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Advances in Difference Equations最新文献

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Dynamical analysis of a novel fractional order SIDARTHE epidemic model of COVID-19 with the Caputo–Fabrizio(CF) derivative 带有卡普托-法布里齐奥（CF）导数的 COVID-19 新型分数阶 SIDARTHE 流行病模型的动力学分析
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2024-01-25 DOI: 10.1186/s13662-024-03798-4
Yu Zhao, Tian-zeng Li, Rong Kang, Xi-liang He
{"title":"Dynamical analysis of a novel fractional order SIDARTHE epidemic model of COVID-19 with the Caputo–Fabrizio(CF) derivative","authors":"Yu Zhao, Tian-zeng Li, Rong Kang, Xi-liang He","doi":"10.1186/s13662-024-03798-4","DOIUrl":"https://doi.org/10.1186/s13662-024-03798-4","url":null,"abstract":"<p>Fabrizio and Caputo suggested an extraordinary definition of fractional derivative, which has been used in many fields. The SIDARTHE infectious disease model with regard to COVID-19 is studied by the new notion in this paper. Making use of the Banach fixed point theorem, the existence and uniqueness of the model’s solution are demonstrated. Then, an efficient method is utilized to deduce the iterative scheme. Finally, some numerical simulations of the model under various fractional orders and parameters are shown. From the computed result, we can see that it not only supports the theoretical demonstration, but also has an intensive insight into the characteristics of the model.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Random exponential attractor for a stochastic reaction-diffusion equation in $L^{2p}(D)$ L^{2p}(D)$中随机反应扩散方程的随机指数吸引子
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2024-01-02 DOI: 10.1186/s13662-023-03795-z
Gang Wang, Chaozhu Hu
{"title":"Random exponential attractor for a stochastic reaction-diffusion equation in $L^{2p}(D)$","authors":"Gang Wang, Chaozhu Hu","doi":"10.1186/s13662-023-03795-z","DOIUrl":"https://doi.org/10.1186/s13662-023-03795-z","url":null,"abstract":"<p>In this paper, we establish some sufficient conditions for the existence of a random exponential attractor for a random dynamical system in a Banach space. As an application, we consider a stochastic reaction-diffusion equation with multiplicative noise. We show that the random dynamical system <span>(phi(t,omega))</span> generated by this stochastic reaction-diffusion equation is uniformly Fréchet differentiable on a positively invariant random set in <span>(L^{2p}(D))</span> and satisfies the conditions of the abstract result, then we obtain the existence of a random exponential attractor in <span>(L^{2p}(D))</span>, where <i>p</i> is the growth of the nonlinearity satisfying <span>(1&lt; pleq 3)</span>.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139079264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Casimir preserving stochastic Lie–Poisson integrators 卡西米尔保全随机李-泊松积分器
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2024-01-02 DOI: 10.1186/s13662-023-03796-y
Erwin Luesink, Sagy Ephrati, Paolo Cifani, Bernard Geurts
{"title":"Casimir preserving stochastic Lie–Poisson integrators","authors":"Erwin Luesink, Sagy Ephrati, Paolo Cifani, Bernard Geurts","doi":"10.1186/s13662-023-03796-y","DOIUrl":"https://doi.org/10.1186/s13662-023-03796-y","url":null,"abstract":"<p>Casimir preserving integrators for stochastic Lie–Poisson equations with Stratonovich noise are developed, extending Runge–Kutta Munthe-Kaas methods. The underlying Lie–Poisson structure is preserved along stochastic trajectories. A related stochastic differential equation on the Lie algebra is derived. The solution of this differential equation updates the evolution of the Lie–Poisson dynamics using the exponential map. The constructed numerical method conserves Casimir-invariants exactly, which is important for long time integration. This is illustrated numerically for the case of the stochastic heavy top and the stochastic sine-Euler equations.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rich dynamics of a delayed SIRS epidemic model with two-age structure and logistic growth 具有双年龄结构和逻辑增长的延迟 SIRS 流行病模型的丰富动态变化
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2023-12-08 DOI: 10.1186/s13662-023-03794-0
Dongxue Yan, Yu Cao
