Pub Date : 2018-01-01DOI: 10.1080/23311835.2018.1429700
E. Omondi, F. Nyabadza, R. Smith
Onchocerciasis (river blindness) is a disease spread from black flies to humans. This disease is responsible for chronic morbidity in sub-Saharan Africa. The principal strategy to achieve onchocerciasis elimination is through mass drug administration with ivermectin, a drug that is effective in the short term but wanes quickly. Ivermectin kills the skin-dwelling microfilariae. It may also kill and/or sterilize adult worms. This treatment protocol occurs bi-annually. Consequently, a system of impulsive differential equations is introduced to model both fixed and non-fixed mass drug administration with ivermectin. We determine the threshold for the proportion of treated individuals that reduces the infection in the human population. In the absence of impulsive mass drug administration with ivermectin, we determine the threshold for eradication and carry out stability analysis. The sensitivity analysis results reveal that the disease is unlikely to be eradicated without extremely low transmission levels or strong vector control. If treatment is included, then treatment at fixed intervals can control but not eradicate the disease. Treatment at non-fixed intervals may produce bursts of infection. Thus, bi-annual mass drug administration with ivermectin that is tailored to eradicate onchocerciasis, can only lead to significant reduction of onchocerciasis. However, to achieve 2020/2025 onchocerciasis elimination goals set by World Health Organization, the human-vector contact should be sufficiently reduced and vector control programmes implemented to supplement an intensive and effective mass drug administration with ivermectin.
{"title":"Modelling the impact of mass administration of ivermectin in the treatment of onchocerciasis (river blindness)","authors":"E. Omondi, F. Nyabadza, R. Smith","doi":"10.1080/23311835.2018.1429700","DOIUrl":"https://doi.org/10.1080/23311835.2018.1429700","url":null,"abstract":"Onchocerciasis (river blindness) is a disease spread from black flies to humans. This disease is responsible for chronic morbidity in sub-Saharan Africa. The principal strategy to achieve onchocerciasis elimination is through mass drug administration with ivermectin, a drug that is effective in the short term but wanes quickly. Ivermectin kills the skin-dwelling microfilariae. It may also kill and/or sterilize adult worms. This treatment protocol occurs bi-annually. Consequently, a system of impulsive differential equations is introduced to model both fixed and non-fixed mass drug administration with ivermectin. We determine the threshold for the proportion of treated individuals that reduces the infection in the human population. In the absence of impulsive mass drug administration with ivermectin, we determine the threshold for eradication and carry out stability analysis. The sensitivity analysis results reveal that the disease is unlikely to be eradicated without extremely low transmission levels or strong vector control. If treatment is included, then treatment at fixed intervals can control but not eradicate the disease. Treatment at non-fixed intervals may produce bursts of infection. Thus, bi-annual mass drug administration with ivermectin that is tailored to eradicate onchocerciasis, can only lead to significant reduction of onchocerciasis. However, to achieve 2020/2025 onchocerciasis elimination goals set by World Health Organization, the human-vector contact should be sufficiently reduced and vector control programmes implemented to supplement an intensive and effective mass drug administration with ivermectin.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1429700","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44960025","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}
Pub Date : 2018-01-01DOI: 10.1080/25742558.2018.1509430
L. Sassanapitax, S. Pianskool, A. Siraworakun
Abstract In this article, we introduce another standard form of linear preservers. This new standard form provides characterizations of the linear transformations on the set of bisymmetric matrices with zero diagonal and zero antidiagonal over antinegative semirings without zero divisors which preserve some sort of term ranks and preserve the matrix that can be determined as the greatest one. The numbers of all possible linear transformations satisfying each condition are also obtained.
{"title":"Term rank preservers of bisymmetric matrices over semirings","authors":"L. Sassanapitax, S. Pianskool, A. Siraworakun","doi":"10.1080/25742558.2018.1509430","DOIUrl":"https://doi.org/10.1080/25742558.2018.1509430","url":null,"abstract":"Abstract In this article, we introduce another standard form of linear preservers. This new standard form provides characterizations of the linear transformations on the set of bisymmetric matrices with zero diagonal and zero antidiagonal over antinegative semirings without zero divisors which preserve some sort of term ranks and preserve the matrix that can be determined as the greatest one. The numbers of all possible linear transformations satisfying each condition are also obtained.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1509430","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41641299","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}
Pub Date : 2018-01-01DOI: 10.1080/25742558.2018.1492887
Monrudee Sirivoravit, U. Leerawat
Abstract In this paper, we study the derangement of 2n persons sitting 2 rows and n columns. In how many ways can the persons rearrange their seating in accordance with the following condition. Each seat is located by one person and reoccupied by another person and each person moves to a horizontal or a vertical or a diagonal neighboring seat. We establish the system of recurrence relations for the solution of this problem and provide the solution of the system of recurrence relations.
