Advances in Difference Equations最新文献_第9页

Moment closure of infectious diseases model on heterogeneous metapopulation network. 异质元种群网络上传染病模型的矩闭性。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2018-01-01 Epub Date: 2018-09-24 DOI: 10.1186/s13662-018-1801-x

Shanshan Feng, Zhen Jin

{"title":"Moment closure of infectious diseases model on heterogeneous metapopulation network.","authors":"Shanshan Feng, Zhen Jin","doi":"10.1186/s13662-018-1801-x","DOIUrl":"https://doi.org/10.1186/s13662-018-1801-x","url":null,"abstract":"The global transmission of infectious diseases poses huge threats to human. Traditional heterogeneous mean-field models on metapopulation networks ignore the heterogeneity of individuals who are in different disease states in subpopulations with the same degree, resulting in inaccuracy in predicting the spread of disease. In this paper, we take heterogeneity of susceptible and infectious individuals in subpopulations with the same degree into account, and propose a deterministic unclosed general model according to Markov process on metapopulation networks to curve the global transmission of diseases precisely. Then we make the general model closed by putting forward two common assumptions: a two-dimensional constant distribution and a two-dimensional log-normal distribution, where the former is equivalent to the heterogeneous mean-field model, and the latter is a system of weighted ordinary differential equations. Further we make a stability analysis for two closed models and illustrate the results by numerical simulations. Next, we conduct a series of numerical simulations and stochastic simulations. Results indicate that our general model extends and optimizes the mean-field model. Finally, we investigate the impacts of total mobility rate on disease transmission and find that timely and comprehensive travel restriction in the early stage is an effective prevention and control of infectious diseases.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-018-1801-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37784249","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: 5

Entire solutions for a reaction-diffusion equation with doubly degenerate nonlinearity. 一类双退化非线性反应扩散方程的全解。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2018-01-01 Epub Date: 2018-04-24 DOI: 10.1186/s13662-018-1606-y

Rui Yan, Xiaocui Li

引用次数: 4

A discrete-time analog for coupled within-host and between-host dynamics in environmentally driven infectious disease. 环境驱动传染病中宿主内和宿主间耦合动力学的离散时间模拟。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2018-01-01 Epub Date: 2018-02-26 DOI: 10.1186/s13662-018-1522-1

Buyu Wen, Jianpeng Wang, Zhidong Teng

{"title":"A discrete-time analog for coupled within-host and between-host dynamics in environmentally driven infectious disease.","authors":"Buyu Wen, Jianpeng Wang, Zhidong Teng","doi":"10.1186/s13662-018-1522-1","DOIUrl":"https://doi.org/10.1186/s13662-018-1522-1","url":null,"abstract":"In this paper, we establish a discrete-time analog for coupled within-host and between-host systems for an environmentally driven infectious disease with fast and slow two time scales by using the non-standard finite difference scheme. The system is divided into a fast time system and a slow time system by using the idea of limit equations. For the fast system, the positivity and boundedness of the solutions, the basic reproduction number and the existence for infection-free and unique virus infectious equilibria are obtained, and the threshold conditions on the local stability of equilibria are established. In the slow system, except for the positivity and boundedness of the solutions, the existence for disease-free, unique endemic and two endemic equilibria are obtained, and the sufficient conditions on the local stability for disease-free and unique endemic equilibria are established. To return to the coupling system, the local stability for the virus- and disease-free equilibrium, and virus infectious but disease-free equilibrium is established. The numerical examples show that an endemic equilibrium is locally asymptotically stable and the other one is unstable when there are two endemic equilibria.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-018-1522-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37784248","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: 6

Global exponential stability of Markovian jumping stochastic impulsive uncertain BAM neural networks with leakage, mixed time delays, and α-inverse Hölder activation functions. 具有泄漏、混合时间延迟和 α 逆霍尔德激活函数的马尔可夫跳跃随机脉冲不确定 BAM 神经网络的全局指数稳定性。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2018-01-01 Epub Date: 2018-03-27 DOI: 10.1186/s13662-018-1553-7

C Maharajan, R Raja, Jinde Cao, G Ravi, G Rajchakit

引用次数: 0

A multi-regions discrete-time epidemic model with a travel-blocking vicinity optimal control approach on patches. 基于旅行阻塞邻近最优控制方法的多区域离散时间流行病模型。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2017-01-01 Epub Date: 2017-04-26 DOI: 10.1186/s13662-017-1168-4

