Pub Date : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.4016
S. Hsu, I. Sun
In this paper we consider a mathematical model of two host species competing for a single -limited resource mediated by parasites. Each host population is divided into susceptible and infective population. We assume that species 1 has the lowest break-even concentration with respect to nutrient, when there is no parasite. Thus species 1 is a superior competitor that outcompetes species 2. When parasites present, the competitive outcome is determined by the contact rate of the superior competitor. We analyze the model by finding the conditions for the existence of various equilibria and doing their stability analysis. Two bifurcation diagrams are presented. The first one is in $beta_1$-$beta_2$ plane (See Figure 3) and the second one is in $R^{(0)}$-line (See Figure 4).
{"title":"Competition of Two Host Species for a Single-Limited Resource Mediated by Parasites","authors":"S. Hsu, I. Sun","doi":"10.5556/J.TKJM.52.2021.4016","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.4016","url":null,"abstract":"In this paper we consider a mathematical model of two host species competing for a single -limited resource mediated by parasites. Each host population is divided into susceptible and infective population. We assume that species 1 has the lowest break-even concentration with respect to nutrient, when there is no parasite. Thus species 1 is a superior competitor that outcompetes species 2. When parasites present, the competitive outcome is determined by the contact rate of the superior competitor. We analyze the model by finding the conditions for the existence of various equilibria and doing their stability analysis. Two bifurcation diagrams are presented. The first one is in $beta_1$-$beta_2$ plane (See Figure 3) and the second one is in $R^{(0)}$-line (See Figure 4).","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82078757","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.4087
Hongming You, Kaijen Cheng
In this work, we consider a mathematical model of an omnivorous ecosystem in which intermediate predators are infected by parasites. We first establish the boundeness and positivity of solution with conditions. Then the existence and local stability of all equilibria are clarified in R4. Finally, some global dynamics will be analyzed.
{"title":"Mathematical Analysis of Intraguild Interactions among Hosts, Parasitoids and Predators","authors":"Hongming You, Kaijen Cheng","doi":"10.5556/J.TKJM.52.2021.4087","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.4087","url":null,"abstract":"In this work, we consider a mathematical model of an omnivorous ecosystem in which intermediate predators are infected by parasites. We first establish the boundeness and positivity of solution with conditions. Then the existence and local stability of all equilibria are clarified in R4. Finally, some global dynamics will be analyzed.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83503772","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.4029
Jong-Shenq Guo
In this paper, we present some recent developments on the application of Schauder’s fixed point theorem to the existence of traveling waves for some three-species predator-prey systems. The existence of traveling waves of predator-prey systems is closely related to the invasion phenomenon of some alien species to the habitat of aboriginal species. Three different three-species predator-prey models with different invaded and invading states are presented. In this paper, we focus on the methodology of deriving the convergence of stale tail of wave profiles.
{"title":"Traveling Wave Solutions for Some Three-Species Predator-Prey Systems","authors":"Jong-Shenq Guo","doi":"10.5556/J.TKJM.52.2021.4029","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.4029","url":null,"abstract":"In this paper, we present some recent developments on the application of Schauder’s fixed point theorem to the existence of traveling waves for some three-species predator-prey systems. The existence of traveling waves of predator-prey systems is closely related to the invasion phenomenon of some alien species to the habitat of aboriginal species. Three different three-species predator-prey models with different invaded and invading states are presented. In this paper, we focus on the methodology of deriving the convergence of stale tail of wave profiles.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77224079","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.3280
Hilal Ahmad, A. Alhevaz, M. Baghipur, Gui-Xian Tian
For a simple connected graph $G$, the convex linear combinations $D_{alpha}(G)$ of $Tr(G)$ and $D(G)$ is defined as $D_{alpha}(G)=alpha Tr(G)+(1-alpha)D(G)$, $0leq alphaleq 1$. As $D_{0}(G)=D(G)$, $2D_{frac{1}{2}}(G)=D^{Q}(G)$, $D_{1}(G)=Tr(G)$ and $D_{alpha}(G)-D_{beta}(G)=(alpha-beta)D^{L}(G)$, this matrix reduces to merging the distance spectral and distance signless Laplacian spectral theories. In this paper, we study the spectral properties of the generalized distance matrix $D_{alpha}(G)$. We obtain some lower and upper bounds for the generalized distance spectral radius, involving different graph parameters and characterize the extremal graphs. Further, we obtain upper and lower bounds for the maximal and minimal entries of the $ p $-norm normalized Perron vector corresponding to spectral radius $ partial(G) $ of the generalized distance matrix $D_{alpha}(G)$ and characterize the extremal graphs.
