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

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Quasi-steady state approximation to a fungal growth model. 真菌生长模型的准稳态近似。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-09-01
A Lamour, F van den Bosch, A J Termorshuizen, M J Jeger
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引用次数: 0
Epidemics in predator-prey models: disease in the predators. 捕食者-猎物模型中的流行病:捕食者的疾病。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-09-01 DOI: 10.1093/IMAMMB/19.3.185
E. Venturino
{"title":"Epidemics in predator-prey models: disease in the predators.","authors":"E. Venturino","doi":"10.1093/IMAMMB/19.3.185","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.3.185","url":null,"abstract":"The author has recently proposed and investigated models for the study of interacting species subject to an additional factor, a disease spreading among one of them, that somehow affects the other one. The inadequacy of such a model comes from the basic assumption on the interacting species. It is well known that the cycles found in the Lotka-Volterra system exhibit a neutral stability, and this phenomenon is carried over to the proposed model. Here we would like to extend the study to account for population dynamics leading to carrying capacities, i.e. logistic behaviour. This corresponds to the so-called quadratic predator-prey models found in the literature. We are able to show that in some cases the trajectories are bounded, and also analyse the local stability of some equilibria.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 3 1","pages":"185-205"},"PeriodicalIF":0.0,"publicationDate":"2002-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.3.185","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182934","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: 304
Epidemics in predator-prey models: disease in the predators. 捕食者-猎物模型中的流行病:捕食者的疾病。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-09-01
Ezio Venturino
{"title":"Epidemics in predator-prey models: disease in the predators.","authors":"Ezio Venturino","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The author has recently proposed and investigated models for the study of interacting species subject to an additional factor, a disease spreading among one of them, that somehow affects the other one. The inadequacy of such a model comes from the basic assumption on the interacting species. It is well known that the cycles found in the Lotka-Volterra system exhibit a neutral stability, and this phenomenon is carried over to the proposed model. Here we would like to extend the study to account for population dynamics leading to carrying capacities, i.e. logistic behaviour. This corresponds to the so-called quadratic predator-prey models found in the literature. We are able to show that in some cases the trajectories are bounded, and also analyse the local stability of some equilibria.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 3","pages":"185-205"},"PeriodicalIF":0.0,"publicationDate":"2002-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"22300896","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
Quasi-steady state approximation to a fungal growth model. 真菌生长模型的准稳态近似。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-09-01 DOI: 10.1093/IMAMMB/19.3.163
A. Lamour, F. C. van den Bosch, A. Termorshuizen, M. Jeger
{"title":"Quasi-steady state approximation to a fungal growth model.","authors":"A. Lamour, F. C. van den Bosch, A. Termorshuizen, M. Jeger","doi":"10.1093/IMAMMB/19.3.163","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.3.163","url":null,"abstract":"In a previous paper, we proposed a fungal growth model (Lamour et al., 2001 IMA J. Math. Appl. Med. Biol., 17, 329-346), describing the colonization and decomposition of substrate, subsequent uptake of nutrients, and incorporation into fungal biomass, and performed an overall-steady-state analysis. In this paper we assume that where nutrient dynamics are much faster than the dynamics of fungal biomass and substrate, the system will reach a quasi-steady-state relatively quickly. We show how the quasi-steady-state approximation is a simplification of the full fungal growth model. We then derive an explicit fungal invasion criterion, which was not possible for the full model, and characterize parameter domains for invasion and extinction. Importantly, the fungal invasion criterion takes two forms: one for systems where carbon is limiting, another for systems where nitrogen is limiting. We focus attention on what happens in the short term immediately following the introduction of a fungus to a fungal-free system by analysing the stability of the trivial steady state, and then check numerically whether the fungus is able to persist. The derived invasion criterion was found to be valid also for the full model. Knowledge of the factors that determine invasion is essential to an understanding of fungal dynamics. The simplified model allows the invasion criterion to be tested with experimental data.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 3 1","pages":"163-83"},"PeriodicalIF":0.0,"publicationDate":"2002-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.3.163","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182911","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
The stability of internal equilibria in predator-prey models with breeding suppression. 具有繁殖抑制的捕食-食饵模型内部平衡的稳定性。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-09-01 DOI: 10.1093/IMAMMB/19.3.207
G. Ruxton, Q. J. Khan, Mohamed Al-Lawatia
{"title":"The stability of internal equilibria in predator-prey models with breeding suppression.","authors":"G. Ruxton, Q. J. Khan, Mohamed Al-Lawatia","doi":"10.1093/IMAMMB/19.3.207","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.3.207","url":null,"abstract":"We present two models that represent the suppression of breeding by prey in response to short-term increases in predation pressure. For both of these models, we have been able to produce analytic conditions for the local stability of the interior steady state, in terms of the values of combinations of these parameters. Although our models are as simple as possible to capture the effect of breeding suppression, the expressions for local stability, even in their simplest form, are complex. Thus, we come to the important conclusion that there is no simple and general rule for the effect of the behaviours described here (anti-predatory breeding suppression and prey switching by predators) on the stability of population dynamics. Rather, effects will be system specific. However, we hope that the results and methodological framework outlined here will provide a useful tool for others to investigate the consequences for particular real systems.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 3 1","pages":"207-19"},"PeriodicalIF":0.0,"publicationDate":"2002-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.3.207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61183192","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: 5
