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A diffusive and delayed viral infection model with nonlinear incidence has been studied, and the global dynamical behaviors of the original model is investigated by constructing Lyapunov functionals. Furthermore, the analysis is carried out for the discrete model which is obtained by applying the nonstandard finite difference (NSFD) scheme to the original continuous model. The global stability for the corresponding equilibria is investigated by constructing discrete Lyapunov functionals as well as the positivity and boundedness of solutions of the corresponding continuous model. The results imply that the discretization scheme can efficiently preserves the qualitative properties of solutions for the original continuous model. Numerical experiments are carried out to support the theoretical results. [ABSTRACT FROM AUTHOR]

A non-standard finite difference scheme is proposed to solve a delayed and diffusive viral infection model with general nonlinear incidence rate. The results show that the discrete model preserves the positivity and boundedness of solutions in order to ensure the well-posedness of the problem. Moreover, this method preserves all equilibria of the original continuous model. By constructing Lyapunov functionals, we show that the global stability of equilibria is completely determined by the basic reproduction number ℜ 0 , which implies that the proposed discrete model can efficiently blue preserve the global stability of equilibria of the corresponding continuous model. Numerical experiments are carried out to support the theoretical results. [ABSTRACT FROM AUTHOR]

An age-structured within-host virus infection model with both virus-to-cell and cell-to-cell infection and antiretroviral therapy is investigated. The global stability analysis of the model is carried out in terms of the basic reproduction number R 0 by constructing Lyapunov functionals. If R 0 ≤ 1 , the infection-free steady state is globally asymptotically stable; if R 0 > 1 , the infection steady state is globally asymptotically stable. The influence of drug therapy on cell-to-cell infection is discussed, which shows that cell-to-cell infection is important for the final outcome of the HIV virus infection and blocking cell-to-cell infection can effectively suppress the HIV virus spread. Moreover, numerical simulations are performed to study the dynamical behavior of solutions of the models. The results show that both the viral production rate and the death rate of infected cells play an important role in the viral dynamics of the model. [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]

In this study, we investigated a delayed vector-borne disease model with partial immunity to reinfection. The equilibria and the threshold of the model were determined according to the basic reproductive number R 0 . The analysis showed that a time delay destabilized the system. Using the delay as a bifurcation parameter, we established the conditions for the stability of the equilibria and the existence of a Hopf bifurcation. We determined the properties of the Hopf bifurcation by applying the normal form theory and center manifold argument, and for the first time, we considered the global continuation of the local Hopf bifurcation for a delayed vector-borne disease epidemic model. Furthermore, we performed some numerical simulations to illustrate our theoretical analysis. Sensitivity analysis showed that preventive control to minimize vector–human contacts and using insecticide to control the vector are effective measures for reducing infections. [ABSTRACT FROM AUTHOR]

The main purpose of the present study is devoted to make a supplement to the recent work of Wang and Sun (2020) for a critical case where the basic reproduction number R 0 = 1 , the heroin-free steady state (HFSS) is globally asymptotically stable by applying Gronwall's inequality, comparison theorem and the properties of semigroup. [ABSTRACT FROM AUTHOR]

The dual five-axis machining machine is state-of-the-art equipment designed for producing thin-walled aerospace parts like skins and panels. It comprises two five-axis machine tools with mirrored synchronous motions: one bi-rotary machine for milling and the other machine for follow-up support. The high absolute accuracy of the five-axis machine tools themselves and the high synchronous motion accuracy between the two machines are both crucial to ensure machining accuracy. This paper proposes an efficient method to measure and identify geometric and dynamic errors of dual five-axis machine tools. Using the R-test combined with three measurement trajectories to measure the absolute motion error of two five-axis machine tools and the synchronous motion error between the two machines. The designed trajectories include the main rotary axis linkage conditions and can fully reflect the primary motion forms of the dual five-axis machine tool. The main position-independent geometric errors and rotational axis linkage dynamic errors are identified by converting quasi-static and dynamic measurement data from three different trajectories into a unified reference coordinate system. The entire process requires only one instrument installation, effectively avoiding time-consuming repetitive installations and calibration processes while reducing the impact of installation errors on results. The effectiveness of the proposed method for measuring and identifying the geometric and dynamic errors is analyzed combined with Monte Carlo simulation. Experiments were carried out on a dual five-axis mirror milling system (MMS) with a 5000 mm X-stroke. Both simulations and experiments confirmed that the proposed method is efficient in quickly identifying key error sources of the MMS. [Display omitted] • An efficient method to measure and identify geometric and dynamic errors during synchronous motion of the MMS is proposed. • A geometric and dynamic error model is introduced for identifying key errors using error sensitivity theory. • A 3-step measurement strategy that enables rapid separation of linkage errors of the MMS is introduced. • Both simulation and experiment show the proposed method could obtain key error sources of the MMS with high efficiency. [ABSTRACT FROM AUTHOR]