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IMA journal of mathematics applied in medicine and biology最新文献

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Approaches to the space-time modelling of infectious disease behaviour. 传染病行为的时空建模方法。
IMA journal of mathematics applied in medicine and biology Pub Date : 2000-03-01
A B Lawson, P Leimich
{"title":"Approaches to the space-time modelling of infectious disease behaviour.","authors":"A B Lawson,&nbsp;P Leimich","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>A new approach to the space-time modelling of infectious diseases is considered. A modulated heterogeneous Poisson process with intensity defined as a function of a two-dimensional susceptibility field is proposed. The model is fitted to a measles epidemic using a proportional hazards approximation.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 1","pages":"1-13"},"PeriodicalIF":0.0,"publicationDate":"2000-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21607409","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
The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response. 考虑病毒电荷和免疫反应的直接传播感染模型的基本繁殖比率。
IMA journal of mathematics applied in medicine and biology Pub Date : 2000-03-01
M B Leite, R C Bassanezi, H M Yang
{"title":"The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response.","authors":"M B Leite,&nbsp;R C Bassanezi,&nbsp;H M Yang","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>In order to describe mathematically the transmission of microparasites, especially directly transmitted infections, it is usual to set up differential equations assuming the mass action law and a homogeneously mixed population. In this paper we analyze such a model taking into account heterogeneity with respect to the infectivity, that is, the variability in the evolution of the interaction between parasite and the human host during the infectious period. The well established biological phenomenon of initial increase in parasite abundance followed by its decrease, due to the interaction between the host's immunological response and the parasite, has thus been taken into account. The variable amount of microparasites eliminated by an infectious individual, and the different (heterogeneous) immunological response build up by the host when in interaction with parasite are present in the model. The analytical expression for the basic reproduction ratio is derived through stability analysis.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 1","pages":"15-31"},"PeriodicalIF":0.0,"publicationDate":"2000-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21607410","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
Therapy burden, drug resistance, and optimal treatment regimen for cancer chemotherapy. 癌症化疗的治疗负担、耐药性和最佳治疗方案。
IMA journal of mathematics applied in medicine and biology Pub Date : 2000-03-01
J L Boldrini, M I Costa
{"title":"Therapy burden, drug resistance, and optimal treatment regimen for cancer chemotherapy.","authors":"J L Boldrini,&nbsp;M I Costa","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Three nonlinear models of tumour cell growth under continuous delivery of cycle nonspecific anticancer agents are studied. A dynamical optimization problem with the objective of minimizing the final level of tumour cells is posed for these mathematical setups. The simplest setup does not possess toxicity constraints, whereas the other setups contain a dynamical equation describing the therapy burden as a toxicity criterion. In addition, the third setting contains the dynamics of drug resistant cells. A discussion concerning the optimal strategies of the respective models is performed.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 1","pages":"33-51"},"PeriodicalIF":0.0,"publicationDate":"2000-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21607411","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
A spatial model of antipredator vigilance. 反捕食者警戒的空间模型。
IMA journal of mathematics applied in medicine and biology Pub Date : 2000-03-01
C J Proctor, M Broom
{"title":"A spatial model of antipredator vigilance.","authors":"C J Proctor,&nbsp;M Broom","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Many species of animals have to perform two contradictory tasks: feeding, and avoiding becoming food for others. A large number of theoretical and empirical studies have investigated the trade-off between feeding and antipredator vigilance, especially in birds. An important factor which has been neglected in these studies is that of the area occupied by the flock. If individuals feed close together, competition increases and feeding rates decrease. However, if individuals space themselves widely, then vigilance efficiency goes down and there is an increased predation risk. We develop a vigilance model which allows birds to control the area the flock occupies as well as their vigilance rate. The optimal strategy is found for the birds under a variety of environmental conditions. In particular the effect of each environmental parameter on this optimum is considered in turn. How the model can be adapted for different bird species is also investigated.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 1","pages":"75-93"},"PeriodicalIF":0.0,"publicationDate":"2000-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21606664","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
Multidimensional counting processes and evoked neuronal activity. 多维计数过程和诱发的神经元活动。
IMA journal of mathematics applied in medicine and biology Pub Date : 2000-03-01
J Vaillant, P Lánský
{"title":"Multidimensional counting processes and evoked neuronal activity.","authors":"J Vaillant,&nbsp;P Lánský","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>It is shown that the joint behaviour of n counting processes can be used for description of neuronal spike generation in a system of n neurons with various synaptic links. This multidimensional process is suggested as a model of neuronal activity evoked by either a homogeneous or an inhomogeneous stimulus during a short time period. Several situations are considered, mainly the joint activity of pairs of neurons. The probability generating functions of the process are obtained for different kinds of intensity functions. The first and second moments of the process are provided as a tool for potential comparison of the model with experimental data.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 1","pages":"53-73"},"PeriodicalIF":0.0,"publicationDate":"2000-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21607412","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
