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Mathematical modelling of the impact of testing, treatment and control of HIV transmission in Kenya 肯尼亚检测、治疗和控制艾滋病毒传播影响的数学模型
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1475590
E. Omondi, Rachel Waema Mbogo, L. Luboobi
{"title":"Mathematical modelling of the impact of testing, treatment and control of HIV transmission in Kenya","authors":"E. Omondi, Rachel Waema Mbogo, L. Luboobi","doi":"10.1080/25742558.2018.1475590","DOIUrl":"https://doi.org/10.1080/25742558.2018.1475590","url":null,"abstract":"Abstract The control of spread of HIV to reduce its effects on a population is an important role of public health. HIV testing and counselling (HTC) and eventual enrolment of infected individuals on anti retro-viral treatment (ART) as soon as possible to reduce the risk of dying is currently the main intervention against HIV. Mathematical models can be used to study the effects of HIV prevention, testing and treatment with ART on HIV patients. In this study, we employ a deterministic model to provide a quantification of HIV prevention, testing and treatment with ART as public health measurements in the fight against HIV infection. Lyapunov function has been used to derive a condition that ensures that the model system is globally asymptotically stable when R0 is less than unity. Through sensitivity analysis, we determine the relative importance of model parameters for disease transmission. The sensitivity analysis results suggest that the effective contact rates are mechanisms fuelling HIV epidemic proliferation while ART efficacy reduces the incidence. The model is fitted to HIV surveillance data obtained from world in data website. Although the results show a high proportion of individuals with HIV in Kenya, the incidence curve is indicative of a declining HIV infection and settling at an endemic steady state. The results are suggestive of the need to promote preventive mechanism against the occurrence of new infections. Moreover, the results show that the combination of several control mechanisms would significantly reduce the spread of the disease, if we maintain the level of each control high.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1475590","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45766623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 25
Hermite–Hadamard’s inequality and Cauchy-type mean operators for positive -semigroups 正半群的Hermite-Hadamard不等式与cauchy型平均算子
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/23311835.2018.1446248
G. Aslam, M. Anwar
{"title":"Hermite–Hadamard’s inequality and Cauchy-type mean operators for positive -semigroups","authors":"G. Aslam, M. Anwar","doi":"10.1080/23311835.2018.1446248","DOIUrl":"https://doi.org/10.1080/23311835.2018.1446248","url":null,"abstract":"Abstract Hermite–Hadamard’s-type inequality is derived using superquadratic maps for positive operator semigroups. A methodical procedure was adopted to obtain the corresponding mean operators.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1446248","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43040303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction 修正
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2019.1519348
Anonymous
{"title":"Correction","authors":"Anonymous","doi":"10.1080/25742558.2019.1519348","DOIUrl":"https://doi.org/10.1080/25742558.2019.1519348","url":null,"abstract":"","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1519348","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44667575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On (Λ, θ)-open sets in topological spaces 论(Λ， θ)拓扑空间中的开集
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1461530
C. Boonpok, C. Viriyapong
{"title":"On (Λ, θ)-open sets in topological spaces","authors":"C. Boonpok, C. Viriyapong","doi":"10.1080/25742558.2018.1461530","DOIUrl":"https://doi.org/10.1080/25742558.2018.1461530","url":null,"abstract":"ABSTRACT This article deals with the notions of -open, -open, -open, -open, and -open sets. Several properties and the relationships between these concepts are discussed. Some characterizations of -extremally disconnected spaces and -hyperconnected spaces are investigated.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1461530","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46081171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 21
Existence and stability for fractional parabolic integro-partial differential equations with fractional Brownian motion and nonlocal condition 具有分数布朗运动和非局部条件的分数抛物型积分偏微分方程的存在性和稳定性
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1460030
M. El-Borai, K. El-Nadi, H. Ahmed, H. El-Owaidy, A. Ghanem, R. Sakthivel
{"title":"Existence and stability for fractional parabolic integro-partial differential equations with fractional Brownian motion and nonlocal condition","authors":"M. El-Borai, K. El-Nadi, H. Ahmed, H. El-Owaidy, A. Ghanem, R. Sakthivel","doi":"10.1080/25742558.2018.1460030","DOIUrl":"https://doi.org/10.1080/25742558.2018.1460030","url":null,"abstract":"In this paper, a nonlinear fractional parabolic stochastic integro-partial differential equations with nonlocal effects driven by a fractional Brownian motion is considered. In particular, first we have formulated the suitable solution form for the fractional partial differential equations with nonlocal effects driven by fractional Brownian motion using a parabolic transform. Next, the existence and uniqueness of solutions are obtained for the fractional stochastic partial differential equations without any restrictions on the characteristic forms when the Hurst parameter of the fractional Brownian motion is less than half. Further, we investigate the stability of the solution for the considered problem. The required result is established by means of standard Picard’s iteration.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1460030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42840874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