{"title":"The 2 x n seating derangements","authors":"Monrudee Sirivoravit, U. Leerawat","doi":"10.1080/25742558.2018.1492887","DOIUrl":"https://doi.org/10.1080/25742558.2018.1492887","url":null,"abstract":"Abstract In this paper, we study the derangement of 2n persons sitting 2 rows and n columns. In how many ways can the persons rearrange their seating in accordance with the following condition. Each seat is located by one person and reoccupied by another person and each person moves to a horizontal or a vertical or a diagonal neighboring seat. We establish the system of recurrence relations for the solution of this problem and provide the solution of the system of recurrence relations.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1492887","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48172991","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}
Pub Date : 2018-01-01DOI: 10.1080/25742558.2018.1477543
Grant Keady, N. Khajohnsaksumeth, N. Khajohnsaksumeth, B. Wiwatanapataphee
Abstract Any function from onto which is decreasing and convex has an inverse which is positive, decreasing and convex. When has some form of generalized convexity we determine additional convexity properties inherited by . When is positive, decreasing and -convex, its inverse is -convex. Related properties which pertain when is a Stieltjes function are developed. The results are illustrated with the Stieltjes function via a transcendental equation.
{"title":"On functions and inverses, both positive, decreasing and convex: And Stieltjes functions","authors":"Grant Keady, N. Khajohnsaksumeth, N. Khajohnsaksumeth, B. Wiwatanapataphee","doi":"10.1080/25742558.2018.1477543","DOIUrl":"https://doi.org/10.1080/25742558.2018.1477543","url":null,"abstract":"Abstract Any function from onto which is decreasing and convex has an inverse which is positive, decreasing and convex. When has some form of generalized convexity we determine additional convexity properties inherited by . When is positive, decreasing and -convex, its inverse is -convex. Related properties which pertain when is a Stieltjes function are developed. The results are illustrated with the Stieltjes function via a transcendental equation.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1477543","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48306822","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}
Pub Date : 2018-01-01DOI: 10.1080/23311835.2018.1559456
M. Ramezani, H. Ramezani
Abstract By using the idea of Pata [V. Pata, A fixed point theorem in metric spaces. J. Fixed Point Theory Appl. 10 (2011) 299–305.] we establish a new common fixed point theorem and as an application, we prove the existence and uniqueness of common solutions for a class of system of functional equations arising in dynamic programming.
摘要利用Pata的思想[V.Pata，度量空间中的不动点定理。J.fixed point Theory Appl.10（2011）299–305.]我们建立了一个新的公共不动点定理，并作为一个应用，证明了动态规划中一类函数方程组公共解的存在性和唯一性。
{"title":"A new generalized contraction and its application in dynamic programming","authors":"M. Ramezani, H. Ramezani","doi":"10.1080/23311835.2018.1559456","DOIUrl":"https://doi.org/10.1080/23311835.2018.1559456","url":null,"abstract":"Abstract By using the idea of Pata [V. Pata, A fixed point theorem in metric spaces. J. Fixed Point Theory Appl. 10 (2011) 299–305.] we establish a new common fixed point theorem and as an application, we prove the existence and uniqueness of common solutions for a class of system of functional equations arising in dynamic programming.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1559456","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49265346","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}
Pub Date : 2018-01-01DOI: 10.1080/25742558.2018.1493761
B. Mohammadi, Farhan Golkarmanesh, Vahid Parvaneh
Abstract In this paper, motivated by the recent work [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537] some generalized nonlinear contractive conditions via implicit functions and α-admissible pairs of multi-valued mappings in the setting of b-metric like spaces have been introduced. Some common fixed point results for such mappings in this framework have been provided. Then, some corollaries and consequences for our obtained results are given. Our results are the multi-valued versions of [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537]. An example also is provided to support our obtained results. The presented results generalize and extend some earlier results in the literature.
{"title":"Common fixed point results via implicit contractions for multi-valued mappings on b-metric like spaces","authors":"B. Mohammadi, Farhan Golkarmanesh, Vahid Parvaneh","doi":"10.1080/25742558.2018.1493761","DOIUrl":"https://doi.org/10.1080/25742558.2018.1493761","url":null,"abstract":"Abstract In this paper, motivated by the recent work [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537] some generalized nonlinear contractive conditions via implicit functions and α-admissible pairs of multi-valued mappings in the setting of b-metric like spaces have been introduced. Some common fixed point results for such mappings in this framework have been provided. Then, some corollaries and consequences for our obtained results are given. Our results are the multi-valued versions of [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537]. An example also is provided to support our obtained results. The presented results generalize and extend some earlier results in the literature.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1493761","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48186533","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}
Pub Date : 2018-01-01DOI: 10.1080/23311835.2018.1431092
Sheng-hong Li, Quanxin Zhu
Abstract In this paper, the probability density and almost sure asymptotic stability of the coupled Van der Pol oscillator system under the noise excitations are investigated. Through the stochastic averaging method and slow changing process theorem, averaged Fokker–Planck–Kolmogorov equation and exact solution of the dynamical system are obtained. Especially, the marginal density functions of the system excited by the additive white noises are derived. Then, the effects of coupled parameters and noise parameters on the marginal density functions are discussed through the numerical figures. In addition, the almost sure asymptotic stability under the parametric excitation by means of the maximal Lyapunov exponent is studied, and the stable demarcation points about noise intensity are presented.