On a branching model of division-within-division. 论分中分的分支模型。
IMA journal of mathematics applied in medicine and biology Pub Date : 1999-12-01
P D O'Neill
{"title":"On a branching model of division-within-division.","authors":"P D O'Neill","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>We consider a deterministic version of a stochastic model for division-within-division processes described by Kimmel (1997, In: Proceedings of the IMA Workshop 'Classical and Modern Branching Processes' (K. Arthreya and P. Jagers, eds.)???? :????). It is shown that the behaviour of the deterministic model can be analyzed by using an associated Markov chain, using the methods of Barbour et al.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4","pages":"395-405"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21523746","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
A Kermack-McKendrick model applied to an infectious disease in a natural population. 应用于自然种群中传染病的Kermack-McKendrick模型。
IMA journal of mathematics applied in medicine and biology Pub Date : 1999-12-01
M G Roberts
{"title":"A Kermack-McKendrick model applied to an infectious disease in a natural population.","authors":"M G Roberts","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The dynamics of a fatal infectious disease in a population regulated by density-dependent constraints are represented as a system of nonlinear integral equations. Survival probabilities and disease transmission coefficients may vary with the time elapsed since infection, and horizontal and vertical modes of transmission are allowed for. Criteria for the existence and stability of steady states are derived, and an example based on the dynamics of tuberculosis is presented. Finally, the relative merits of this approach, and the familiar compartmental models based on differential equations are discussed.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4","pages":"319-32"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21523743","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
Modelling corneal epithelial wound closure in the presence of physiological electric fields via a moving boundary formalism. 在生理电场存在下，通过移动边界形式模拟角膜上皮伤口闭合。
IMA journal of mathematics applied in medicine and biology Pub Date : 1999-12-01
E A Gaffney, P K Maini, C D McCaig, M Zhao, J V Forrester
{"title":"Modelling corneal epithelial wound closure in the presence of physiological electric fields via a moving boundary formalism.","authors":"E A Gaffney,&nbsp;P K Maini,&nbsp;C D McCaig,&nbsp;M Zhao,&nbsp;J V Forrester","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>A new framework for the modelling of corneal epithelial wound healing is presented, which can include the presence of a physiological electric field. The difficulty inherent in the inclusion of this biological phenomenon motivates our use of a moving boundary formalism. A key conclusion is that the model predicts a linear relation between the wound healing speed and the physiological electric field strengths over a physiologically large range of electric field strength. Another key point is that this linear relationship between electric field strength and wound healing speed is robust to variations in critical parameters that are difficult to estimate. The linearity is also robust to different realizations of the modelling framework presented.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4","pages":"369-93"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21523745","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
Density-dependent dynamics and superinfection in an epidemic model. 流行病模型中的密度依赖动力学和重复感染。
IMA journal of mathematics applied in medicine and biology Pub Date : 1999-12-01
J Mena-Lorca, J X Velasco-Hernandez, C Castillo-Chavez
{"title":"Density-dependent dynamics and superinfection in an epidemic model.","authors":"J Mena-Lorca,&nbsp;J X Velasco-Hernandez,&nbsp;C Castillo-Chavez","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>A mathematical model of the interaction between two pathogen strains and a single host population is studied. Variable population size, density-dependent mortality, disease-related deaths (virulence), and superinfection are incorporated into the model. Results indicate that coexistence of the two strains is possible depending on the magnitude of superinfection. Global asymptotic stability of the steady-state that gives coexistence for both strains under suitable and biologically feasible constraints is proved.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4","pages":"307-17"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21523742","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
Modelling corneal epithelial wound closure in the presence of physiological electric fields via a moving boundary formalism. 在生理电场存在下，通过移动边界形式模拟角膜上皮伤口闭合。
IMA journal of mathematics applied in medicine and biology Pub Date : 1999-12-01 DOI: 10.1093/IMAMMB/16.4.369
E. Gaffney, P. Maini, C. McCaig, Min Zhao, J. Forrester
{"title":"Modelling corneal epithelial wound closure in the presence of physiological electric fields via a moving boundary formalism.","authors":"E. Gaffney, P. Maini, C. McCaig, Min Zhao, J. Forrester","doi":"10.1093/IMAMMB/16.4.369","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.4.369","url":null,"abstract":"A new framework for the modelling of corneal epithelial wound healing is presented, which can include the presence of a physiological electric field. The difficulty inherent in the inclusion of this biological phenomenon motivates our use of a moving boundary formalism. A key conclusion is that the model predicts a linear relation between the wound healing speed and the physiological electric field strengths over a physiologically large range of electric field strength. Another key point is that this linear relationship between electric field strength and wound healing speed is robust to variations in critical parameters that are difficult to estimate. The linearity is also robust to different realizations of the modelling framework presented.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4 1","pages":"369-93"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.4.369","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61179536","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: 22
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