Advances in Difference Equations最新文献_第7页

Analysis of the stochastic model for predicting the novel coronavirus disease. 预测新型冠状病毒疾病的随机模型分析。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-10-08 DOI: 10.1186/s13662-020-03025-w

Ndolane Sene

引用次数: 0

Stochastic mathematical model for the spread and control of Corona virus. 冠状病毒传播与控制的随机数学模型。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-10-14 DOI: 10.1186/s13662-020-03029-6

Sultan Hussain, Anwar Zeb, Akhter Rasheed, Tareq Saeed

{"title":"Stochastic mathematical model for the spread and control of Corona virus.","authors":"Sultan Hussain, Anwar Zeb, Akhter Rasheed, Tareq Saeed","doi":"10.1186/s13662-020-03029-6","DOIUrl":"https://doi.org/10.1186/s13662-020-03029-6","url":null,"abstract":"This work is devoted to a stochastic model on the spread and control of corona virus (COVID-19), in which the total population of a corona infected area is divided into susceptible, infected, and recovered classes. In reality, the number of individuals who get disease, the number of deaths due to corona virus, and the number of recovered are stochastic, because nobody can tell the exact value of these numbers in the future. The models containing these terms must be stochastic. Such numbers are estimated and counted by a random process called a Poisson process (or birth process). We construct an SIR-type model in which the above numbers are stochastic and counted by a Poisson process. To understand the spread and control of corona virus in a better way, we first study the stability of the corresponding deterministic model, investigate the unique nonnegative strong solution and an inequality managing of which leads to control of the virus. After this, we pass to the stochastic model and show the existence of a unique strong solution. Next, we use the supermartingale approach to investigate a bound managing of which also leads to decrease of the number of infected individuals. Finally, we use the data of the COVOD-19 in USA to calculate the intensity of Poisson processes and verify our results.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-03029-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38609908","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: 8

Dynamics of an HIV model with cytotoxic T-lymphocyte memory. 具有细胞毒性t淋巴细胞记忆的HIV模型动力学。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-10-17 DOI: 10.1186/s13662-020-03035-8

Chunhua Liu, Lei Kong

引用次数: 0

Dynamics analysis of a delayed virus model with two different transmission methods and treatments. 两种不同传播方式和处理的延迟病毒模型动力学分析。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-01-06 DOI: 10.1186/s13662-019-2438-0

Tongqian Zhang, Junling Wang, Yuqing Li, Zhichao Jiang, Xiaofeng Han

引用次数: 325

Andronov-Hopf and Neimark-Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations. 时滞微分方程和差分方程中的Andronov-Hopf和neimmark - sacker分岔及其在疾病和动物种群模型中的应用。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-04-29 DOI: 10.1186/s13662-020-02646-5

Rachadawan Darlai, Elvin J Moore, Sanoe Koonprasert

{"title":"Andronov-Hopf and Neimark-Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations.","authors":"Rachadawan Darlai, Elvin J Moore, Sanoe Koonprasert","doi":"10.1186/s13662-020-02646-5","DOIUrl":"https://doi.org/10.1186/s13662-020-02646-5","url":null,"abstract":"In many areas, researchers might think that a differential equation model is required, but one might be forced to use an approximate difference equation model if data is only available at discrete points in time. In this paper, a detailed comparison is given of the behavior of continuous and discrete models for two representative time-delay models, namely a model for HIV and an extended logistic growth model. For each model, there are seven different time-delay versions because there are seven different positions to include time delays. For the seven different time-delay versions of each model, proofs are given of necessary and sufficient conditions for the existence and stability of equilibrium points and for the existence of Andronov-Hopf bifurcations in the differential equations and Neimark-Sacker bifurcations in the difference equations. We show that only five of the seven time-delay versions have bifurcations and that all bifurcation versions have supercritical limit cycles with one having a repelling cycle and four having attracting cycles. Numerical simulations are used to illustrate the analytical results and to show that critical times for Neimark-Sacker bifurcations are less than critical times for Andronov-Hopf bifurcations but converge to them as the time step of the discretization tends to zero.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-02646-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37959962","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