{"title":"Bounds for Generalized Distance Spectral Radius and the Entries of the Principal Eigenvector","authors":"Hilal Ahmad, A. Alhevaz, M. Baghipur, Gui-Xian Tian","doi":"10.5556/J.TKJM.52.2021.3280","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3280","url":null,"abstract":"For a simple connected graph $G$, the convex linear combinations $D_{alpha}(G)$ of $Tr(G)$ and $D(G)$ is defined as $D_{alpha}(G)=alpha Tr(G)+(1-alpha)D(G)$, $0leq alphaleq 1$. As $D_{0}(G)=D(G)$, $2D_{frac{1}{2}}(G)=D^{Q}(G)$, $D_{1}(G)=Tr(G)$ and $D_{alpha}(G)-D_{beta}(G)=(alpha-beta)D^{L}(G)$, this matrix reduces to merging the distance spectral and distance signless Laplacian spectral theories. In this paper, we study the spectral properties of the generalized distance matrix $D_{alpha}(G)$. We obtain some lower and upper bounds for the generalized distance spectral radius, involving different graph parameters and characterize the extremal graphs. Further, we obtain upper and lower bounds for the maximal and minimal entries of the $ p $-norm normalized Perron vector corresponding to spectral radius $ partial(G) $ of the generalized distance matrix $D_{alpha}(G)$ and characterize the extremal graphs.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72408753","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.3430
Peter D. Johnson, Alexis Krumpelman
The Babai numbers and the upper chromatic number are parameters that can be assigned to any metric space. They can, therefore, be assigned to any connected simple graph. In this paper we make progress in the theory of the first Babai number and the upper chromatic number in the simple graph setting, with emphasis on graphs of diameter 2.
{"title":"On the Babai and Upper Chromatic Numbers of Graphs of Diameter 2","authors":"Peter D. Johnson, Alexis Krumpelman","doi":"10.5556/J.TKJM.52.2021.3430","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3430","url":null,"abstract":"The Babai numbers and the upper chromatic number are parameters that can be assigned to any metric space. They can, therefore, be assigned to any connected simple graph. In this paper we make progress in the theory of the first Babai number and the upper chromatic number in the simple graph setting, with emphasis on graphs of diameter 2.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80086162","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.3367
B. S. Ogundare, J. Akingbade
In this paper, asymptotic stability and global asymptotic stability of solutions to a deterministic and compartmental mathematical model of measles infection is considered using the ideas of the Jacobian determinant as well as the second method of Lyapunov, criteria/conditions that guaranteed asymptotic stability of disease free equilibrium and endemic equilibrium were established. Also the basic reproductive number $R_0$ was obtained. The results in this work compliments existing work and provided further information in controlling the disease in an open population.
{"title":"Boundedness and Stability Properties of Solutions of Mathematical Model of Measles.","authors":"B. S. Ogundare, J. Akingbade","doi":"10.5556/J.TKJM.52.2021.3367","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3367","url":null,"abstract":"In this paper, asymptotic stability and global asymptotic stability of solutions to a deterministic and compartmental mathematical model of measles infection is considered using the ideas of the Jacobian determinant as well as the second method of Lyapunov, criteria/conditions that guaranteed asymptotic stability of disease free equilibrium and endemic equilibrium were established. Also the basic reproductive number $R_0$ was obtained. The results in this work compliments existing work and provided further information in controlling the disease in an open population.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85758469","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.3047
K. O. Babalola, Mashood Sidiq
Recent studies in the class of Bazilevi$check{c}$ maps as a whole has compelled the development, in this work, of certain complex-parameter integral iterations of Caratheodory maps. The iterations are employed in a similar manner as in cite{BA} to study a certain subfamily of those Bazilevi$check{c}$ maps.
