This paper focuses on the development and analysis of the endemic model for disease control in an aged-structured population in Nigeria. Upon the model framework development, the model equations were transformed into proportions with rate of change of the different compartments forming the model, thereby reducing the model equations from twelve to ten homogenous ordinary differential equations. The model exhibits two equilibria, the endemic state and the disease-free equilibrium state while successfully achieving a Reproductive Number R_0=0. The deterministic endemic susceptible-exposed-infected-removed-undetectable=untransmissible-susceptible (SEIRUS) model is analyzed for the existence and stability of the disease-free equilibrium state. We established that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number 0≤R_0<1. Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect treatment rate and the net transmission rate on recovery for both juvenile and adult sub-population in an age-structured population.
{"title":"Application of an age-structured deterministic endemic model for disease control in Nigeria","authors":"Victor A. Okhuese, Oduwole Henry Kehinde","doi":"10.28919/eml/4668","DOIUrl":"https://doi.org/10.28919/eml/4668","url":null,"abstract":"This paper focuses on the development and analysis of the endemic model for disease control in an aged-structured population in Nigeria. Upon the model framework development, the model equations were transformed into proportions with rate of change of the different compartments forming the model, thereby reducing the model equations from twelve to ten homogenous ordinary differential equations. The model exhibits two equilibria, the endemic state and the disease-free equilibrium state while successfully achieving a Reproductive Number R_0=0. The deterministic endemic susceptible-exposed-infected-removed-undetectable=untransmissible-susceptible (SEIRUS) model is analyzed for the existence and stability of the disease-free equilibrium state. We established that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number 0≤R_0<1. Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect treatment rate and the net transmission rate on recovery for both juvenile and adult sub-population in an age-structured population.","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122925297","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}
In this paper, we define and investigate a new class for higher-order derivatives of harmonic multivalent functions. We obtain coefficient inequalities, distortion bounds, extreme points, convex combination. Our results extend corresponding previously known results.
{"title":"Study of a new class for higher-order derivatives of harmonic multivalent functions","authors":"A. Wanas, F. Maghool","doi":"10.28919/eml/3940","DOIUrl":"https://doi.org/10.28919/eml/3940","url":null,"abstract":"In this paper, we define and investigate a new class for higher-order derivatives of harmonic multivalent functions. We obtain coefficient inequalities, distortion bounds, extreme points, convex combination. Our results extend corresponding previously known results.","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"57 34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115834174","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}
Jonathan Gustafsson, B. Akers, Jonah A. Reeger, Srihari Y. Sritharan
High Energy Laser (HEL) propagation through turbulent atmosphere is examined via numerical simulation. The beam propagation is modeled with the paraxial equation, which in turn is written as a system of equations for a quantum fluid, via the Madelung transform. A finite volume solver is applied to the quantum fluid equations, which supports sharp gradients in beam intensity. The atmosphere is modeled via a coupled advection-diffusion equation whose initial data have Kolmogorov spectrum. In this model the combined effects of thermal blooming, beam slewing, and deep turbulence are simulated.
{"title":"Atmospheric propagation of high energy lasers","authors":"Jonathan Gustafsson, B. Akers, Jonah A. Reeger, Srihari Y. Sritharan","doi":"10.28919/eml/3888","DOIUrl":"https://doi.org/10.28919/eml/3888","url":null,"abstract":"High Energy Laser (HEL) propagation through turbulent atmosphere is examined via numerical simulation. The beam propagation is modeled with the paraxial equation, which in turn is written as a system of equations for a quantum fluid, via the Madelung transform. A finite volume solver is applied to the quantum fluid equations, which supports sharp gradients in beam intensity. The atmosphere is modeled via a coupled advection-diffusion equation whose initial data have Kolmogorov spectrum. In this model the combined effects of thermal blooming, beam slewing, and deep turbulence are simulated.","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"164 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123950750","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}
In this paper we charaterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form [ left{ begin{array}{l} x^{prime }=xleft( Pleft( x,yright) +Rleft( x,yright) ln leftvert frac{Aleft( x,yright) }{Bleft( x,yright) }rightvert right) , y^{prime }=yleft( Qleft( x,yright) +Rleft( x,yright) ln leftvert frac{Aleft( x,yright) }{Bleft( x,yright) }rightvert right) , end{array} right. ] where $Aleft(x,yright)$, $Bleft(x,yright)$, $Pleft( x,yright)$, $Qleft(x,yright)$, $Rleft(x,yright)$ are homogeneous polynomials of degree $a$, $a$, $n$, $n$, $m$ respectively. Concrete example exhibiting the applicability of our result is introduced.
{"title":"On the class of two dimensional Kolmogorov systems","authors":"R. Boukoucha, Mouna Yahiaoui","doi":"10.28919/eml/3939","DOIUrl":"https://doi.org/10.28919/eml/3939","url":null,"abstract":"In this paper we charaterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form [ left{ begin{array}{l} x^{prime }=xleft( Pleft( x,yright) +Rleft( x,yright) ln leftvert frac{Aleft( x,yright) }{Bleft( x,yright) }rightvert right) , y^{prime }=yleft( Qleft( x,yright) +Rleft( x,yright) ln leftvert frac{Aleft( x,yright) }{Bleft( x,yright) }rightvert right) , end{array} right. ] where $Aleft(x,yright)$, $Bleft(x,yright)$, $Pleft( x,yright)$, $Qleft(x,yright)$, $Rleft(x,yright)$ are homogeneous polynomials of degree $a$, $a$, $n$, $n$, $m$ respectively. Concrete example exhibiting the applicability of our result is introduced.","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"29 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128371972","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}
This paper addresses the problem of estimating the mean of the number of persons possessing a rare sensitive attribute utilizing the Poisson distribution in survey sampling. Properties of the proposed randomized response model have been studied along with recommendations. It is also shown that the proposed model is more efficient than Land et al. (2011) when the proportion of persons possessing a rare unrelated attribute is known. Numerical illustration is also given in support of the present study.