On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach. 冠状病毒(2019-nCov)最优控制数学模型研究数值方法。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-09-25 DOI: 10.1186/s13662-020-02982-6

N H Sweilam, S M Al-Mekhlafi, A O Albalawi, D Baleanu

引用次数: 1

Analysis of Caputo fractional-order model for COVID-19 with lockdown. 新型冠状病毒肺炎的Caputo分数阶模型分析

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-08-03 DOI: 10.1186/s13662-020-02853-0

Idris Ahmed, Isa Abdullahi Baba, Abdullahi Yusuf, Poom Kumam, Wiyada Kumam

{"title":"Analysis of Caputo fractional-order model for COVID-19 with lockdown.","authors":"Idris Ahmed, Isa Abdullahi Baba, Abdullahi Yusuf, Poom Kumam, Wiyada Kumam","doi":"10.1186/s13662-020-02853-0","DOIUrl":"https://doi.org/10.1186/s13662-020-02853-0","url":null,"abstract":"One of the control measures available that are believed to be the most reliable methods of curbing the spread of coronavirus at the moment if they were to be successfully applied is lockdown. In this paper a mathematical model of fractional order is constructed to study the significance of the lockdown in mitigating the virus spread. The model consists of a system of five nonlinear fractional-order differential equations in the Caputo sense. In addition, existence and uniqueness of solutions for the fractional-order coronavirus model under lockdown are examined via the well-known Schauder and Banach fixed theorems technique, and stability analysis in the context of Ulam-Hyers and generalized Ulam-Hyers criteria is discussed. The well-known and effective numerical scheme called fractional Euler method has been employed to analyze the approximate solution and dynamical behavior of the model under consideration. It is worth noting that, unlike many studies recently conducted, dimensional consistency has been taken into account during the fractionalization process of the classical model.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-02853-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38297077","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: 74

Dynamics of a fractional order mathematical model for COVID-19 epidemic. COVID-19 流行病分数阶数学模型的动力学。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-08-14 DOI: 10.1186/s13662-020-02873-w

Zizhen Zhang, Anwar Zeb, Oluwaseun Francis Egbelowo, Vedat Suat Erturk

{"title":"Dynamics of a fractional order mathematical model for COVID-19 epidemic.","authors":"Zizhen Zhang, Anwar Zeb, Oluwaseun Francis Egbelowo, Vedat Suat Erturk","doi":"10.1186/s13662-020-02873-w","DOIUrl":"10.1186/s13662-020-02873-w","url":null,"abstract":"In this work, we formulate and analyze a new mathematical model for COVID-19 epidemic with isolated class in fractional order. This model is described by a system of fractional-order differential equations model and includes five classes, namely, S (susceptible class), E (exposed class), I (infected class), Q (isolated class), and R (recovered class). Dynamics and numerical approximations for the proposed fractional-order model are studied. Firstly, positivity and boundedness of the model are established. Secondly, the basic reproduction number of the model is calculated by using the next generation matrix approach. Then, asymptotic stability of the model is investigated. Lastly, we apply the adaptive predictor-corrector algorithm and fourth-order Runge-Kutta (RK4) method to simulate the proposed model. Consequently, a set of numerical simulations are performed to support the validity of the theoretical results. The numerical simulations indicate that there is a good agreement between theoretical results and numerical ones.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7427275/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38297526","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

Stochastic dynamics in a delayed epidemic system with Markovian switching and media coverage. 具有马尔可夫切换和媒介覆盖的延迟流行病系统的随机动力学。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-08-26 DOI: 10.1186/s13662-020-02894-5

Chao Liu, Jane Heffernan

引用次数: 1

Modeling the effects of contact tracing on COVID-19 transmission. 接触者追踪对COVID-19传播影响的建模

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-09-21 DOI: 10.1186/s13662-020-02972-8

Ali Traoré, Fourtoua Victorien Konané

引用次数: 1