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How to model honeybee population dynamics: stage structure and seasonality 如何模拟蜜蜂种群动态:阶段结构和季节性
Mathematics in applied sciences and engineering Pub Date : 2020-03-22 DOI: 10.5206/mase/10559
Jun Chen, K. Messan, Marisabel Rodriguez Messan, G. DeGrandi-Hoffman, Dingyong Bai, Yun Kang
{"title":"How to model honeybee population dynamics: stage structure and seasonality","authors":"Jun Chen, K. Messan, Marisabel Rodriguez Messan, G. DeGrandi-Hoffman, Dingyong Bai, Yun Kang","doi":"10.5206/mase/10559","DOIUrl":"https://doi.org/10.5206/mase/10559","url":null,"abstract":"Western honeybees (Apis Mellifera) serve extremely important roles in our ecosystem and economics as  they are responsible for pollinating $ 215 billion dollars annually over the world.  Unfortunately,  honeybee population and their colonies have been declined dramatically. The purpose of this article is to explore how we should model honeybee population with age structure and validate the model using empirical data so that we can identify different factors that lead to the survival and healthy of the honeybee colony.  Our theoretical study combined with simulations and data validation suggests that the proper age structure incorporated in the model  and seasonality are important for modeling honeybee population.  Specifically, our work implies that the model assuming that (1) the adult bees are survived from the egg population rather than the brood population; and (2) seasonality in the queen egg laying rate, give the better fit than other honeybee models. The related theoretical and numerical analysis of the most fit model indicate that (a) the survival of honeybee colonies requires a large queen egg-laying rate and smaller values of the other life history parameter values in addition to proper initial condition; (b) both brood and adult bee populations are increasing with respect to the increase in the egg-laying rate and the decreasing in other parameter values; and (c) seasonality may promote/suppress the survival of the honeybee colony. ","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47224548","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: 6
Analysis of solutions and disease progressions for a within-host Tuberculosis model 宿主内结核病模型的解决方案和疾病进展分析
Mathematics in applied sciences and engineering Pub Date : 2020-03-07 DOI: 10.5206/mase/10221
Wenjing Zhang, Federico Frascoli, J. Heffernan
{"title":"Analysis of solutions and disease progressions for a within-host Tuberculosis model","authors":"Wenjing Zhang, Federico Frascoli, J. Heffernan","doi":"10.5206/mase/10221","DOIUrl":"https://doi.org/10.5206/mase/10221","url":null,"abstract":"Mycobacterium tuberculosis infection can lead to different disease outcomes, we analyze awith-in host tuberculosis infection model considering interactions between macrophages, T lym-phocytes, and tuberculosis bacteria to understand the dynamics of disease progression. Fourcoexisting equilibria that reflect TB disease dynamics are present: clearance, latency, and pri-mary disease, with low and high pathogen loads. We also derive the conditions for backwardand forward bifurcations and for global stable disease free equilibrium, which affect how thedisease progresses. Numerical bifurcation analysis and simulations elucidate the dynamics offast and slow disease progression.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49397674","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: 7
Viewpoints on modelling: Comments on "Achilles and the tortoise: Some caveats to mathematical modelling in biology" 建模观点——评《阿喀琉斯与乌龟：生物学数学建模的几点注意事项》
Mathematics in applied sciences and engineering Pub Date : 2020-02-29 DOI: 10.5206/mase/10267
J. Lei
{"title":"Viewpoints on modelling: Comments on \"Achilles and the tortoise: Some caveats to mathematical modelling in biology\"","authors":"J. Lei","doi":"10.5206/mase/10267","DOIUrl":"https://doi.org/10.5206/mase/10267","url":null,"abstract":"Mathematical modelling has been proven to be useful in understanding some problems from biological science, provided that it is used properly. However, it has also attracted some criticisms as partially presented in a recent  opinion article cite{Gilbert2018} from biological community. This note intends to clarify some confusion and misunderstanding in regard to mathematically modelling by commenting on those critiques raised in cite{Gilbert2018}, with a hope of initiating some further discussion so that both applied mathematicians and biologist can better use mathematical modelling and better understand the results from modelling.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45875970","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
Global asymptotic stability of a delayed plant disease model 一类时滞植物病害模型的全局渐近稳定性
Mathematics in applied sciences and engineering Pub Date : 2020-02-24 DOI: 10.5206/mase/9451
Yuming Chen, Chongwu Zheng
