell transmission and cytotoxic T lymphocyte immune response. The time delay describes the phenomenon between viral entry and viral production. We show the nonnegativity and boundedness of solution, obtain the steady states, and prove local asymptotic stability of the steady states. Then the optimal control problem with antiretroviral therapy and pharmacological delay is posed. We establish and analyze two types of objective functions: one is linear control and the other is quadratic control. Numerical simulations have been performed to verify the stability of steady states and show the optimal control strategies and the effects of control on cells concentration by Matlab and Lingo. [ABSTRACT FROM AUTHOR]

Viral dynamics within plant hosts can be important for understanding plant disease prevalence and impacts. However, few mathematical modeling efforts aim to characterize within-plant viral dynamics. In this paper, we derive a simple system of delay differential equations that describes the spread of infection throughout the plant by barley and cereal yellow dwarf viruses via the cell-to-cell mechanism. By incorporating ratio-dependent incidence function and logistic growth of the healthy cells, the model can capture a wide range of biologically relevant phenomena via the disease-free, endemic, mutual extinction steady states, and a stable periodic orbit. We show that when the basic reproduction number is less than 1(R0 < 1), the disease-free steady state is asymptotically stable. When R0 > 1, the dynamics either converge to the endemic equilibrium or enter a periodic orbit. Using a ratio-dependent transformation, we show that if the infection rate is very high relative to the growth rate of healthy cells, then the system collapses to the mutual extinction steady state. Numerical and bifurcation simulations are provided to demonstrate our theoretical results. Finally, we carry out parameter estimation using experimental data to characterize the effects of varying nutrients on the dynamics of the system. Our parameter estimates suggest that varying the nutrient supply of nitrogen and phosphorous can alter the dynamics of the infection in plants, specifically reducing the rate of viral production and the rate of infection in certain cases. [ABSTRACT FROM AUTHOR]

In this paper, a delayed virus infection model with cell-to-cell transmission and CTL immune response is investigated. In the model, time delay is incorporated into the CTL response. By constructing Lyapunov functionals, global dynamical properties of the two boundary equilibria are established. Our results show that time delay in the CTL response process may lead to sustained oscillation. To further investigate the nature of the oscillation, we apply the method of multiple time scales to calculate the normal form on the center manifold of the model. At the end of the paper, numerical simulations are carried out, which support our theoretical results. [ABSTRACT FROM AUTHOR]

This paper formulates a virus dynamics model with impairment of B‐cell functions. The model incorporates two modes of viral transmission: cell‐free and cell‐to‐cell. The cell‐free and cell‐cell incidence rates are modeled by general functions. The model incorporates both, latently and actively, infected cells as well as three distributed time delays. Nonnegativity and boundedness properties of the solutions are proven to show the well‐posedness of the model. The model admits two equilibria that are determined by the basic reproduction number R0. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations. The effect of impairment of B‐cell functions and time delays on the virus dynamics are studied. We have shown that if the functions of B‐cell is impaired, then the concentration of viruses is increased in the plasma. Moreover, we have observed that increasing the time delay will suppress the viral replication. [ABSTRACT FROM AUTHOR]

HIV preferentially infects activated CD4+ T cells. Current antiretroviral therapy cannot eradicate the virus. Viral infection of other cells such as macrophages may contribute to viral persistence during antiretroviral therapy. In addition to cell-free virus infection, macrophages can also get infected when engulfing infected CD4+ T cells as innate immune sentinels. How macrophages affect the dynamics of HIV infection remains unclear. In this paper, we develop an HIV model that includes the infection of CD4+ T cells and macrophages via cell-free virus infection and cell-to-cell viral transmission. We derive the basic reproduction number and obtain the local and global stability of the steady states. Sensitivity and viral dynamics simulations show that even when the infection of CD4+ T cells is completely blocked by therapy, virus can still persist and the steady-state viral load is not sensitive to the change of treatment efficacy. Analysis of the relative contributions to viral replication shows that cell-free virus infection leads to the majority of macrophage infection. Viral transmission from infected CD4+ T cells to macrophages during engulfment accounts for a small fraction of the macrophage infection and has a negligible effect on the total viral production. These results suggest that macrophage infection can be a source contributing to HIV persistence during suppressive therapy. Improving drug efficacies in heterogeneous target cells is crucial for achieving HIV eradication in infected individuals. [ABSTRACT FROM AUTHOR]

