Advances in Difference Equations最新文献_第4页

Asymptotic iteration method for solving Hahn difference equations. 求解Hahn差分方程的渐近迭代法。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-07-30 DOI: 10.1186/s13662-021-03511-9

Lucas MacQuarrie, Nasser Saad, Md Shafiqul Islam

{"title":"Asymptotic iteration method for solving Hahn difference equations.","authors":"Lucas MacQuarrie, Nasser Saad, Md Shafiqul Islam","doi":"10.1186/s13662-021-03511-9","DOIUrl":"https://doi.org/10.1186/s13662-021-03511-9","url":null,"abstract":"Hahn's difference operator <math><msub><mi>D</mi> <mrow><mi>q</mi> <mo>;</mo> <mi>w</mi></mrow> </msub> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mi>f</mi> <mo>(</mo> <mi>q</mi> <mi>x</mi> <mo>+</mo> <mi>w</mi> <mo>)</mo> <mo>-</mo> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo> <mo>/</mo> <mo>(</mo> <mo>(</mo> <mi>q</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mi>x</mi> <mo>+</mo> <mi>w</mi> <mo>)</mo></math> , <math><mi>q</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo></math> , <math><mi>w</mi> <mo>></mo> <mn>0</mn></math> , <math><mi>x</mi> <mo>≠</mo> <mi>w</mi> <mo>/</mo> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>q</mi> <mo>)</mo></math> is used to unify the recently established difference and q-asymptotic iteration methods (DAIM, qAIM). The technique is applied to solve the second-order linear Hahn difference equations. The necessary and sufficient conditions for polynomial solutions are derived and examined for the <math><mo>(</mo> <mi>q</mi> <mo>;</mo> <mi>w</mi> <mo>)</mo></math> -hypergeometric equation.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"354"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8570312/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39609666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Stability of an HTLV-HIV coinfection model with multiple delays and CTL-mediated immunity. 具有多重延迟和ctl介导免疫的HTLV-HIV共感染模型的稳定性

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-05-25 DOI: 10.1186/s13662-021-03416-7

N H AlShamrani

{"title":"Stability of an HTLV-HIV coinfection model with multiple delays and CTL-mediated immunity.","authors":"N H AlShamrani","doi":"10.1186/s13662-021-03416-7","DOIUrl":"https://doi.org/10.1186/s13662-021-03416-7","url":null,"abstract":"In the literature, several mathematical models have been formulated and developed to describe the within-host dynamics of either human immunodeficiency virus (HIV) or human T-lymphotropic virus type I (HTLV-I) monoinfections. In this paper, we formulate and analyze a novel within-host dynamics model of HTLV-HIV coinfection taking into consideration the response of cytotoxic T lymphocytes (CTLs). The uninfected <math><mi>CD</mi> <msup><mn>4</mn> <mo>+</mo></msup> <mi>T</mi></math> cells can be infected via HIV by two mechanisms, free-to-cell and infected-to-cell. On the other hand, the HTLV-I has two modes for transmission, (i) horizontal, via direct infected-to-cell touch, and (ii) vertical, by mitotic division of active HTLV-infected cells. It is well known that the intracellular time delays play an important role in within-host virus dynamics. In this work, we consider six types of distributed-time delays. We investigate the fundamental properties of solutions. Then, we calculate the steady states of the model in terms of threshold parameters. Moreover, we study the global stability of the steady states by using the Lyapunov method. We conduct numerical simulations to illustrate and support our theoretical results. In addition, we discuss the effect of multiple time delays on stability of the steady states of the system.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"270"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-021-03416-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38953292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

A mathematical model for the spread of COVID-19 and control mechanisms in Saudi Arabia. 沙特阿拉伯COVID-19传播和控制机制的数学模型。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-05-14 DOI: 10.1186/s13662-021-03410-z