{"title":"Complex-Parameter Integral Iterations of Caratheodory Maps","authors":"K. O. Babalola, Mashood Sidiq","doi":"10.5556/j.tkjm.51.2020.3047","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.3047","url":null,"abstract":"Recent studies in the class of Bazilevi$check{c}$ maps as a whole has compelled the development, in this work, of certain complex-parameter integral iterations of Caratheodory maps. The iterations are employed in a similar manner as in cite{BA} to study a certain subfamily of those Bazilevi$check{c}$ maps.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72376041","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.3087
N. Khan, Talha Usma, M. Aman
Abstract. In this paper, we introduce a new generalization of the Wright function by using an extended beta function and study some classical properties of this function. We establish several formulas involving integral transforms (e.g. Jacobi transform, Gegenbauer transform) and the generalized family of Wright function that does not seem to be reported in the literature even for the basic Wright function. Furthermore, we discuss other results including the recurrence relation, derivative formula, fractional derivative formula and also a partly bilateral and partly unilateral generating relation for the generalized Wright function.
{"title":"Generalized Wright Function and Its Properties Using Extended Beta Function","authors":"N. Khan, Talha Usma, M. Aman","doi":"10.5556/j.tkjm.51.2020.3087","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.3087","url":null,"abstract":"Abstract. In this paper, we introduce a new generalization of the Wright function by using an extended beta function and study some classical properties of this function. We establish several formulas involving integral transforms (e.g. Jacobi transform, Gegenbauer transform) and the generalized family of Wright function that does not seem to be reported in the literature even for the basic Wright function. Furthermore, we discuss other results including the recurrence relation, derivative formula, fractional derivative formula and also a partly bilateral and partly unilateral generating relation for the generalized Wright function.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75919751","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.2860
Shaibu Osman, O. Makinde, D. Theuri
Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.
{"title":"Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control.","authors":"Shaibu Osman, O. Makinde, D. Theuri","doi":"10.5556/j.tkjm.51.2020.2860","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.2860","url":null,"abstract":"Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81525195","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.3188
F. Pashaie
A well-known conjecture of Bang Yen-Chen says that the only biharmonic Euclidean submanifolds are minimal ones. In this paper, we consider an extended condition (namely, $L_1$-biharmonicity) on non-degenerate timelike hypersurfaces of the pseudo-Euclidean space $E_1^4$. A Lorentzian hypersurface $x: M_1^3rightarrowE_1^4$ is called $L_1$-biharmonic if it satisfies the condition $L_1^2x=0$, where $L_1$ is the linearized operator associated to the first variation of 2-th mean curvature vector field on $M_1^3$. According to the multiplicities of principal curvatures, the $L_1$-extension of Chen's conjecture is affirmed for Lorentzian hypersurfaces with constant ordinary mean curvature in pseudo-Euclidean space $E_1^4$. Additionally, we show that there is no proper $L_1$-biharmonic $L_1$-finite type connected orientable Lorentzian hypersurface in $E_1^4$.
Bang yan - chen的一个著名猜想是:双调和欧氏子流形是最小流形。本文研究了伪欧几里德空间E_1^4$上的非退化类时超曲面上的一个扩展条件(即$L_1$-双谐性)。如果满足条件$L_1^2x=0$，则称为$L_1$-双调和，其中$L_1$是与$M_1^3$上的第2平均曲率向量场的第一次变分相关的线性化算子。根据主曲率的多重性，在伪欧几里德空间E_1^4$中，对具有常平均曲率的洛伦兹超曲面，证实了Chen猜想的L_1 -推广。此外，我们还证明了$E_1^4$中不存在固有的$L_1$-双调和$L_1$-有限型连通可定向洛伦兹超曲面。
{"title":"On $L_1$-biharmonic timelike hypersurfaces in pseudo-Euclidean space $E_1^4$","authors":"F. Pashaie","doi":"10.5556/j.tkjm.51.2020.3188","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.3188","url":null,"abstract":"A well-known conjecture of Bang Yen-Chen says that the only biharmonic Euclidean submanifolds are minimal ones. In this paper, we consider an extended condition (namely, $L_1$-biharmonicity) on non-degenerate timelike hypersurfaces of the pseudo-Euclidean space $E_1^4$. A Lorentzian hypersurface $x: M_1^3rightarrowE_1^4$ is called $L_1$-biharmonic if it satisfies the condition $L_1^2x=0$, where $L_1$ is the linearized operator associated to the first variation of 2-th mean curvature vector field on $M_1^3$. According to the multiplicities of principal curvatures, the $L_1$-extension of Chen's conjecture is affirmed for Lorentzian hypersurfaces with constant ordinary mean curvature in pseudo-Euclidean space $E_1^4$. Additionally, we show that there is no proper $L_1$-biharmonic $L_1$-finite type connected orientable Lorentzian hypersurface in $E_1^4$.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77161092","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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