This paper investigates the global dynamics of Chikungunya virus (CHIKV) infection model with antibody immune response. We incorporate two ways of transmissions CHIKV-to-cell and cell-to-cell. We incorporate three types of discrete time delays into the model. The first time delay is the time between CHIKV entry an uninfected monocyte to become latent infected. The second time delay is the time between CHIKV entry on uninfected monocyte and the production of immature CHIKV. The third time delay represents the CHIKV's maturation time. Nonnegativity and boundedness properties of the solutions are proven. Further, global stability of the equilibria is established by constructing Lyapunov functions and by applying applying LaSalle's invariance principle. [ABSTRACT FROM AUTHOR]

In this paper, a delayed virus model with two different transmission methods and treatments is investigated. This model is a time-delayed version of the model in (Zhang et al. in Comput. Math. Methods Med. 2015:758362, 2015). We show that the virus-free equilibrium is locally asymptotically stable if the basic reproduction number is smaller than one, and by regarding the time delay as a bifurcation parameter, the existence of local Hopf bifurcation is investigated. The results show that time delay can change the stability of the endemic equilibrium. Finally, we give some numerical simulations to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Direct cell‐to‐cell transmission of HIV‐1 is a more efficient means of virus infection than virus‐to‐cell transmission. In this paper, we incorporate both these transmissions into an HIV‐1 virus model with nonlinear general incidence rate, intracellular delay, and cytotoxic T lymphocyte (CTL) immune responses. This model admits three types of equilibria: infection‐free equilibrium, CTL‐inactivated equilibrium, and CTL‐activated equilibrium. By using Lyapunov functionals and LaSalle invariance principle, it is verified that global threshold dynamics of the model can be explicitly described by the basic reproduction numbers. [ABSTRACT FROM AUTHOR]

In this paper, we develop a diffusive and delayed hepatitis B virus (HBV) infection model, which incorporates both virus‐to‐cell and cell‐to‐cell transmissions along with cytotoxic T lymphocyte (CTL) immune response. Two threshold parameters ℜ0$$ {\mathfrak{\Re}}_0 $$ (basic reproduction number) and ℜ1$$ {\mathfrak{\Re}}_1 $$ (immune response reproduction number) are defined, which determine the dynamic behavior of the model. Employing the approach of Lyapunov functionals, we show that the infection‐free steady state is globally asymptotically stable when ℜ0≤1$$ {\mathfrak{\Re}}_0\le 1 $$; the immune‐free infected steady state is globally asymptotically stable when ℜ1≤1<ℜ0$$ {\mathfrak{\Re}}_1\le 1<{\mathfrak{\Re}}_0 $$; and the immune‐present steady state is globally asymptotically stable when ℜ0>1,ℜ1>1$$ {\mathfrak{\Re}}_0>1,{\mathfrak{\Re}}_1>1 $$, and φ(I)=I$$ \varphi (I)=I $$. We perform the sensitivity and uncertainly analysis on ℜ0$$ {\mathfrak{\Re}}_0 $$ with respect to parameters and find that the most important parameter that drives the HBV infection is the mortality of HBV DNA capsids. Moreover, the theoretical results are supported with numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we incorporate immune systems into an HIV model, which considers both logistic target-cell proliferation and viral cell-to-cell transmission. We study the dynamics of this model including the existence and stability of equilibria. Based on the existence of equilibria, we focus on the backward bifurcation and forward bifurcation. Considering the stability of equilibria, Hopf bifurcation is discussed by identifying the basic reproduction number R 0 as bifurcation parameter. The direction and stability of Hopf bifurcation are investigated by computing the first Lyapunov exponent. Specially, the effects of immune response on the basic reproduction number R 0 and viral dynamics are addressed by deriving the sensitivity analysis. As a result, we find that the removal rate of infected cells by cytotoxic T lymphocytes (CTLs), γ 1 , is the predominant factor of R 0 . However, we conclude from numerical results that it is unfeasible to decrease R 0 by increasing the value of γ 1 constantly. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions. These dynamics are investigated by the proposed model to point out the importance and complexity of immune responses in fighting HIV replication. [ABSTRACT FROM AUTHOR]