Mostafa Bachar, Mohamed A Khamsi, Messaoud Bounkhel

{"title":"A mathematical model for the spread of COVID-19 and control mechanisms in Saudi Arabia.","authors":"Mostafa Bachar, Mohamed A Khamsi, Messaoud Bounkhel","doi":"10.1186/s13662-021-03410-z","DOIUrl":"https://doi.org/10.1186/s13662-021-03410-z","url":null,"abstract":"In this work, we develop and analyze a nonautonomous mathematical model for the spread of the new corona-virus disease (COVID-19) in Saudi Arabia. The model includes eight time-dependent compartments: the dynamics of low-risk <math><msub><mi>S</mi> <mi>L</mi></msub> </math> and high-risk <math><msub><mi>S</mi> <mi>M</mi></msub> </math> susceptible individuals; the compartment of exposed individuals E; the compartment of infected individuals (divided into two compartments, namely those of infected undiagnosed individuals <math><msub><mi>I</mi> <mi>U</mi></msub> </math> and the one consisting of infected diagnosed individuals <math><msub><mi>I</mi> <mi>D</mi></msub> </math> ); the compartment of recovered undiagnosed individuals <math><msub><mi>R</mi> <mi>U</mi></msub> </math> , that of recovered diagnosed <math><msub><mi>R</mi> <mi>D</mi></msub> </math> individuals, and the compartment of extinct Ex individuals. We investigate the persistence and the local stability including the reproduction number of the model, taking into account the control measures imposed by the authorities. We perform a parameter estimation over a short period of the total duration of the pandemic based on the COVID-19 epidemiological data, including the number of infected, recovered, and extinct individuals, in different time episodes of the COVID-19 spread.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"253"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-021-03410-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38996186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 12

Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. 具有垂直传播和媒体覆盖的新型确定性和随机SIR流行病模型的全球动力学。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-12-04 DOI: 10.1186/s13662-020-03145-3

Xiaodong Wang, Chunxia Wang, Kai Wang

引用次数: 3

A numerical solution by alternative Legendre polynomials on a model for novel coronavirus (COVID-19). 新型冠状病毒(COVID-19)模型的交替Legendre多项式数值解。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-09-25 DOI: 10.1186/s13662-020-02984-4

Elham Hashemizadeh, Mohammad Ali Ebadi

引用次数: 5

SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order. 利用分数阶Caputo导数建立新冠肺炎传播的SEIR流行病模型。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-09-14 DOI: 10.1186/s13662-020-02952-y

Shahram Rezapour, Hakimeh Mohammadi, Mohammad Esmael Samei

引用次数: 77

A fractional system of delay differential equation with nonsingular kernels in modeling hand-foot-mouth disease. 手足口病模型中具有非奇异核的时滞微分方程的分数阶系统。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-09-29 DOI: 10.1186/s13662-020-02993-3

Behzad Ghanbari

{"title":"A fractional system of delay differential equation with nonsingular kernels in modeling hand-foot-mouth disease.","authors":"Behzad Ghanbari","doi":"10.1186/s13662-020-02993-3","DOIUrl":"10.1186/s13662-020-02993-3","url":null,"abstract":"In this article, we examine a computational model to explore the prevalence of a viral infectious disease, namely hand-foot-mouth disease, which is more common in infants and children. The structure of this model consists of six sub-populations along with two delay parameters. Besides, by taking advantage of the Atangana-Baleanu fractional derivative, the ability of the model to justify different situations for the system has been improved. Discussions about the existence of the solution and its uniqueness are also included in the article. Subsequently, an effective numerical scheme has been employed to obtain several meaningful approximate solutions in various scenarios imposed on the problem. The sensitivity analysis of some existing parameters in the model has also been investigated through several numerical simulations. One of the advantages of the fractional derivative used in the model is the use of the concept of memory in maintaining the substantial properties of the understudied phenomena from the origin of time to the desired time. It seems that the tools used in this model are very powerful and can effectively simulate the expected theoretical conditions in the problem, and can also be recommended in modeling other computational models in infectious diseases.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"536"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7523494/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38553430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A stochastic SIR epidemic model with Lévy jump and media coverage. 具有lsamvy跃变和媒体报道的随机SIR流行病模型。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-02-12 DOI: 10.1186/s13662-020-2521-6

Yingfen Liu, Yan Zhang, Qingyun Wang

引用次数: 2

Bifurcation analysis of a SEIR epidemic system with governmental action and individual reaction. 具有政府作用和个体反应的SEIR流行病系统的分岔分析。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-10-01 DOI: 10.1186/s13662-020-02997-z

Abdelhamid Ajbar, Rubayyi T Alqahtani

引用次数: 5

Stochastic SIRC epidemic model with time-delay for COVID-19. 针对 COVID-19 的带有时间延迟的随机 SIRC 流行病模型。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-09-18 DOI: 10.1186/s13662-020-02964-8

F A Rihan, H J Alsakaji, C Rajivganthi

{"title":"Stochastic SIRC epidemic model with time-delay for COVID-19.","authors":"F A Rihan, H J Alsakaji, C Rajivganthi","doi":"10.1186/s13662-020-02964-8","DOIUrl":"10.1186/s13662-020-02964-8","url":null,"abstract":"Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number <math><msubsup><mi>R</mi> <mn>0</mn> <mi>s</mi></msubsup> </math> for the stochastic model which is smaller than <math><msub><mi>R</mi> <mn>0</mn></msub> </math> of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2020 1","pages":"502"},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7499021/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38411033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0