Advances in Difference Equations最新文献

Objective

Cervical cancer (CC), serving as a primary public health challenge, significantly threatens women’s health. However, in terms of change-points, there is still a lack of epidemiological studies on the incidence of HPV infection and CC in Xinjiang,China. This research aims to identify significant changes in the trends of HPV infection and CC prevalence in Xinjiang through change-point analysis (CPA) to provide scientific guidance to health authorities.

Methods

HPV infection and CC time-series data (from January 2011 to December 2019) were collected and analyzed. Meanwhile, their change-points were detected with binary segmentation method and the PELT method. Furthermore, patients were assigned into three groups based on their different ages and subsequently subjected to an analysis employing a segmented regression model (SRM).

Results

It was evident that for the monthly HPV time series, the binary segmentation method detected three change points in August 2015, February 2016, and September 2017 (with the most HPV cases). In contrast, the PELT method detected two change-points in September 2015 and April 2017 (with the most HPV cases). For the monthly CC time series, the binary segmentation method identified two change points in October 2012 and August 2019 (with the most CC cases), whereas the PELT method identified three change points in October 2012, August 2019 (with the most CC cases), and October 2019. The SRM demonstrated varying numbers of change points in distinct groups, with HPV infection and CC having the higher growth rate in the 30–49 and 40–59 age groups, respectively. Based on above results, this research was conductive to comprehending the epidemiology of HPV infection and CC in Xinjiang. In addition, it offered scientific guidance for future prevention and management measures for both HPV infection and CC.

The abnormal aggregation of proteins into amyloid fibrils, usually implemented by a series of biochemical reactions, is associated with various neurodegenerative disorders. Considering the intrinsic stochasticity in the involving biochemical reactions, a general chemical master equation model for describing the process from oligomer production to fibril formation is established, and then the lower-order statistical moments of different molecule species are captured by the derivative matching closed system, and the long-time accuracy is verified using the Gillespie algorithm. It is revealed that the aggregation of monomers into oligomers is highly dependent on the initial number of misfolded monomers; the formation of oligomers can be effectively inhibited by reducing the misfolding rate, the primary nucleation rate, elongation rate, and secondary nucleation rate; as the conversion rate decreases, the number of oligomers increases over a long time scale. In particular, sensitivity analysis shows that the quantities of oligomers are more sensitive to monomer production and protein misfolding; the secondary nucleation is more important than the primary nucleation in oligomer formation. These findings are helpful for understanding and predicting the dynamic mechanism of amyloid aggregation from the viewpoint of quantitative analysis.

We propose, in this paper, a novel stochastic SIRS epidemic model to characterize the effect of uncertainty on the distribution of infectious disease, where the general incidence rate and Ornstein–Uhlenbeck process are also introduced to describe the complexity of disease transmission. First, the existence and uniqueness of the global nonnegative solution of our model is obtained, which is the basis for the discussion of the dynamical behavior of the model. And then, we derive a sufficient condition for exponential extinction of infectious diseases. Furthermore, through constructing a Lyapunov function and using Fatou’s lemma, we obtain a sufficient criterion for the existence and ergodicity of a stationary distribution, which implies the persistence of the disease. In addition, the specific form of the density function of the model near the quasiendemic equilibrium is proposed by solving the corresponding Fokker–Planck equation and using some relevant algebraic equation theory. Finally, we explain the above theoretical results through some numerical simulations.

We study the convergence properties of gradient descent for training deep linear neural networks, i.e., deep matrix factorizations, by extending a previous analysis for the related gradient flow. We show that under suitable conditions on the stepsizes gradient descent converges to a critical point of the loss function, i.e., the square loss in this article. Furthermore, we demonstrate that for almost all initializations gradient descent converges to a global minimum in the case of two layers. In the case of three or more layers, we show that gradient descent converges to a global minimum on the manifold matrices of some fixed rank, where the rank cannot be determined a priori.

We propose a unified stochastic SIR model driven by Lévy noise. The model is structural enough to allow for time-dependency, nonlinearity, discontinuity, demography, and environmental disturbances. We present concise results on the existence and uniqueness of positive global solutions and investigate the extinction and persistence of the novel model. Examples and simulations are provided to illustrate the main results.

Google mobility data has been widely used in COVID-19 mathematical modeling to understand disease transmission dynamics. This review examines the extensive literature on the use of Google mobility data in COVID-19 mathematical modeling. We mainly focus on over a dozen influential studies using Google mobility data in COVID-19 mathematical modeling, including compartmental and metapopulation models. Google mobility data provides valuable insights into mobility changes and interventions. However, challenges persist in fully elucidating transmission dynamics over time, modeling longer time series and accounting for individual-level correlations in mobility patterns, urging the incorporation of diverse datasets for modeling in the post-COVID-19 landscape.

We investigate a competitive diffusion–advection Lotka–Volterra model with more general nonlinear boundary condition. Based on some new ideas, techniques, and the theory of the principal spectral and monotone dynamical systems, we establish the influence of the following parameters on the dynamical behavior of system (1.2): advection rates (alpha _{u}) and (alpha _{v}), interspecific competition intensities (c_{u}) and (c_{v}), the resources functions (r_{u}) and (r_{v}) of the two competitive species, and nonlinear boundary functions (g_{1}) and (g_{2}). The models of (Tang and Chen in J. Differ. Equ. 269(2):1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264:4176–4198, 2018) are particular cases of our results when (g_{i}equiv const) for (i=1,2), and hence this paper extends some of the conclusions from (Tang and Chen in J. Differ. Equ. 269(2):1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264:4176–4198, 2018).

The general kinetic theory of coarse-grained systems is presented in the abstract formalism of communication theory developed by Shannon and Weaver, Khinchin and Kolmogorov. The martingale theory shows that, under reasonable, general hypotheses, coarse-grained systems can be approximated by generalized Markov systems. For mixing systems, the Kolmogorov entropy production can be defined for nonstationary processes as Kolmogorov defined it for stationary processes.

Hilfer fractional derivative is an important and interesting operator in fractional calculus, and it can be applicable in pure theories and other fields. It yields to other notable definitions, Ψ-Hilfer, ((k,Psi ))-Hilfer derivatives, etc. Motivated by the concepts of the proportional fractional derivative and ((k,Psi ))-Hilfer fractional derivative, we first introduce new definitions of integral and derivative, termed the ((rho ,k,Psi ))-proportional integral and ((rho ,k,Psi ))-proportional Hilfer fractional derivative. This type of fractional derivative is advantageous as it aligns with earlier studies on fractional differential equations. Additionally, we present a more generalized version of the ((rho ,alpha ,beta ,k,r))-resolvent family, followed by an exploration of its properties. By analyzing the generalized resolvent family, we examine the existence of mild solutions to the ((rho ,k,Psi ))-proportional Hilfer fractional Cauchy problem, supported by an illustrative example to show the main result.

Here, we consider here Hyperbolic Nonlinear Schrödinger Equations (HNLS) that occur as asymptotic models in the modulational regime when the Hessian of the dispersion relation is not positive (or negative) definite. We review classical examples, well-known results, and main open questions.