{"title":"Rich dynamics of a delayed SIRS epidemic model with two-age structure and logistic growth","authors":"Dongxue Yan, Yu Cao","doi":"10.1186/s13662-023-03794-0","DOIUrl":"https://doi.org/10.1186/s13662-023-03794-0","url":null,"abstract":"<p>This paper studies a two-age structured SIRS epidemic model with logistic growth of susceptible population and two-time delays. We simultaneously introduce two-time delays, i.e., the immunity and incubation periods, into this dynamic system and investigate their impact on different dynamic behaviors for the model. By means of the <span>(C_{0})</span>-semigroup theory, the model is transformed into a non-densely defined abstract Cauchy problem, and the condition of the existence and uniqueness of the endemic equilibrium is obtained. Following the spectral analysis, the characteristic equation technique, and the Hopf bifurcation theorem, we show that different combinations of the two delays perform a vital role in the instability/stability as well as the Hopf bifurcation results of equilibrium solutions. We numerically provide some graphical representations to check the main theoretical results and show the rich dynamics by varying the two delay parameters.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138561626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A central limit theorem for a classical gas 经典气体的中心极限定理
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2023-11-23 DOI: 10.1186/s13662-023-03793-1
Hans Zessin, Suren Poghosyan
{"title":"A central limit theorem for a classical gas","authors":"Hans Zessin, Suren Poghosyan","doi":"10.1186/s13662-023-03793-1","DOIUrl":"https://doi.org/10.1186/s13662-023-03793-1","url":null,"abstract":"<p>For a class of translation-invariant pair potentials <i>ϕ</i> in <span>((mathbb{R}^{d},zlambda ))</span> satisfying a stability and regularity condition, we choose <i>z</i> so small that the associated collection <span>(mathcal{ G}(phi,zlambda ))</span> of Gibbs processes contains at least the stationary process G, which is a Gibbs process in the sense of DLR and is given by the limiting Gibbs process with empty boundary conditions. Using an abstract version of the method of cluster expansions and Dobrushin’s approach to the central limit theorem, we present a central limit theorem for the particle numbers of G.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reproduction number projection for the COVID-19 pandemic COVID-19大流行的繁殖数预测
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2023-11-22 DOI: 10.1186/s13662-023-03792-2
Ryan Benjamin
{"title":"Reproduction number projection for the COVID-19 pandemic","authors":"Ryan Benjamin","doi":"10.1186/s13662-023-03792-2","DOIUrl":"https://doi.org/10.1186/s13662-023-03792-2","url":null,"abstract":"<p>The recently derived Hybrid-Incidence Susceptible-Transmissible-Removed (HI-STR) prototype is a deterministic compartment model for epidemics and an alternative to the Susceptible-Infected-Removed (SIR) model. The HI-STR predicts that pathogen transmission depends on host population characteristics including population size, population density and social behaviour common within that population.</p><p>The HI-STR prototype is applied to the ancestral Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2) to show that the original estimates of the Coronavirus Disease 2019 (COVID-19) basic reproduction number <span>(mathcal{R}_{0})</span> for the United Kingdom (UK) could have been projected onto the individual states of the United States of America (USA) prior to being detected in the USA.</p><p>The Imperial College London (ICL) group’s estimate of <span>(mathcal{R}_{0})</span> for the UK is projected onto each USA state. The difference between these projections and the ICL’s estimates for USA states is either not statistically significant on the paired Student <i>t</i>-test or not epidemiologically significant.</p><p>The SARS-CoV2 Delta variant’s <span>(mathcal{R}_{0})</span> is also projected from the UK to the USA to prove that projection can be applied to a Variant of Concern (VOC). Projection provides both a localised baseline for evaluating the implementation of an intervention policy and a mechanism for anticipating the impact of a VOC before local manifestation.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability and control in a stochastic model of malaria population dynamics 疟疾种群动态随机模型的稳定性和控制
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2023-11-15 DOI: 10.1186/s13662-023-03791-3
Peter J. Witbooi, Sibaliwe Maku Vyambwera, Garth J. van Schalkwyk, Grant E. Muller