In this paper, we propose a within-host HIV-1 epidemic model with cell-to-virus and cell-to-cell transmission. By mathematical analysis, we obtain the basic reproduction number $\mathcal {R}_{0}$ , which determines the viral persistence and the basic reproduction number $\mathcal {R}_{0}^{\mathrm{cc}}$ with respect to cell-to-cell transmission which is not strong enough, i.e., it is less than 1. If the basic reproduction number is less than 1, then the viral-free steady state $E_{0}$ is globally asymptotically stable, which is proved by fluctuation lemma and comparison method; if $\mathcal {R}_{0}>1$ is greater than 1, the endemic steady state $E^{*}$ is globally asymptotically stable, which is proved by constructing the Lyapunov functional. Antiretoviral therapy is implemented to suppress the viral replication. Protease inhibitors for cell-to-cell transmission play an important role in controlling cell-to-cell infection. Under some circumstances, the effects of the cell-to-cell infection process are more sensitive than those of cell-to-virus transmission. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with an age-structured HIV infection model incorporating latency and cell-to-cell transmission. The model is a hybrid system consisting of coupled ordinary differential equations and partial differential equations. First, we address the relative compactness and persistence of the solution semi-flow, and the existence of a global attractor. Then, applying the approach of Lyapunov functionals, we establish the global stability of the infection-free equilibrium and the infection equilibrium, which is completely determined by the basic reproduction number. [ABSTRACT FROM AUTHOR]

Age structure and cell-to-cell transmission are two major infection mechanisms in modeling spread of infectious diseases. We propose an age-structured viral infection model with latency, infection age-structure and cell-to-cell transmission. This paper aims to reveal the basic reproduction number and prove it to be a sharp threshold determining whether the infection dies out or not. Mathematical analysis is presented on relative compactness of the orbit, existence of a global attractor, and uniform persistence of system. We further investigate local and global stability of the infection-free and infection equilibrium. [ABSTRACT FROM AUTHOR]

HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states. Numerical simulations have been performed to illustrate the theoretical results and evaluate the effects of time delays and fractions of infection leading to latency on the virus dynamics. The estimates of the relative contributions to the HIV latent reservoir and the virus population from the two modes of transmission have also been provided. [ABSTRACT FROM PUBLISHER]

In this paper, we designed and analysed a discrete model to solve a delayed within-host viral infection model by using non-standard finite difference scheme. The original model that we considered was a delayed viral infection model with cell-to-cell transmission, cell-mediated immune response and general nonlinear incidence. We show that the discrete model has equilibria which are exactly the same as those of the original continuous model and the conditions for those equilibria to be globally asymptotically stable are consistent with the original continuous model with no restriction on the time step size. The results imply that the discretization scheme can efficiently preserves the qualitative properties of solutions for corresponding continuous model. [ABSTRACT FROM PUBLISHER]

Hepatitis C virus (HCV) can establish infection via two distinct modes: virus-to-cell infection and cell-to-cell transmission. These infections prompt the activation of two types of adaptive immune responses: the cytotoxic T lymphocyte response and the antibody response. In this paper, we study HCV dynamics by developing a multiscale model that incorporates both modes of infection as well as the two types of immune responses. We derive both the basic reproduction number of virus and four immune reproduction numbers for the model. We identify five equilibria, the existence of which depends on the values of basic reproduction number of virus and the immune reproduction numbers. We also establish the global asymptotic stability of the equilibria by employing Lyapunov functions, which further underscores the profound impact of the aforementioned reproduction numbers on the model's overall stability. [ABSTRACT FROM AUTHOR]

