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A model of viral infection with self-proliferation of cytotoxic lymphocytes (CTLs) with a nonlinear infection rate and free boundaries is proposed, and its global dynamics are studied. The existence, uniqueness and uniform estimates of the global solution are proved, as well as the behavior of the components of the solution and the unknown boundary over large time intervals. With the help of the basic reproductive number , sufficient conditions are created for the spread or disappearance of the virus. [ABSTRACT FROM AUTHOR]

The authors propose and analyze a viral infection model with defectively infected cells and age of the latently infected cells. The existence of steady states is determined by the basic reproduction number of virus. With the Lyapunov's direct method, they establish a threshold dynamics of the model with the basic reproduction number of virus as the threshold parameter. To achieve it, a novel procedure is proposed. Its novelties are two-folded. On one hand, the coefficients involved in the specific forms of the used Lyapunov functionals for the two feasible steady states are determined by the same set of inequalities. On the other hand, for the infection steady state, a new approach is proposed to check whether the derivative of the Lyapunov functional candidate along solutions is negative (semi-)definite or not. This procedure not only simplifies the analysis but also exhibits the relationship between the two Lyapunov functionals for the two feasible steady states. Moreover, the procedure is expected to be applicable for other similar models. [ABSTRACT FROM AUTHOR]

We study a viral infection model incorporating both cell-to-cell infection and immune chemokines. Based on experimental results in the literature, we make a standing assumption that the cytotoxic T lymphocytes (CTL) will move toward the location with more infected cells, while the diffusion rate of CTL is a decreasing function of the density of infected cells. We first establish the global existence and ultimate boundedness of the solution via a priori energy estimates. We then define the basic reproduction number of viral infection R 0 and prove (by the uniform persistence theory, Lyapunov function technique and LaSalle invariance principle) that the infection-free steady state E 0 is globally asymptotically stable if R 0 < 1 . When R 0 > 1 , then E 0 becomes unstable, and another basic reproduction number of CTL response R 1 becomes the dynamic threshold in the sense that if R 1 < 1 , then the CTL-inactivated steady state E 1 is globally asymptotically stable; and if R 1 > 1 , then the immune response is uniform persistent and, under an additional technical condition the CTL-activated steady state E 2 is globally asymptotically stable. To establish the global stability results, we need to prove point dissipativity, obtain uniform persistence, construct suitable Lyapunov functions, and apply the LaSalle invariance principle. [ABSTRACT FROM AUTHOR]

To provide insights into the spreading speed and propagation dynamics of viruses within a host, in this paper, we investigate the traveling wave solutions and minimal wave speed for a degenerate viral infection dynamical model with a nonlocal dispersal operator and saturated incidence rate. It is found that the minimal wave speed c ∗ is the threshold that determines the existence of traveling wave solutions. The existence of traveling fronts connecting a virus-free steady state and a positive steady state with wave speed c ≥ c ∗ is established by using Schauder's fixed-point theorem, limiting arguments, and the Lyapunov functional. The nonexistence of traveling fronts for c < c ∗ is proven by the Laplace transform. In particular, the lower-bound estimation of the traveling wave solutions is provided by adopting a rescaling method and the comparison principle, which is a crucial prerequisite for demonstrating that the traveling semifronts connect to the positive steady state at positive infinity by using the Lyapunov method and is a challenge for some nonlocal models. Moreover, simulations show that the asymptotic spreading speed may be larger than the minimal wave speed and the spread of the virus may be postponed if the diffusion ability or diffusion radius decreases. The spreading speed may be underestimated or overestimated if local dispersal is adopted. [ABSTRACT FROM AUTHOR]

This paper is concerned with a degenerate and time delayed virus infection model with spatial heterogeneity and general incidence. The well‐posedness of the system, including global existence, uniqueness, and ultimately boundedness of the solutions, as well as the existence of a global attractor, is discussed. The basic reproduction number R0$\mathcal {R}_0$ is defined and a characterization of R0$\mathcal {R}_0$ is presented. Without the compactness of the solution semiflow, we establish the global dynamics of the system based on R0$\mathcal {R}_0$. In addition, when the system is spatially homogeneous, the unique infection steady state is globally asymptotically stable. Simulations are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