摘要本文研究了耦合Van der Pol振荡系统在噪声激励下的概率密度和几乎肯定渐近稳定性。通过随机平均法和慢变过程定理，得到了动力系统的平均Fokker–Planck–Kolmogorov方程和精确解。特别推导了系统在加性白噪声激励下的边缘密度函数。然后，通过数值计算讨论了耦合参数和噪声参数对边缘密度函数的影响。此外，利用最大李雅普诺夫指数研究了参数激励下的几乎肯定渐近稳定性，并给出了噪声强度的稳定分界点。
{"title":"Probability density and stochastic stability for the coupled Van der Pol oscillator system","authors":"Sheng-hong Li, Quanxin Zhu","doi":"10.1080/23311835.2018.1431092","DOIUrl":"https://doi.org/10.1080/23311835.2018.1431092","url":null,"abstract":"Abstract In this paper, the probability density and almost sure asymptotic stability of the coupled Van der Pol oscillator system under the noise excitations are investigated. Through the stochastic averaging method and slow changing process theorem, averaged Fokker–Planck–Kolmogorov equation and exact solution of the dynamical system are obtained. Especially, the marginal density functions of the system excited by the additive white noises are derived. Then, the effects of coupled parameters and noise parameters on the marginal density functions are discussed through the numerical figures. In addition, the almost sure asymptotic stability under the parametric excitation by means of the maximal Lyapunov exponent is studied, and the stable demarcation points about noise intensity are presented.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1431092","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48734868","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}
Pub Date : 2018-01-01DOI: 10.1080/25742558.2018.1475612
A. Zendehdel, Parisa Ahmadi Ghotbi
Abstract In this study, we define the fractional random variable. The concept of convergence in fractional probability, almost surely convergence and some related theorems and examples are studied with the purpose of expanding the fractional probability theory parallel to the classical one. It is shown that almost surely convergence in the fractional probability space does not lead to the convergence in fractional probability. And, some valuable features related to fractional probability theory such as Cauchy function in fractional probability are discussed. We proved that a fractional random variable converges in fractional probability if it is Cauchy in fractional probability. Finally, the well-known 0-1 Kolmogorov theorem is proved in a fractional probability space.
{"title":"Convergence in fractional probability space and 0-1 Kolmogorov theorem","authors":"A. Zendehdel, Parisa Ahmadi Ghotbi","doi":"10.1080/25742558.2018.1475612","DOIUrl":"https://doi.org/10.1080/25742558.2018.1475612","url":null,"abstract":"Abstract In this study, we define the fractional random variable. The concept of convergence in fractional probability, almost surely convergence and some related theorems and examples are studied with the purpose of expanding the fractional probability theory parallel to the classical one. It is shown that almost surely convergence in the fractional probability space does not lead to the convergence in fractional probability. And, some valuable features related to fractional probability theory such as Cauchy function in fractional probability are discussed. We proved that a fractional random variable converges in fractional probability if it is Cauchy in fractional probability. Finally, the well-known 0-1 Kolmogorov theorem is proved in a fractional probability space.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1475612","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47341808","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}
Pub Date : 2018-01-01DOI: 10.1080/25742558.2018.1507122
P. E. Oguntunde, M. A. Khaleel, A. Adejumo, H. Okagbue, A. Opanuga, F. Owolabi
Abstract The Gompertz inverse exponential (GoIE) distribution using the Gompertz generalized family of distributions was derived and introduced in this article. Some basic statistical properties of the model were derived and discussed in minute details. The model parameters were estimated using the maximum likelihood estimation method. Real-life applications were provided and the GoIE distribution provides better fits than the Gompertz exponential, Gompertz Weibull and Gompertz Lomax distributions.
{"title":"The Gompertz Inverse Exponential (GoIE) distribution with applications","authors":"P. E. Oguntunde, M. A. Khaleel, A. Adejumo, H. Okagbue, A. Opanuga, F. Owolabi","doi":"10.1080/25742558.2018.1507122","DOIUrl":"https://doi.org/10.1080/25742558.2018.1507122","url":null,"abstract":"Abstract The Gompertz inverse exponential (GoIE) distribution using the Gompertz generalized family of distributions was derived and introduced in this article. Some basic statistical properties of the model were derived and discussed in minute details. The model parameters were estimated using the maximum likelihood estimation method. Real-life applications were provided and the GoIE distribution provides better fits than the Gompertz exponential, Gompertz Weibull and Gompertz Lomax distributions.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1507122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42371235","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}
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