A non-linear model for a sexually transmitted disease with contact tracing. 具有接触者追踪的性传播疾病的非线性模型。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-09-01 DOI: 10.1093/IMAMMB/19.3.221
H. Arazoza, R. Lounes
{"title":"A non-linear model for a sexually transmitted disease with contact tracing.","authors":"H. Arazoza, R. Lounes","doi":"10.1093/IMAMMB/19.3.221","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.3.221","url":null,"abstract":"A non-linear model is developed for an epidemic with contact tracing, and its dynamic is studied. We present the data for the Cuban HIV/AIDS epidemic and fit the non-linear model, we obtain estimates for the size of the Cuban HIV epidemic, and for the mean time for detecting a person that is infected with HIV.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"20 1","pages":"221-34"},"PeriodicalIF":0.0,"publicationDate":"2002-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.3.221","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61183335","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: 65
The effects of re-infection in directly transmitted infections modelled with vaccination. 用疫苗模拟直接传播感染中再感染的效果。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-06-01 DOI: 10.1093/IMAMMB/19.2.113
H. Yang
{"title":"The effects of re-infection in directly transmitted infections modelled with vaccination.","authors":"H. Yang","doi":"10.1093/IMAMMB/19.2.113","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.2.113","url":null,"abstract":"We propose a mathematical model to deal with directly transmitted infections incorporating the loss of immunity. The model is developed taking into account a constant contact rate among individuals and an age-dependent vaccination rate. Based on this model, we analyse the effects of re-infection in a community under a vaccination strategy.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"28 1","pages":"113-35"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.2.113","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182592","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: 3
Population-induced oscillations in blended SI-SEI epidemiological models. 混合SI-SEI流行病学模型中的种群诱发振荡。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-06-01
Piero Manfredi, Ernesto Salinelli
{"title":"Population-induced oscillations in blended SI-SEI epidemiological models.","authors":"Piero Manfredi,&nbsp;Ernesto Salinelli","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The effects of standard patterns of population growth in blended SI-SEI models (of which models for 'fast and slow' tuberculosis are an instance) are considered. When the incidence has the 'true mass action' form, the system is globally stable under both exponential and logistic population dynamics, whereas sustained oscillations occur in the case of bilinear incidence. This shows in the final analysis, the minimal dynamical ingredients needed to generate oscillations in basic epidemiological models: provided the population is exponentially growing and the incidence is bilinear, at least a fraction of the newly exposed individuals must enter the infective state with a delay.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 2","pages":"95-112"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"22284874","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
Population-induced oscillations in blended SI-SEI epidemiological models. 混合SI-SEI流行病学模型中的种群诱发振荡。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-06-01 DOI: 10.1093/IMAMMB/19.2.95
P. Manfredi, E. Salinelli
{"title":"Population-induced oscillations in blended SI-SEI epidemiological models.","authors":"P. Manfredi, E. Salinelli","doi":"10.1093/IMAMMB/19.2.95","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.2.95","url":null,"abstract":"The effects of standard patterns of population growth in blended SI-SEI models (of which models for 'fast and slow' tuberculosis are an instance) are considered. When the incidence has the 'true mass action' form, the system is globally stable under both exponential and logistic population dynamics, whereas sustained oscillations occur in the case of bilinear incidence. This shows in the final analysis, the minimal dynamical ingredients needed to generate oscillations in basic epidemiological models: provided the population is exponentially growing and the incidence is bilinear, at least a fraction of the newly exposed individuals must enter the infective state with a delay.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 2 1","pages":"95-112"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.2.95","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182828","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: 8
Modelling plant virus epidemics in a plantation-nursery system. 在种植-苗圃系统中模拟植物病毒流行。
IMA journal of mathematics applied in medicine and biology Pub Date : 2002-06-01 DOI: 10.1093/IMAMMB/19.2.75
M. Jeger, F. C. van den Bosch, M. Dutmer
{"title":"Modelling plant virus epidemics in a plantation-nursery system.","authors":"M. Jeger, F. C. van den Bosch, M. Dutmer","doi":"10.1093/IMAMMB/19.2.75","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.2.75","url":null,"abstract":"The material used for propagation and planting of many perennial crop plants is derived from vegetative cuttings which are first multiplied in a nursery. This situation was modelled to analyse the dynamics of a plant virus epidemic in a combined nursery-plantation system and the comparative effects of disease management activities in the plantation and in the nursery. The plant populations were partitioned into healthy and diseased categories and were linked according to basic SI models of disease transmission. Removal of diseased plants and replanting operations in both the plantation and nursery were included in the model and two variants were analysed in which mother plants (from which cuttings were taken) remained in the plantation or were harvested. The former is shown to be the limiting case for a large number of cuttings per plant. A criterion was derived for the invasion of disease into a healthy combined system. This consisted of four additive terms: the basic reproductive numbers of disease in the plantation alone and in the nursery alone, and two terms describing the cycling of diseased material between the plantation and nursery. Disease can still invade the system with basic reproductive numbers in the plantation or in the nursery less than 1 depending on the magnitude of cycling. Under some conditions only diseased plants remain in the plantation and nursery. For such a case a criterion was derived for the invasion of healthy plants into a fully diseased system. This depended on replanting rates in the plantation and nursery, and infection, mortality and removal rates of healthy plants.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 2 1","pages":"75-94"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.2.75","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182771","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: 11
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