We propose a general model to investigate the effect of the distinct dispersal coefficients infected and susceptible hosts in the pathogen dynamics. The mathematical challenge lies in the fact that the investigated model is partially degenerate and the solution map is not compact. The spatial heterogeneity of the model parameters and the distinct diffusion coefficients induce infection in the low-risk regions. In fact, as infection dispersal increases, the reproduction of the pathogen particles decreases. The dynamics of the investigated model is governed by the value of the basic reproduction number R0. If R0 ≤ 1, then the pathogen particles extinct, and for R0 > 1 the pathogen particles persist, and there is at least one positive steady state. The asymptotic profile of the positive steady state is shown in the case when one or both diffusion coefficients for the host tends to zero or infinity. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic analysis of spatially heterogeneous viral transmission, incorporating cell‐to‐cell transmission, virus nonlocal dispersal, and intracellular delay. Due to the noncompactness of the semiflow, we used the Kuratowski measure of noncompactness to demonstrate the existence of a global compact attractor. This noncompactness issue generates difficulties in calculating the basic reproduction number R0$$ {R}_0 $$, which is the principal eigenvalue of the next‐generation operator. The threshold role of this number is determined, where we derived two different cases: (i) the global stability of the virus‐free steady state, which is globally stable for R0<1$$ {R}_0<1 $$ by the Lyapunov direct method, and (ii) the global stability of the virus steady state for R0>1$$ {R}_0>1 $$. Indeed, the second case is demonstrated through several steps that include uniform persistence, the existence of a virus steady state, and the global stability of the virus steady state. The results are supported by different graphical representations with proper biological justifications. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global attractivity of a nonlocal reaction-diffusion viral infection model. By constructing suitable Lyapunov functionals, we show that the solutions of the model converge to a unique endemic equilibrium when the basic reproduction number is greater than one. The global attractivity for certain models with specific net growth rate and cell-to-cell transmissions are investigated as examples for illustration. Our results improve and generalize some known results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fractional-order viral infection model, which includes latent infection, a Holling type II response function, and a time-delay representing viral production. Based on the characteristic equations for the model, certain sufficient conditions guarantee local asymptotic stability of infection-free and interior steady states. Whenever the time-delay crosses its critical value (threshold parameter), a Hopf bifurcation occurs. Furthermore, we use LaSalle’s invariance principle and Lyapunov functions to examine global stability for infection-free and interior steady states. Our results are illustrated by numerical simulations.

In this paper, an age-structured within-host viral infection model with cell-to-cell transmission and general humoral immune response is investigated. We give a rigorous mathematical analysis on some necessary technical materials, including the relative compactness and persistence of the solution semiflow, and existence of a global attractor. By subtle construction and estimates of a Lyapunov functional, we show that the global dynamics is determined by two sharp thresholds, namely, basic reproduction number $\Re_0$ and immune-response reproduction number $\Re_1$. When $\Re_0 < 1$, the virus-free steady state is globally asymptotically stable, which means that the viruses are cleared and immune-response is not active; when $\Re_1 < 1 < \Re_0$, the immune-inactivated infection steady state exists and is globally asymptotically stable; and when $\Re_1>1$, which implies that $\Re_0>1$, the immune-activated infection steady state exists and is globally asymptotically stable. Numerical simulations are given to support our theoretical results.

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]

