IMA journal of mathematics applied in medicine and biology最新文献_第4页

Genetic associations under mixed mating systems: the Bennett-Binet effect. 混合交配系统下的遗传关联:班尼特-比奈效应。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-12-01 DOI: 10.1093/IMAMMB/18.4.327

J. Vargas, R. F. Castillo

引用次数: 4

Analysis and comparison of multimodal cancer treatments. 多种肿瘤治疗方法的分析与比较。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-12-01 DOI: 10.1093/IMAMMB/18.4.343

D. Beil, L. Wein

{"title":"Analysis and comparison of multimodal cancer treatments.","authors":"D. Beil, L. Wein","doi":"10.1093/IMAMMB/18.4.343","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.4.343","url":null,"abstract":"We analyse the sequence in which the three most commonly prescribed cancer treatments--surgery (S), chemotherapy (C) and radiotherapy (R)--should be administered. A system of ordinary differential equations is formulated that captures the various local and systemic effects of the three modes of treatment, as well as the first-order effects of the inter-relationship between the primary tumour and the distant metastatic tumours, including primary tumour shedding and the primary tumour's effect on the rate of angiogenesis in the metastatic tumours. Under a set of stated assumptions on the parameter values, we find the exact cancer cure probability (subject to toxicity constraints) for the six permutation schedules (i.e. SCR, CSR, CRS, SRC, RSC, RCS) and for two novel schedules, SRCR and RSCR, that apply radiotherapy in disjoint, optimally timed portions. We show analytically that SRCR and RSCR are the two best-performing (i.e. highest cure probability) schedules among the eight considered. Further, SRCR is shown to be optimal among all possible schedules, provided a modest condition is satisfied on the delay of initial angiogenesis experienced by the patient's dormant tumours.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 4 1","pages":"343-76"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.4.343","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182437","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: 18

An application of a weak solution of the cable equation to the Rall model of a nerve cell. 索方程弱解在神经细胞Rall模型中的应用。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-12-01 DOI: 10.1093/IMAMMB/18.4.377

W. Krzyzanski

引用次数: 1

Mathematical modelling of quorum sensing in bacteria. 细菌群体感应的数学模型。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-09-01 DOI: 10.1093/IMAMMB/18.3.263

J. Ward, J. King, A. Koerber, P. Williams, J. Croft, R. Sockett

{"title":"Mathematical modelling of quorum sensing in bacteria.","authors":"J. Ward, J. King, A. Koerber, P. Williams, J. Croft, R. Sockett","doi":"10.1093/IMAMMB/18.3.263","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.3.263","url":null,"abstract":"The regulation of density-dependent behaviour by means of quorum sensing is widespread in bacteria, the relevant phenomena including bioluminescence and population expansion by swarming, as well as virulence. The process of quorum sensing is regulated by the production and monitoring of certain molecules (referred to as QSMs); on reaching an apparent threshold concentration of QSMs (reflecting high bacterial density) the bacterial colony in concert 'switches on' the density-dependent trait. In this paper a mathematical model which describes bacterial population growth and quorum sensing in a well mixed system is proposed and studied. We view the population of bacteria as consisting of down-regulated and up-regulated sub-populations, with QSMs being produced at a much faster rate by the up-regulated cells. Using curve fitting techniques for parameter estimation, solutions of the resulting system of ordinary differential equations are shown to agree well with experimental data. Asymptotic analysis in a biologically relevant limit is used to investigate the timescales for up-regulation of an exponentially growing population of bacteria, revealing the existence of bifurcation between limited and near-total up-regulation. For a fixed population of cells steady-state analysis reveals that in general one physical steady-state solution exists and is linearly stable; we believe this solution to be a global attractor. A bifurcation between limited and near-total up-regulation is also discussed in the steady-state limit.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 3 1","pages":"263-92"},"PeriodicalIF":0.0,"publicationDate":"2001-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.3.263","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181958","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: 132

A mathematical treatment of AIDS and condom use. 艾滋病和避孕套使用的数学处理。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-09-01 DOI: 10.1093/IMAMMB/18.3.225