{"title":"Nimble randomization device for estimating a rare sensitive attribute using Poisson distribution","authors":"T. A. Tarray","doi":"10.28919/eml/4159","DOIUrl":"https://doi.org/10.28919/eml/4159","url":null,"abstract":"This paper addresses the problem of estimating the mean of the number of persons possessing a rare sensitive attribute utilizing the Poisson distribution in survey sampling. Properties of the proposed randomized response model have been studied along with recommendations. It is also shown that the proposed model is more efficient than Land et al. (2011) when the proportion of persons possessing a rare unrelated attribute is known. Numerical illustration is also given in support of the present study.","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124203567","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}
In this paper we consider a class of semilinear discrete (difference) inclusions in a Hilbert space. As is well-known, the discrete inclusions, in particular, are mathematical models of discrete-time switched systems. For the considered inclusions we suggest explicit exponential stability conditions. Our results are new even in the finite-dimensional case. An illustrative example is given.
{"title":"Stability of semilinear discrete inclusions in a Hilbert space","authors":"M. Gil'","doi":"10.28919/eml/4222","DOIUrl":"https://doi.org/10.28919/eml/4222","url":null,"abstract":"In this paper we consider a class of semilinear discrete (difference) inclusions in a Hilbert space. As is well-known, the discrete inclusions, in particular, are mathematical models of discrete-time switched systems. For the considered inclusions we suggest explicit exponential stability conditions. Our results are new even in the finite-dimensional case. An illustrative example is given.","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114848144","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}
By making use of fractional integral, we study fuzzy subordination methods to obtain some interesting results of operator defined by generalized Mittag-Leffler function in the open unit disk.
{"title":"Fuzzy subordination results for fractional integral associated with generalized Mittag-Leffler function","authors":"A. Wanas, A. Majeed","doi":"10.28919/eml/4073","DOIUrl":"https://doi.org/10.28919/eml/4073","url":null,"abstract":"By making use of fractional integral, we study fuzzy subordination methods to obtain some interesting results of operator defined by generalized Mittag-Leffler function in the open unit disk.","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121165106","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}
The object of this paper to study an application of the fractional calculus techniques for a certain class 𝑀𝑅(𝑝, 𝑚, 𝜀, 𝜎, 𝜇) of multivalent analytic functions with negative coefficients in the open unit disk. Distortiontheorems for the fractional derivative and fractional integration are obtained. Also, we gain results about coefficientinequality, neighborhood property and radii of starlikeness and convexity
{"title":"An application of fractional calculus on a certain class of multivalent analytic functions with negative coefficients","authors":"A. Wanas, S. Mahmood","doi":"10.28919/eml/4003","DOIUrl":"https://doi.org/10.28919/eml/4003","url":null,"abstract":"The object of this paper to study an application of the fractional calculus techniques for a certain class 𝑀𝑅(𝑝, 𝑚, 𝜀, 𝜎, 𝜇) of multivalent analytic functions with negative coefficients in the open unit disk. Distortiontheorems for the fractional derivative and fractional integration are obtained. Also, we gain results about coefficientinequality, neighborhood property and radii of starlikeness and convexity","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127256541","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}
The purpose of this paper is to introduce some results associated with the strong differential subordinations of analytic functions defined in the open unit disk and closed unit disk of the complex plane.
本文的目的是介绍复平面的开单位盘和闭单位盘上定义的解析函数的强微分从属关系的一些结果。
{"title":"Some results for strong differential subordination of analytic functions defined by differential operator","authors":"Asraa Abdul Jaleel Husien","doi":"10.28919/eml/4118","DOIUrl":"https://doi.org/10.28919/eml/4118","url":null,"abstract":"The purpose of this paper is to introduce some results associated with the strong differential subordinations of analytic functions defined in the open unit disk and closed unit disk of the complex plane.","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128178341","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}
In this research article, the discreet role of Cytotoxic T Lymphocyte (CTL) during the Hepatitis C Virus infection has been studied. To explore the implications of the CTL responses, we have formulated a model considering the dynamics of the population of uninfected liver cells, infected liver cells, HCV and CTL responses. Since the actual incidence rate is probably not linear over the entire range of virus and uninfected liver cells. So, here we have assumed that there exists a saturation effect in disease transmission rate. We have analysed the model by both analytical as well as numerical approaches. We have found out the threshold condition that determines the existence and stability of the endemic equilibrium.
{"title":"The effect of immune responses in HCV disease progression","authors":"A. Chatterjee, M. Singh, B. Kumar","doi":"10.28919/eml/3992","DOIUrl":"https://doi.org/10.28919/eml/3992","url":null,"abstract":"In this research article, the discreet role of Cytotoxic T Lymphocyte (CTL) during the Hepatitis C Virus infection has been studied. To explore the implications of the CTL responses, we have formulated a model considering the dynamics of the population of uninfected liver cells, infected liver cells, HCV and CTL responses. Since the actual incidence rate is probably not linear over the entire range of virus and uninfected liver cells. So, here we have assumed that there exists a saturation effect in disease transmission rate. We have analysed the model by both analytical as well as numerical approaches. We have found out the threshold condition that determines the existence and stability of the endemic equilibrium.","PeriodicalId":364975,"journal":{"name":"Engineering Mathematics Letters","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127471692","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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