As important companion animals, dogs may serve as intermediate hosts for transmitting influenza virus to humans. However, knowledge regarding H3N2 canine influenza virus (CIV) pathogenicity is not comprehensive, which directly affects the animal models of pathogenicity in H3N2 CIV vaccine research. Here, to assess H3N2 CIV pathogenicity, we utilized 30 ten-week-old purpose-bred beagles intratracheally or intranasally inoculated with 10 6 50% egg-infectious dose. Intratracheal inoculation was more virulent to dogs than intranasal inoculation as shown by lung pathology score, histopathological changes, clinical symptoms, and body temperature. More intense virus replication was observed in the upper and lower respiratory tracts by intratracheal than intranasal inoculation according to nasal swabs, various organ virus titers, and antigen expression. These results may enhance the H3N2 CIV infection model, providing a more complete experimental basis for studying intrinsic H3N2 CIV pathogenic mechanism, and also serving a reference role for CIV prevention and treatment. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the stability of a CD 4 + T cell viral infection model with diffusion. First, we discuss the well-posedness of the model and the existence of endemic equilibrium. Second, by analyzing the roots of the characteristic equation, we establish the local stability of the virus-free equilibrium. Furthermore, by constructing suitable Lyapunov functions, we show that the virus-free equilibrium is globally asymptotically stable if the threshold value ℛ 0 ≤ 1 ; the endemic equilibrium is globally asymptotically stable if ℛ 0 > 1 and d u ∗ − δ w ∗ ≥ 0. Finally, we give an application and numerical simulations to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors of a viral infection model with cytotoxic T-lymphocyte (CTL) immune response, immune response delay and production delay are investigated. The threshold values for virus infection and immune response are established. By means of Lyapunov functionals methods and LaSalle's invariance principle, sufiicient conditions for the global stability of the infection-free and CTL-absent equilibria are established. Global stability of the CTL-present infection equilibrium is also studied when there is no immune delay in the model. Furthermore, to deal with the local stability of the CTL-present infection equilibrium in a general case with two delays being positive, we extend an existing geometric method to treat the associated characteristic equation. When the two delays are positive, we show some conditions for Hopf bifurcation at the CTL-present infection equilibrium by using the immune delay as a bifurcation parameter. Numerical simulations are performed in order to illustrate the dynamical behaviors of the model. [ABSTRACT FROM AUTHOR]

In this paper, a discrete-time analog of a viral infection model with nonlinear incidence and CTL immune response is established by using the Micken non-standard finite difference scheme. The two basic reproduction numbers $R_{0}$ and $R_{1}$ are defined. The basic properties on the positivity and boundedness of solutions and the existence of the virus-free, the no-immune, and the infected equilibria are established. By using the Lyapunov functions and linearization methods, the global stability of the equilibria for the model is established. That is, when $R_{0}\leq1$ then the virus-free equilibrium is globally asymptotically stable, and under the additional assumption $(A_{4})$ when $R_{0}>1$ and $R_{1}\leq1$ then the no-immune equilibrium is globally asymptotically stable and when $R_{0}>1$ and $R_{1}>1$ then the infected equilibrium is globally asymptotically stable. Furthermore, the numerical simulations show that even if assumption $(A_{4})$ does not hold, the no-immune equilibrium and the infected equilibrium also may be globally asymptotically stable. [ABSTRACT FROM AUTHOR]

In this paper, the sharp threshold properties of a (2n + 1)-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected target cells, n classes of infected cells and nonlinear incidence rate h(x, v). Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model. [ABSTRACT FROM AUTHOR]

In this paper, we investigate global dynamics for a distributed time delayed HCV infection model. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. By employing the method of Lyapunov functional, we prove that the uninfected equilibrium is global asymptotically stable if the basic reproduction number is less than one, it is unstable and the infected equilibrium is global asymptotically stable if the basic reproduction number is larger than one. The simulations results are in good accordance with our analytic results. [ABSTRACT FROM AUTHOR]

In this letter, we establish a viral infection model with the effect of pyroptosis and chemotaxis. Choosing chemotaxis coefficient as the bifurcation parameter, we derive the necessary condition for the existence of Turing instability. We observe that chemotaxis can induce Turing instability, which may lead to steady state bifurcation or Hopf bifurcation, and spatial patterns. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global attractivity of the positive steady state for a time-delayed viral infection model when R 0 > 1. Our study solves the open problem left in a recent work of Yang and Wei (2020) by Lyapunov functional method. [ABSTRACT FROM AUTHOR]

In this paper, we present and study a stochastic viral infection model with lytic and nonlytic immune responses driven by Lévy noise. First, we show that this model has unique positive global solution. Using the Lyapunov method, we prove that disease-free equilibrium is stable. Furthermore, we give sufficient conditions for the persistence in mean of the viral infection. Finally, we illustrate our theoretical results by some numerical simulations. It is shown that even if the basic reproduction number is greater that unity, we can have the extinction of the infection. • We present a viral infection model driven by Lévy noise. • The model has a unique global positive solution. • Sufficient conditions for persistence in mean and extinction are established. • Numerical results confirm the theoretical findings. [ABSTRACT FROM AUTHOR]