The spread of prion‐like protein aggregates is a common driver of pathogenesis in various neurodegenerative diseases, including Alzheimer's disease (AD) and related Tauopathies. Tau pathologies exhibit a clear progressive spreading pattern that correlates with disease severity. Clinical observation combined with complementary experimental studies has shown that Tau preformed fibrils (PFF) are prion‐like seeds that propagate pathology by entering cells and templating misfolding and aggregation of endogenous Tau. While several cell surface receptors of Tau are known, they are not specific to the fibrillar form of Tau. Moreover, the underlying cellular mechanisms of Tau PFF spreading remain poorly understood. Here, it is shown that the lymphocyte‐activation gene 3 (Lag3) is a cell surface receptor that binds to PFF but not the monomer of Tau. Deletion of Lag3 or inhibition of Lag3 in primary cortical neurons significantly reduces the internalization of Tau PFF and subsequent Tau propagation and neuron‐to‐neuron transmission. Propagation of Tau pathology and behavioral deficits induced by injection of Tau PFF in the hippocampus and overlying cortex are attenuated in mice lacking Lag3 selectively in neurons. These results identify neuronal Lag3 as a receptor of pathologic Tau in the brain，and for AD and related Tauopathies, a therapeutic target. [ABSTRACT FROM AUTHOR]

Human herpes simplex virus (HSV), a double-stranded DNA virus belonging to the Herpesviridae family and alpha herpesvirus subfamily, is one of the most epidemic pathogens in the population. Cell-to-cell spread is a special intercellular transmission mechanism of HSV that indicates the virulence of this virus. Through numerous studies on mutant HSV strains, many viral and host proteins involved in this process have been identified; however, the mechanisms remain poorly understood. Here, we evaluated the effect of the membrane protein genes US7 and UL56 on cell-to-cell spread in vitro between two HSV-1 (HB94 and HN19) strains using a plaque assay, syncytium formation assay, and the CRISPR/Cas9 technique. US7 knockout resulted in the inhibition of viral cell-to-cell spread; additionally, glycoprotein I (US7) of the HB94 strain was found to promote cell-to-cell spread compared to that of the HN19 strain. UL56 knockout did not affect plaque size and syncytium formation; however, the gene product of UL56 from the HN19 strain inhibited plaque formation and membrane infusion. This study presents preliminary evidence of the functions of US7 and UL56 in the cell-to-cell spread of HSV-1, which will provide important clues to reveal the mechanisms of cell-to-cell spread, and contributes to the clinical drugs development. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we revisit a diffusive virus dynamics model with general incidence function and time delay. One novelty of our model is that we introduce cell-to-cell transmission via formation of virological synapses to reflect the fact that it may play a more important role in virus spreading in addition to virus-to-cell infection. We justify the well-posedness of the model and identify the basic reproduction number ℜ 0 for the model to be a sharp threshold value. The global stability of equilibria is determined by constructing suitable Lyapunov functionals in the sense that: the infection-free equilibrium is globally asymptotically stable if ℜ 0 ≤ 1 , and when ℜ 0 > 1 , the global asymptotic stability of infection equilibrium implies that the infection will persist. A significant impact of the cell-to-cell transmission is that they increase the basic reproduction number. If one neglects either the cell-to-cell transmission or virus-to-cell infection, the basic reproduction number of the model that is under-evaluated. Last, we perform numerical simulation to support our theoretic results. We set the domain of the viruses to be a two-dimensional square domain with the homogeneous Neumann boundary conditions to reflect the spatial spreading. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability analysis of a virus dynamics model with CTL immune response and with both cell-to-cell and virus-to-cell transmissions. The model contains three types of distributed time delays. The existence and global stability of all steady states of the model are determined by two parameters, the basic reproduction number (R0) and the CTL immune response activation number (R1). By using suitable Lyapunov functionals, we show that if R0 ≤ 1, then the infection-free steady state E0 is globally asymptotically stable; if R1 ≤ 1 < R0, then the CTL-inactivated infection steady state E1 is globally asymptotically stable; if R1 > 1, then the CTL-activated infection steady state E2 is globally asymptotically stable. Numerical simulations are conducted to support the theoretical results. [ABSTRACT FROM AUTHOR]