D. Greenhalgh, M. Doyle, F. Lewis

{"title":"A mathematical treatment of AIDS and condom use.","authors":"D. Greenhalgh, M. Doyle, F. Lewis","doi":"10.1093/IMAMMB/18.3.225","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.3.225","url":null,"abstract":"In this paper we examine the impact of condom use on the sexual transmission of human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) amongst a homogeneously mixing male homosexual population. We first derive a multi-group SIR-type model of HIV/AIDS transmission where the homosexual population is split into subgroups according to frequency of condom use. Both susceptible and infected individuals can transfer between the different groups. We then discuss in detail an important special case of this model which includes two risk groups and perform an equilibrium and stability analysis for this special case. Our analysis shows that this model can exhibit unusual behaviour. As normal, if the basic reproduction number, R0, is greater than unity then there is a unique disease-free equilibrium which is locally unstable and a unique endemic equilibrium. However, when R0 is less than unity two endemic equilibrium solutions can also co-exist simultaneously with the disease-free solution which is locally stable. Numerical simulations using realistic parameter values confirm this and we find that in certain circumstances the disease-free solution and one of the endemic solutions are both locally asymptotically stable, while the other endemic solution is unstable. This unusual behaviour has important implications for control of the disease as reducing R0 to less than unity no longer guarantees eradication of the disease. For a restricted special case of this two-group model we show that there is only the disease-free equilibrium for R0 < or = 1 which is globally stable. For R0 > 1 the disease-free equilibrium is unstable and there is a unique endemic equilibrium which is locally stable. We then attempt to fit the model to HIV and AIDS incidence data from San Francisco, USA. The paper concludes with a brief discussion.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 3 1","pages":"225-62"},"PeriodicalIF":0.0,"publicationDate":"2001-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.3.225","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182378","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: 46

Evaluating plasma holds in the presence of multiple infections. 在多重感染的情况下评估血浆持有量。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-09-01 DOI: 10.1093/IMAMMB/18.3.215

E. H. Kaplan

引用次数: 1

Evaluating plasma holds in the presence of multiple infections. 评估多种感染情况下的血浆保持量。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-09-01

E H Kaplan

引用次数: 0

The use of multistate life-table models for improving population health. 使用多州生命表模型改善人口健康。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-06-01

M G Roberts, M I Tobias

引用次数: 0

Variable maturation velocity and parameter sensitivity in a model of haematopoiesis. 造血模型中的可变成熟速度和参数敏感性。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-06-01 DOI: 10.1093/IMAMMB/18.2.193

J. Bélair, J. Mahaffy

引用次数: 23

A model of Gambian sleeping sickness with open vector populations. 冈比亚昏睡病的开放媒介种群模型。

IMA journal of mathematics applied in medicine and biology Pub Date : 2001-06-01 DOI: 10.1093/IMAMMB/18.2.99

M. Artzrouni, J. Gouteux

{"title":"A model of Gambian sleeping sickness with open vector populations.","authors":"M. Artzrouni, J. Gouteux","doi":"10.1093/IMAMMB/18.2.99","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.2.99","url":null,"abstract":"A compartmental model of Gambian sleeping sickness is described that takes into account density-dependent migratory flows of infected flies. Equilibrium and stability theorems are given which show that with a basic reproduction number R0 below unity, then in the absence of reinvasion the disease goes to extinction. However, even a low prevalence rate among reinvading flies can then bring about significant equilibrium prevalence rates among humans. For a set of realistic parameter values we show that even in the case of a virulent parasite that keeps infected individuals in the first stage for as little as 4 or 8 months (durations for which there would be extinction with no infected reinvading flies) there is a prevalence rate in the range 13.0-36.9%, depending on whether 1 or 2% of reinvading flies are infected. A rate of convergence of the population dynamics is introduced and is interpreted in terms of a halving time of the infected population. It is argued that the persistence and/or extension of Gambian sleeping sickness foci could be due either to a continuous reinvasion of infected flies or to slow dynamics.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 2 1","pages":"99-117"},"PeriodicalIF":0.0,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.2.99","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181831","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: 20