Omar Zakary, Mostafa Rachik, Ilias Elmouki, Samih Lazaiz

{"title":"A multi-regions discrete-time epidemic model with a travel-blocking vicinity optimal control approach on patches.","authors":"Omar Zakary, Mostafa Rachik, Ilias Elmouki, Samih Lazaiz","doi":"10.1186/s13662-017-1168-4","DOIUrl":"10.1186/s13662-017-1168-4","url":null,"abstract":"We study, in this paper, infection dynamics when an epidemic emerges to many regions which are connected with their neighbors by any kind of anthropological movement. For this, we devise a multi-regions discrete-time model with the three classical SIR compartments, describing the spatial-temporal behaviors of homogenous susceptible, infected and removed populations. We suppose a large geographical domain, presented by a grid of colored cells, to exhibit at each instant i the spatial propagation of an epidemic which affects its different parts or sub-domains that we call here cells or regions. In order to minimize the number of infected individuals in some regions, we suggest an optimal control approach based on a travel-blocking vicinity strategy which aims to control a group of cells, or a patch, by restricting movements of infected people coming from its neighboring cells. We apply a discrete version of Pontryagin's maximum principle to state the necessary conditions and characterization of the travel-blocking optimal controls. We provide cellular simulations based on discrete progressive-regressive iterative schemes associated with the obtained multi-points boundary value problems. For illustrating the modeling and optimal control approaches, we consider an example of 100 regions.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-017-1168-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37784247","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

Entire functions sharing a small function with their two difference operators. 整个函数与它们的两个差分运算符共享一个小函数。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2017-01-01 Epub Date: 2017-08-01 DOI: 10.1186/s13662-017-1281-4

Feng Lü, Yanfeng Wang, Junfeng Xu

引用次数: 0

Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay. 具有泄漏延迟的马尔可夫跳变离散时间BAM神经网络的增强鲁棒有限时间无源性。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2017-01-01 Epub Date: 2017-10-10 DOI: 10.1186/s13662-017-1378-9

C Sowmiya, R Raja, Jinde Cao, G Rajchakit, Ahmed Alsaedi

引用次数: 43

Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence. 具有一般非线性发病率的一类离散 SEIRS 流行病模型的全局动力学。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2016-01-01 Epub Date: 2016-05-06 DOI: 10.1186/s13662-016-0846-y

Xiaolin Fan, Lei Wang, Zhidong Teng

引用次数: 0

Global dynamics for discrete-time analog of viral infection model with nonlinear incidence and CTL immune response. 具有非线性发生率和CTL免疫应答的病毒感染模型离散时间模拟的全局动力学。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2016-01-01 Epub Date: 2016-05-23 DOI: 10.1186/s13662-016-0862-y

Jianpeng Wang, Zhidong Teng, Hui Miao

{"title":"Global dynamics for discrete-time analog of viral infection model with nonlinear incidence and CTL immune response.","authors":"Jianpeng Wang, Zhidong Teng, Hui Miao","doi":"10.1186/s13662-016-0862-y","DOIUrl":"https://doi.org/10.1186/s13662-016-0862-y","url":null,"abstract":"In this paper, a discrete-time analog of a viral infection model with nonlinear incidence and CTL immune response is established by using the Micken non-standard finite difference scheme. The two basic reproduction numbers <math><msub><mi>R</mi> <mn>0</mn></msub> </math> and <math><msub><mi>R</mi> <mn>1</mn></msub> </math> are defined. The basic properties on the positivity and boundedness of solutions and the existence of the virus-free, the no-immune, and the infected equilibria are established. By using the Lyapunov functions and linearization methods, the global stability of the equilibria for the model is established. That is, when <math><msub><mi>R</mi> <mn>0</mn></msub> <mo>≤</mo> <mn>1</mn></math> then the virus-free equilibrium is globally asymptotically stable, and under the additional assumption <math><mo>(</mo> <msub><mi>A</mi> <mn>4</mn></msub> <mo>)</mo></math> when <math><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></math> and <math><msub><mi>R</mi> <mn>1</mn></msub> <mo>≤</mo> <mn>1</mn></math> then the no-immune equilibrium is globally asymptotically stable and when <math><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></math> and <math><msub><mi>R</mi> <mn>1</mn></msub> <mo>></mo> <mn>1</mn></math> then the infected equilibrium is globally asymptotically stable. Furthermore, the numerical simulations show that even if assumption <math><mo>(</mo> <msub><mi>A</mi> <mn>4</mn></msub> <mo>)</mo></math> does not hold, the no-immune equilibrium and the infected equilibrium also may be globally asymptotically stable.","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-016-0862-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37784246","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: 31

Global stability of the endemic equilibrium of a discrete SIR epidemic model. 离散SIR流行病模型地方性平衡的全局稳定性。

IF 4.1 3区数学

Advances in Difference Equations Pub Date : 2013-01-01 Epub Date: 2013-02-25 DOI: 10.1186/1687-1847-2013-42

Xia Ma, Yicang Zhou, Hui Cao

引用次数: 36