Introduction: Intercellular adhesion molecule 1 (ICAM-1) is a critical molecule responsible for interactions between cells. Previous studies have suggested that ICAM-1 triggers cell-to-cell transmission of HIV-1 or HTLV-1, that SARS-CoV-2 shares several features with these viruses via interactions between cells, and that SARS-CoV-2 cell-to-cell transmission is associated with COVID-19 severity. From these previous arguments, it is assumed that ICAM-1 can be related to SARS-CoV-2 cell-to-cell transmission in COVID-19 patients. Indeed, the time-dependent change of the ICAM-1 expression level has been detected in COVID-19 patients. However, signaling pathways that consist of ICAM-1 and other molecules interacting with ICAM-1 are not identified in COVID-19. For example, the current COVID-19 Disease Map has no entry for those pathways. Therefore, discovering unknown ICAM1-associated pathways will be indispensable for clarifying the mechanism of COVID-19. Materials and methods: This study builds ICAM1-associated pathways by gene network inference from single-cell omics data and multiple knowledge bases. First, single-cell omics data analysis extracts coexpressed genes with significant differences in expression levels with spurious correlations removed. Second, knowledge bases validate the models. Finally, mapping the models onto existing pathways identifies new ICAM1-associated pathways. Results: Comparison of the obtained pathways between different cell types and time points reproduces the known pathways and indicates the following two unknown pathways: (1) upstream pathway that includes proteins in the non-canonical NF-κB pathway and (2) downstream pathway that contains integrins and cytoskeleton or motor proteins for cell transformation. Discussion: In this way, data-driven and knowledge-based approaches are integrated into gene network inference for ICAM1-associated pathway construction. The results can contribute to repairing and completing the COVID-19 Disease Map, thereby improving our understanding of the mechanism of COVID-19. [ABSTRACT FROM AUTHOR]

In this work, we analyse the dynamics of a five-dimensional hepatitis C virus infection mathematical model including the spatial mobility of hepatitis C virus particles, the transmission of hepatitis C virus infection by mitosis process of infected hepatocytes with logistic growth, time delays, antibody response and cytotoxic T lymphocyte (CTL) immune response with general incidence functions for both modes of infection transmission, namely virus-to-cell as well as cell-to-cell. Firstly, we prove rigorously the existence, the uniqueness, the positivity and the boundedness of the solution of the initial value and boundary problem associated with the new constructed model. Secondly, we found that the basic reproductive number is the sum of the basic reproduction number determined by cell-free virus infection, determined by cell-to-cell infection and determined by proliferation of infected cells. It is proved the existence of five spatially homogeneous equilibria known as infection-free, immune-free, antibody response, CTL response and antibody and CTL responses. By using the linearization methods, the local stability of the latter is established under some rigorous conditions. Finally, we proved the existence of periodic solutions by highlighting the occurrence of a Hopf bifurcation for a certain threshold value of one delay. [ABSTRACT FROM AUTHOR]

Considering the drug treatment strategy in both virus-to-cell and cell-to-cell transmissions, this paper presents an HIV model with Filippov control. Given the threshold level $ N_t $, when the total number of infected cells is less or greater than threshold level $ N_t $, the threshold dynamics of the model are studied by using the Routh-Hurwitz Criterion. When the total number of infected cells is equal to $ N_t $, the sliding mode equations are obtained by Utkin equivalent control method, and the dynamics are studied. In addition, the optimal control strategy is introduced for the case that the number of infected cells is greater than $ N_t $. By dynamic programming, the Hamilton-Jacobi-Bellman (HJB) equation is constructed, and the optimal control is obtained. Numerical simulations are presented to illustrate the validity of our results.

