Jun Chen, K. Messan, Marisabel Rodriguez Messan, G. DeGrandi-Hoffman, Dingyong Bai, Yun Kang
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.
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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}
{"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}
{"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}
{"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}
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