Non-linear unit root testing with arctangent trend: Simulation and applications in finance 具有反正切趋势的非线性单位根检验：仿真及其在金融中的应用
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1458555
Deniz Ilalan, Özgür Özel
{"title":"Non-linear unit root testing with arctangent trend: Simulation and applications in finance","authors":"Deniz Ilalan, Özgür Özel","doi":"10.1080/25742558.2018.1458555","DOIUrl":"https://doi.org/10.1080/25742558.2018.1458555","url":null,"abstract":"Abstract We consider arctangent as the logistic function and compute the asymptotic critical values of the related non-linear unit root test via Monte Carlo simulation. While doing so, we got inspiration from some pioneering articles and use first-order Taylor approximation. We observe that this newly proposed test exhibits higher power than some well-known linear and non-linear tests. We apply our test to some stock indexes and find out that a non-linear arctangent trend can be at stage, rather than a linear unit root process.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1458555","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45953658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical model of malaria transmission dynamics with distributed delay and a wide class of nonlinear incidence rates 具有分布延迟和一类非线性发病率的疟疾传播动力学数学模型
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1564531
Ousmane Koutou, B. Traoré, B. Sangaré
{"title":"Mathematical model of malaria transmission dynamics with distributed delay and a wide class of nonlinear incidence rates","authors":"Ousmane Koutou, B. Traoré, B. Sangaré","doi":"10.1080/25742558.2018.1564531","DOIUrl":"https://doi.org/10.1080/25742558.2018.1564531","url":null,"abstract":"Abstract Generally, the infection process of most vector-borne diseases involves a latent period in both human hosts and vectors. With regards to other publications, Tian and Song have recently proposed an SIR-SI model to analyze the effects of the incubation period on a vector-borne disease with nonlinear transmission rate. But they were silent on the fact that the partially immune individuals are slightly infective to mosquitoes. So, by considering that the partially immune individuals remain slightly infective to mosquitoes, a similar work has been done in this paper for malaria global transmission dynamics following an SIRS-SI pattern. The basic reproduction ratio has been calculated using the next-generation matrix method. Furthermore, using the characteristic equations and inequality analytical techniques, conditions are given under which the system exhibits threshold behavior as follows: when R0 < 1, the disease-free equilibrium is globally asymptotically stable meaning that the disease will eventually die out; and the unique endemic equilibrium is globally asymptotically stable when R0 > 1 meaning that the disease will persist. Finally, some numerical simulations have been performed to illustrate our theoretical results.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1564531","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41651567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
On asymptotic stability of a class of time–delay systems 一类时滞系统的渐近稳定性
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1473709
Serbun Ufuk Değer, Y. Bolat
{"title":"On asymptotic stability of a class of time–delay systems","authors":"Serbun Ufuk Değer, Y. Bolat","doi":"10.1080/25742558.2018.1473709","DOIUrl":"https://doi.org/10.1080/25742558.2018.1473709","url":null,"abstract":"Abstract In this paper, we give some new necessary and sufficient conditions for the asymptotic stability of a class of time–delay systems of the form where is a real number, is a real constant matrix, and , are positive numbers such that .","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1473709","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43777434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Periodic wave shock solutions of Burgers equations Burgers方程的周期波冲击解
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1463597
Saida Bendaas
{"title":"Periodic wave shock solutions of Burgers equations","authors":"Saida Bendaas","doi":"10.1080/25742558.2018.1463597","DOIUrl":"https://doi.org/10.1080/25742558.2018.1463597","url":null,"abstract":"In this paper, we present an new approach for the study of Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parameter and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock-type solution for the cauchy problem of the inviscid burgers equation. The results are formulated in classical mathematics and proved with infinitesimal techniques of nonstandard analysis.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1463597","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48683682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
On the relationship between the turning and singular points in Sturm–Liouville equations Sturm–Liouville方程中转向点与奇异点的关系
Cogent mathematics & statistics Pub Date : 2018-01-01 DOI: 10.1080/25742558.2018.1464880
Y. Khalili, A. Neamaty
{"title":"On the relationship between the turning and singular points in Sturm–Liouville equations","authors":"Y. Khalili, A. Neamaty","doi":"10.1080/25742558.2018.1464880","DOIUrl":"https://doi.org/10.1080/25742558.2018.1464880","url":null,"abstract":"Abstract In this article, we present some results about the Sturm–Liouville equation with turning points and singularities and transform them to each other. By applying a change of a variable, we can transform the differential equation with a turning point to the differential equation with a singularity. Also we will prove that a differential equation with a singularity will be transformed to a differential equation with a turning point in some cases.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1464880","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45892220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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