Direct cell-to-cell transmission of HIV-1 is proved to be a more efficient means of virus infection than virus-to-cell transmission. In this paper, we incorporate both virus-to-cell and cell-to-cell transmissions into an HIV-1 virus model, which also contains intracellular delay and humoral immunity. By analyzing the characteristic equations, the local stability of feasible equilibria is established. By using Lyapunov functionals and LaSalle’s invariance principle, it is verified that global threshold dynamics of the model can be explicitly described by immune-inactivated reproduction rate and immune-activated reproduction rate. Numerical simulations are carried out to illustrate the corresponding theoretical results. [ABSTRACT FROM AUTHOR]

Recent studies reveal that cell-to-cell transmission via formation of virological synapses can contribute significantly to virus spread, and hence, may play a more important role than virus-to-cell infection in some situations. Age-structured models can be employed to study the variations w.r.t. infection age in modeling the death rate and virus production rate of infected cells. Considering the above characteristics for within-host dynamics of HIV, in this paper, we formulate an age-structured hybrid model to explore the effects of the two infection modes in viral production and spread. We offer a rigorous analysis for the model, including addressing the relative compactness and persistence of the solution semiflow, and existence of a global attractor. By subtle construction and estimates of Lyapunov functions, we show that the global attractor actually consists of an singleton, being either the infection free steady state if the basic reproduction number is less than one, or the infection steady state if the basic reproduction number is larger than one. [ABSTRACT FROM AUTHOR]

A diffusive and delayed viral dynamics model which incorporates cell-to-cell transmission, cell-mediated immune responses and general nonlinear incidence is investigated. By constructing Lyapunov functionals, it is shown that the global threshold dynamics of the model is fully determined by the basic reproduction numbers of the virus and the immune response, R 0 and R 1 . The result implies that both the basic reproduction number of the virus and the immune response might be underevaluated without considering either the virus-to-cell transmission or cell-to-cell transmission. The main results obtained in this paper extend some known results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global dynamics of a PDE viral infection model with cell-to-cell transmission and spatial heterogeneity. The basic reproduction number ℜ 0 , which is a threshold value that predicts whether the infection will go to extinction or not, is defined in a variational characterization. In quite a general setting in which every parameter can be spatially heterogeneous, it is shown that if ℜ 0 ≤ 1 , then the infection-free steady state is globally asymptotically stable, while if ℜ 0 > 1 , then the system is uniformly persistent and the infection steady state is globally asymptotically stable. The proof is based on the construction of the Lyapunov functions and usage of the Green's first identity. Finally, numerical simulation is performed in order to verify the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study the threshold dynamics of an HIV-1 viral infection model with cell-mediated immune responses and direct cell-to-cell transmission mechanism. The model demonstrates global threshold dynamics with respect to the reproductive numbers for viral infection ℜ 0 and for CTL immune response ℜ 1 . The proofs of main results come from suitable uses of analyzing the characteristic equation and constructing Lyapunov functionals. Specifically, if ℜ 0 < 1, the infection-free equilibrium E 0 is locally and globally asymptotically stable, and the viruses are cleared. If ℜ 1 < 1 < ℜ 0 , the CTL-inactivated equilibrium E 1 is locally and globally asymptotically stable, and the infection becomes chronic but without persistent CTLs response. If ℜ 1 > 1, the CTL-activated equilibrium E 2 is locally and globally asymptotically stable, and the infection is chronic with persistent CTLs response. Numerical simulations are performed to support our results. [ABSTRACT FROM AUTHOR]

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spreads efficiently by spike-mediated, direct cell-to-cell transmission. However, the underlying mechanism is poorly understood. Herein, we demonstrate that the tight junction protein occludin (OCLN) is critical to this process. SARS-CoV-2 infection alters OCLN distribution and expression and causes syncytium formation that leads to viral spread. OCLN knockdown fails to alter SARS-CoV-2 binding but significantly lowers internalization, syncytium formation, and transmission. OCLN overexpression also has no effect on virus binding but enhances virus internalization, cell-to-cell transmission, and replication. OCLN directly interacts with the SARS-CoV-2 spike, and the endosomal entry pathway is involved in OCLN-mediated cell-to-cell fusion rather than in the cell surface entry pathway. All SARS-CoV-2 strains tested (prototypic, alpha, beta, gamma, delta, kappa, and omicron) are dependent on OCLN for cell-to-cell transmission, although the extent of syncytium formation differs between strains. We conclude that SARS-CoV-2 utilizes OCLN as an internalization factor for cell-to-cell transmission. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a diffusive within-host virus dynamics model with both virus-to-cell and cell-to-cell transmissions. Then, we consider the discretization of the model by using nonstandard finite difference scheme. It is then followed by the investigation of the global stability of the equilibria of the discrete model. Our study shows that if the basic reproduction number R 0 ≤ 1 , then the infection-free equilibrium is globally asymptotically stable; however if R 0 > 1 , then the infection equilibrium is globally asymptotically stable. Numerical simulations are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose an HIV model with latent reservoir, delayed CTL immune response and immune impairment in which both virus-to-cell infection and cell-to-cell viral transmission are considered. By using Lyapunov functionals and LaSalle’s invariance principle, it is verified that when time delay is equal to zero, the global threshold dynamics of the model is determined by the basic reproduction ratio. With the help of uniform persistence theory for infinite dimensional systems, we obtain the uniform persistence when the basic reproduction ratio is greater than unity. By choosing time delay as a bifurcation parameter and analyzing the corresponding characteristic equation of the system, we establish the existence of Hopf bifurcation at the chronic-infection equilibrium. Numerical simulations are carried out to illustrate the corresponding theoretical results.

