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A new viral infection model with cell-to-cell infection and periodic antiretroviral therapy was proposed and analyzed. With the help of defined basic reproduction number ℜ 0 , we proved that if ℜ 0 < 1 , then the infection-free steady state is globally attractive. If ℜ 0 > 1 , then the infection is uniformly persistent. Furthermore, the globally asymptotical stability of infection-free steady state has been established for the critical case of ℜ 0 = 1. Also, the global asymptotic stability of the infection steady state for a special case of the model has been established by applying the method of Lyapunov. Numerical simulations show that increasing the drug efficacy for blocking virus-to-cell infection, cell-to-cell infection and producing non-infectious virus contributes to weakening the severity of viral infection. [ABSTRACT FROM AUTHOR]

In this paper, a delayed cytokine-enhanced viral infection model incorporating nonlinear incidence and immune response is proposed and studied. The global stabilities of the equilibria of the model are characterized by constructing suitable Lyapunov functionals. The existence and properties of local Hopf bifurcation are discussed by regarding the immunity delay as the bifurcation parameter. Moreover, the global existence of Hopf bifurcation has been proved by regarding the immune delay as the bifurcation parameter. Numerical simulations are carried out to validate the obtained results. The results show that ignoring the cytokine-enhanced effect makes the infection risk underevaluated. The simulations show that increasing the immune delay destabilizes the model and generates a Hopf bifurcation and stability switches occurs. Moreover, it shows that immune delay may dominate the intracellular delays in such a viral infection model which means that the immune system of the host itself is complicated during virus infection. [ABSTRACT FROM AUTHOR]

In this study, a small phase angle resonant controller (SPARC) is designed to suppress the current harmonics in a permanent magnet synchronous motor (PMSM). First, the analytical model of the PMSM is established. Second, a SPARC is designed to improve the problem of the overly large phase angle of the resonant controller at the resonant frequency. Third, the frequency error caused by the SPARC discretisation is compensated online. Finally, an experimental platform is built for the PMSM harmonic suppression, and the effectiveness and feasibility of the proposed method are verified through a comparison with the method of motor control using quasi‐resonant controller. [ABSTRACT FROM AUTHOR]

In this paper, we investigated a new heroin–cocaine epidemic model which incorporates spatial heterogeneity and nonlinear incidence rate. The main project of this paper is to explore the threshold dynamics in terms of the basic reproduction number $ \mathcal {R}_0 $ R 0 , which was defined by applying the next-generation operator. The threshold type results shown that if $ \mathcal {R}_0 \lt 1 $ R 0 < 1 , then the drug-free steady state is globally asymptotically stable. If $ \mathcal {R}_0 \gt 1 $ R 0 > 1 , then heroin–cocaine spread is uniformly persistent. Furthermore, the globally asymptotic stability of the drug-free steady state has been established for the critical case of $ \mathcal {R}_0=1 $ R 0 = 1 by analysing the local asymptotic stability and global attractivity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the spatiotemporal patterns of solutions to diffusive nonlocal Nicholson’s blowflies equations, wherein a natural death rate of the immature population is included in the distribution function. We first prove the positivity and boundedness of positive solutions in the model by using the minimum principle and the method of lower and upper solutions. Subsequently, we conduct a detailed bifurcation and stability analysis to obtain conditions on all the diffusion coefficients and the death rate coefficient of the immature population required for the emergence of spatiotemporal patterns, including spatially nonhomogeneous time periodic orbits. Our results indicate that the model can undergo Hopf bifurcation when the diffusion rate of the mature population passes through a sequence of critical values. Additionally, we examine the dependence of Hopf bifurcation points and bifurcated oscillations on model parameters, including the diffusion rate and death rate of the immature population. Finally, we report numerical simulations based on the bifurcation analysis to demonstrate the theoretical results, and it will help us better understand the ecological characteristics and behavioral patterns of the blowfly population. [ABSTRACT FROM AUTHOR]

Ground subsidence is regarded as one of the most common geohazards accompanied with the rapid urban expansion in recent years. In the last two decades, Wuhan located in the alluvial Jinaghan Plain has experienced great urban expansion with increased subsidence issues, i.e. soft foundation subsidence and karst collapses. Here we investigated subsidence rates in Wuhan city with 2015-2019 Sentinel-1 SAR images. We found that the overall subsidence over Wuhan region is significantly correlated with the distribution of engineering geological regions (EGSs). We further validated the InSAR measurements with better than 5 mm accuracy by comparing with leveling measurements. Subsidence centers in Qingling-jiangdi, Houhu, Qingshan and Dongxihu area were identified with displacement rates of approximately 30 mm/yr. Our results demonstrated that the dominant driven factor is ongoing constructions and the subsidence centers shifted with construction intensities. Qingling-Jiangdi area in our study is a well-known sites of karst collapses. We find the nonlinear subsidence of this area is correlated with the water level variations of the Yangtze River. [ABSTRACT FROM AUTHOR]

In this paper, a multigroup SVIR epidemic model with reaction-diffusion and nonlinear incidence is investigated. We first establish the well-posedness of the model. Then, the basic reproduction number ℜ 0 is established and shown as a threshold: the disease-free steady state is globally asymptotically stable if ℜ 0 < 1 , while the disease will be persistent when ℜ 0 > 1. Moreover, applying the classical method of Lyapunov and a recently developed graph-theoretic approach, we established the global stability of the endemic equilibria for a special case. [ABSTRACT FROM AUTHOR]

The goal of this paper is to investigate the dynamical behavior of a general nonlinear delayed viral infection model with cytotoxic T lymphocyte (CTL) immune response. The intrinsic growth rate of uninfected hepatocytes, incidence rate of infection, removal rate of infected hepatocytes and capsids, production and removal rate of viruses, activation rate of CTLs, and decay rate of CTLs are given by general nonlinear functions with a set of conditions on these general nonlinear functions, which make the analysis of the model more difficult. The global threshold dynamics with respect to the reproduction numbers for viral infection R0 and for CTL immune response R1 have been presented by constructing suitable Lyapunov functionals. Numerical simulations are carried out for a model with specific forms of the general functions to confirm the theoretical results and show that both the numerical and theoretical results are consistent. [ABSTRACT FROM AUTHOR]

A delayed multi-group SVEIR epidemic model with vaccination and a general incidence function has been formulated and studied in this paper. Mathematical analysis shows that the basic reproduction number [ABSTRACT FROM AUTHOR]

Pandemics, such as Covid-19 and AIDS, tend to be highly contagious and have the characteristics of global spread and existence of multiple virus strains. To analyze the competition among different strains, a high dimensional SIR model studying multiple strains' competition in patchy environments is introduced in this work. By introducing the basic reproductive number of different strains, we found global stability conditions of disease-free equilibrium and persistence conditions of the model. The competition exclusion conditions of that model are also given. This work gives some insights into the properties of the multiple strain patchy model and all of the analysis methods used in this work could be used in other related high dimension systems.