{"title":"Stability and control in a stochastic model of malaria population dynamics","authors":"Peter J. Witbooi, Sibaliwe Maku Vyambwera, Garth J. van Schalkwyk, Grant E. Muller","doi":"10.1186/s13662-023-03791-3","DOIUrl":"https://doi.org/10.1186/s13662-023-03791-3","url":null,"abstract":"<p>This article proves a stability theorem for the disease-free equilibrium of a stochastic differential equations model of malaria disease dynamics. The theorem is formulated in terms of an invariant which is similar to the basic reproduction number of a related deterministic model. Compared to the deterministic model, stability of the disease-free equilibrium holds more generally for the stochastic model. The optimal control theory is applied to the stochastic model, revealing some important new insights. Theoretical results are illustrated by way of simulations.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation 基于再现核的伪谱法求解时间分数阶扩散波方程
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2022-08-23 DOI: 10.1186/s13662-022-03726-4
Mojtaba Fardi, Shrideh K. Qasem Al-Omari, Serkan Araci
{"title":"A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation","authors":"Mojtaba Fardi, Shrideh K. Qasem Al-Omari, Serkan Araci","doi":"10.1186/s13662-022-03726-4","DOIUrl":"https://doi.org/10.1186/s13662-022-03726-4","url":null,"abstract":"<p>In this paper, we focus on the development and study of the finite difference/pseudo-spectral method to obtain an approximate solution for the time-fractional diffusion-wave equation in a reproducing kernel Hilbert space. Moreover, we make use of the theory of reproducing kernels to establish certain reproducing kernel functions in the aforementioned reproducing kernel Hilbert space. Furthermore, we give an approximation to the time-fractional derivative term by applying the finite difference scheme by our proposed method. Over and above, we present an appropriate technique to derive the numerical solution of the given equation by utilizing a pseudo-spectral method based on the reproducing kernel. Then, we provide two numerical examples to support the accuracy and efficiency of our proposed method. Finally, we apply numerical experiments to calculate the quality of our approximation by employing discrete error norms.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Numerical analysis of a linear second-order finite difference scheme for space-fractional Allen–Cahn equations 空间分数阶Allen-Cahn方程线性二阶有限差分格式的数值分析
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2022-08-20 DOI: 10.1186/s13662-022-03725-5
Kai Wang, Jundong Feng, Hongbo Chen, Changling Xu
{"title":"Numerical analysis of a linear second-order finite difference scheme for space-fractional Allen–Cahn equations","authors":"Kai Wang, Jundong Feng, Hongbo Chen, Changling Xu","doi":"10.1186/s13662-022-03725-5","DOIUrl":"https://doi.org/10.1186/s13662-022-03725-5","url":null,"abstract":"<p>In this paper, we construct a new linear second-order finite difference scheme with two parameters for space-fractional Allen–Cahn equations. We first prove that the discrete maximum principle holds under reasonable constraints on time step size and coefficient of stabilized term. Secondly, we analyze the maximum-norm error. Thirdly, we can see that the proposed scheme is unconditionally energy-stable by defining the modified energy and selecting the appropriate parameters. Finally, two numerical examples are presented to verify the theoretical results.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators 应用不动点方法求解一类新算子的矩阵差分方程
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2022-08-17 DOI: 10.1186/s13662-022-03724-6
Hasanen A. Hammad, Mohamed Elmursi, Rashwan A. Rashwan, Hüseyin Işık
{"title":"Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators","authors":"Hasanen A. Hammad, Mohamed Elmursi, Rashwan A. Rashwan, Hüseyin Işık","doi":"10.1186/s13662-022-03724-6","DOIUrl":"https://doi.org/10.1186/s13662-022-03724-6","url":null,"abstract":"<p>The goal of this paper is to present a new class of operators satisfying the Prešić-type rational <i>η</i>-contraction condition in the setting of usual metric spaces. New fixed point results are also obtained for these operators. Our results generalize, extend, and unify many papers in this direction. Moreover, two examples are derived to support and document our theoretical results. Finally, to strengthen our paper and its contribution to applications, some convergence results for a class of matrix difference equations are investigated.</p>","PeriodicalId":49245,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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