The Chikungunya virus (CHIKV) is a mosquito-borne alphavirus that affects the world's popula-tion with chikungunya disease. Adaptation of the viral life cycle to their host cells' environment is a key step for establishing their infection and pathogenesis. Recently, the accumulating evidence advocates a principal role of extracellular vesicles (EVs), including exosomes, in both the infection and pathogenesis of infectious diseases. However, the participation of exosomes in CHIKV infec-tion and transmission is not well clarified. Here, we demonstrated that the CHIKV RNA and pro-teins were captured in exosomes, which were released by viral-infected epithelial cells. A viral genomic element in the isolated exosomes was infectious to naïve mammalian epithelial cells. The assay of particle size distribution and transmission electron microscopy (TEM) revealed CHIKV-derived exosomes with a size range from 50 to 250 nm. Treatments with RNase A, Triton X-100, and immunoglobulin G antibodies from CHIKV-positive patient plasma indicated that in-fectious viral elements are encompassed inside the exosomes. Interestingly, our viral plaque for-mation also exhibited that infectious viral elements might be securely transmitted to neighboring cells by a secreted exosomal pathway. Taken together, our recent findings emphasize the evidence for a complementary means of CHIKV infection and suggest the role of exosome-mediated CHIKV transmission. [ABSTRACT FROM AUTHOR]

Based on some important biological meanings, we propose a class of HIV infection models incorporating both classical cell-free virus diffusion and direct cell-to-cell transmission. According to recent studies, the direct cell-to-cell transfer of HIV is a significantly more efficient mode of retroviral dissemination. In the first part of our analysis, we show that our model possesses non-negative solutions. Then, we derive sufficient conditions for the asymptotic stability of equilibriums. The analytical solutions are verified by simulation results. At the end of the paper, some important conclusions are given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global properties of two general models of pathogen infection with immune deficiency. Both pathogen-to-cell and cell-to-cell transmissions are considered. Latently infected cells are included in the second model. We show that the solutions are nonnegative and bounded. Lyapunov functions are organized to prove the global asymptotic stability for uninfected and infected steady states of the models. Analytical expressions for the basic reproduction number $\mathcal{R}_{0}$ and the necessary condition under which the uninfected and infected steady states are globally asymptotically stable are established. We prove that if $\mathcal{R}_{0}$ < 1 then the uninfected steady state is globally asymptotically stable (GAS), and if $\mathcal{R}_{0}$ > 1 then the infected steady state is GAS. Numerical simulations are performed and used to support the analytical results.

Abstract In this paper, the dynamical behaviors for multiple delayed latent virus model with virus-to-cell infection and cell-to-cell transmissions and humoral immunity are investigated. The virus-to-cell and cell-to-cell incidence rates are modeled by general nonlinear functions. The basic reproduction number R 0 $R_{0}$ and the humoral immune response number R 1 $R_{1}$ are calculated and proved to be threshold conditions determining the local and global properties of the virus model. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is presented, and the effects of some key parameters on viral dynamics are revealed by numerical simulations.