{"title":"Global asymptotic stability of a delayed plant disease model","authors":"Yuming Chen, Chongwu Zheng","doi":"10.5206/mase/9451","DOIUrl":"https://doi.org/10.5206/mase/9451","url":null,"abstract":"In this paper, we consider the following system of delayed differentialequations,[left{begin {array}{rcl}frac {dS(t)}{dt} & = & sigma phi-beta S(t)I(t-tau)-eta S(t),frac {dI(t)}{dt} & = & sigma(1-phi)+betaS(t)I(t-tau)-(eta+omega)I(t),end {array}right.]which can be used to model plant diseases. Here $phiin (0,1]$,$tauge 0$, and all other parameters are positive. The case where $phi=1$ is well studiedand there is a threshold dynamics. Thesystem always has a disease-free equilibrium, which is globallyasymptotically stable if the basic reproduction number $R_0triangleqfrac{betasigma}{eta(eta+omega)}le 1$ and is unstable if$R_0>1$; when $R_0>1$, the system also has a unique endemic equilibrium,which is globally asymptotically stable. In this paper, we study thecase where $phiin (0,1)$. It turns out that the system only has anendemic equilibrium, which is globally asymptotically stable. Thelocal stability is established by the linearizationmethod while the global attractivity is obtained by the Lyapunovfunctional approach. The theoretical results are illustrated withnumerical simulations.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49640073","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: 4
A prey-predator system with herd behaviour of prey in a rapidly fluctuating environment 在快速波动的环境中具有群体行为的捕食系统
Mathematics in applied sciences and engineering Pub Date : 2019-12-06 DOI: 10.5206/mase/8196
G. Samanta, A. Mondal, D. Sahoo, P. Dolai
{"title":"A prey-predator system with herd behaviour of prey in a rapidly fluctuating environment","authors":"G. Samanta, A. Mondal, D. Sahoo, P. Dolai","doi":"10.5206/mase/8196","DOIUrl":"https://doi.org/10.5206/mase/8196","url":null,"abstract":"A statistical theory of non-equilibrium fluctuation in damped Volterra-Lotka prey-predator system where prey population lives in herd in a rapidly fluctuating random environment has been presented. The method is based on the technique of perturbation approximation of non-linear coupled stochastic differential equations. The characteristic of group-living of prey population has been emphasized using square root of prey density in the functional response.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47893584","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
Existence and metastability of non-constant steady states in a Keller-Segel model with density-suppressed motility 具有密度抑制运动的Keller-Segel模型中非恒定稳态的存在性和亚稳态
Mathematics in applied sciences and engineering Pub Date : 2019-09-30 DOI: 10.5206/MASE/8120
Manjun Ma, Peng Xia, Yazhou Han, Jicheng Tao
{"title":"Existence and metastability of non-constant steady states in a Keller-Segel model with density-suppressed motility","authors":"Manjun Ma, Peng Xia, Yazhou Han, Jicheng Tao","doi":"10.5206/MASE/8120","DOIUrl":"https://doi.org/10.5206/MASE/8120","url":null,"abstract":"We are concerned with stationary solutions of a Keller-SegelModel with density-suppressed motility and without cell proliferation. we establish the existence and the analytical approximation of non-constant stationary solutions by applying the phase plane analysis and bifurcation analysis. We show that the one-step solutions is stable and two or more-step solutions are always unstable. Then we further show that two or more-step solutions possess metastability. Our analytical results are corroborated by direct simulations of the underlying system.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47822030","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: 2
The Minimum Spanning Tree with Node Index ≤ 2 Is Equivalent to the Minimum Traveling Salesman Tour 节点索引≤2的最小生成树等价于最小旅行推销员游
Mathematics in applied sciences and engineering Pub Date : 2019-09-09 DOI: 10.1201/b22521-8
Santosh Kumar, E. Munapo, C. Sigauke, Masar Al-Rabeeah
{"title":"The Minimum Spanning Tree with Node Index ≤ 2 Is Equivalent to the Minimum Traveling Salesman Tour","authors":"Santosh Kumar, E. Munapo, C. Sigauke, Masar Al-Rabeeah","doi":"10.1201/b22521-8","DOIUrl":"https://doi.org/10.1201/b22521-8","url":null,"abstract":"","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75066292","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
Application of Optimization Techniques to Support Eco-Efficiency Assessment in Manufacturing Processes 应用优化技术支持制造过程的生态效率评估
Mathematics in applied sciences and engineering Pub Date : 2019-09-09 DOI: 10.1201/b22521-1
P. Peças, A. Alves, Diogo Jorge
{"title":"Application of Optimization Techniques to Support Eco-Efficiency Assessment in Manufacturing Processes","authors":"P. Peças, A. Alves, Diogo Jorge","doi":"10.1201/b22521-1","DOIUrl":"https://doi.org/10.1201/b22521-1","url":null,"abstract":"","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88619002","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
Thermal Radiation Effects on the Fundamental Flows of a Ree–Eyring Hydromagnetic Fluid through Porous Medium with Slip Boundary Conditions 热辐射对具有滑移边界条件的三环磁流体在多孔介质中的基本流动的影响
Mathematics in applied sciences and engineering Pub Date : 2019-09-09 DOI: 10.1201/b22521-7
K. Ramesh
{"title":"Thermal Radiation Effects on the Fundamental Flows of a Ree–Eyring Hydromagnetic Fluid through Porous Medium with Slip Boundary Conditions","authors":"K. Ramesh","doi":"10.1201/b22521-7","DOIUrl":"https://doi.org/10.1201/b22521-7","url":null,"abstract":"","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73514302","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
Application of Finite Element Method in Enhancing the Performance of Biomedical Implants 有限元法在生物医学植入物性能提升中的应用
Mathematics in applied sciences and engineering Pub Date : 2019-09-09 DOI: 10.1201/b22521-3
M. Pant, Mohit Kumar, S. Garg
{"title":"Application of Finite Element Method in Enhancing the Performance of Biomedical Implants","authors":"M. Pant, Mohit Kumar, S. Garg","doi":"10.1201/b22521-3","DOIUrl":"https://doi.org/10.1201/b22521-3","url":null,"abstract":"","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87828972","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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