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

{"title":"Modelling plant virus epidemics in a plantation-nursery system.","authors":"M J Jeger,&nbsp;F Van Den Bosch,&nbsp;M Y Dutmer","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 2","pages":"75-94"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"22284872","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":"The effects of re-infection in directly transmitted infections modelled with vaccination.","authors":"Hyun Mo Yang","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 2","pages":"113-35"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"22284875","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":"A delay differential equation model on harmful algal blooms in the presence of toxic substances.","authors":"J Chattopadhyay,&nbsp;R R Sarkar,&nbsp;A El Abdllaoui","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The periodic nature of blooms is the main characteristic in marine plankton ecology. Release of toxic substances by phytoplankton species or toxic phytoplankton reduce the growth of zooplankton by decreasing grazing pressure and have an important role in planktonic blooms. A simple mathematical model of phytoplankton-zooplankton systems with such characteristics is proposed and analysed. As the process of liberation of toxic substances by phytoplankton species is still not clear, we try to describe a suitable mechanism to explain the cyclic nature of bloom dynamics by using different forms of toxin liberation process. To substantiate our analytical findings numerical simulations are performed and these adequately resemble the results obtained in our field study.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 2","pages":"137-61"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"22284876","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":"A delay differential equation model on harmful algal blooms in the presence of toxic substances.","authors":"J. Chattopadhyay, R. Sarkar, A. E. Abdllaoui","doi":"10.1093/IMAMMB/19.2.137","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.2.137","url":null,"abstract":"The periodic nature of blooms is the main characteristic in marine plankton ecology. Release of toxic substances by phytoplankton species or toxic phytoplankton reduce the growth of zooplankton by decreasing grazing pressure and have an important role in planktonic blooms. A simple mathematical model of phytoplankton-zooplankton systems with such characteristics is proposed and analysed. As the process of liberation of toxic substances by phytoplankton species is still not clear, we try to describe a suitable mechanism to explain the cyclic nature of bloom dynamics by using different forms of toxin liberation process. To substantiate our analytical findings numerical simulations are performed and these adequately resemble the results obtained in our field study.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 2 1","pages":"137-61"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.2.137","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182660","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":"Fluid flow in the anterior chamber of a human eye.","authors":"C. Canning, M. Greaney, J. Dewynne, A. Fitt","doi":"10.1093/IMAMMB/19.1.31","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.1.31","url":null,"abstract":"A simple model is presented to analyse fluid flow in the anterior chamber of a human eye. It is shown that under normal conditions such flow inevitably occurs. The flow, whose reduced Reynolds number is small, is viscosity dominated and is driven by buoyancy effects which are present because of the temperature difference between the front and back of the anterior chamber. In cases of severe eye trauma or as a result of certain diseases and medical conditions, particulate matter may be introduced into the anterior chamber. The motion and distribution of such particles is analysed and it is shown that the model is capable of predicting well-established and observed features that may be present in a traumatized eye such as hyphemas, keratic precipitates, hypopyons and Krukenberg spindles.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"26 1","pages":"31-60"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.1.31","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182830","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":"Asymmetric growth of models of avascular solid tumours: exploiting symmetries.","authors":"Helen Byrne,&nbsp;Paul Matthews","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>In this paper a mathematical model of avascular tumour growth is studied. Attention focuses on the stability of radially symmetric model solutions to perturbations involving spherical harmonics Ylm (theta, phi). Linear theory is used to identify bifurcation points at which the radially symmetric steady state loses stability. The first modes to become unstable are shown to correspond to the l = 2 spherical harmonics. Results from group theory and weakly nonlinear analysis indicate the structure of the l = 2 bifurcation point is a transcritical bifurcation in which all nontrivial solution branches are unstable. By proceeding to third order and focusing on a special set of parameter values for which the quadratic terms are negligible, it is shown that the system's behaviour in a neighbourhood of the l = 2 bifurcation point is governed by a subcritical bifurcation. In consequence, the nontrivial asymmetric solution branches in a neighbourhood of the bifurcation point are unstable. The branches of asymmetric solutions bound the domain of attraction of the radially symmetric tumour configuration where it is locally stable. The analytical results that are derived lead us to conjecture that any stable asymmetric tumour structures will involve spherical harmonics of order l > or = 3.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 1","pages":"1-29"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"22089486","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":"Modelling the transmission dynamics of Ross River virus in Southwestern Australia.","authors":"Y. Choi, C. Comiskey, M. Lindsay, J. Cross, M. Anderson","doi":"10.1093/IMAMMB/19.1.61","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.1.61","url":null,"abstract":"During the 1995-1996 Australian financial year, over 1300 notifications of Ross River (RR) virus disease were notified in humans from Southwestern Australia. Due to the mild symptoms of the disease, it is difficult to diagnose and subclinical infections are common. However, these subclinical infections do give rise to immunity. For planning and control, it is important for public health authorities to estimate the true number of people who have contracted the disease and to assess the impact of key epidemiological parameters. A mathematical model was developed to describe the transmission of RR virus between its hosts (humans and kangaroos) and its vectors (mosquitoes). For this model, the threshold conditions and relative removal rates were calculated and interpreted. Finally, a computer program was written to simulate the model in order to estimate the total number, both clinical and sub clinical human infections given known and hypothetical epidemiological parameter values. Within this simulation sensitivity of the results to changes in the parameters were examined. The analysis of the threshold conditions conformed well to established principles of arboviral transmission and control. It was observed that conditions which can prevent an outbreak occuring include reducing the number of susceptibles in host and vector populations, reducing the infection rates between hosts and vectors and shortening the duration of viraemia. Results on the sensitivity analysis showed that some parameters such as the extrinsic incubation period, mosquito mortality rate in winter and the proportion of Western Grey Kangaroos in the marsupial population have little effect on human incidence. However, the transmission rate between hosts and vectors, vector-mortality rate in summer and the proportion of infectious vectors among infected vectors have pronounced effects. The simulation results on the ratio of clinical to subclinical human infections predicted a minimum ratio of 1:2 and a maximum ratio of 1:65, which is consistent with data obtained during previous sero-epidemiological studies.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 1 1","pages":"61-74"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.1.61","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182468","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":"Fluid flow in the anterior chamber of a human eye.","authors":"C R Canning,&nbsp;M J Greaney,&nbsp;J N Dewynne,&nbsp;A D Fitt","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>A simple model is presented to analyse fluid flow in the anterior chamber of a human eye. It is shown that under normal conditions such flow inevitably occurs. The flow, whose reduced Reynolds number is small, is viscosity dominated and is driven by buoyancy effects which are present because of the temperature difference between the front and back of the anterior chamber. In cases of severe eye trauma or as a result of certain diseases and medical conditions, particulate matter may be introduced into the anterior chamber. The motion and distribution of such particles is analysed and it is shown that the model is capable of predicting well-established and observed features that may be present in a traumatized eye such as hyphemas, keratic precipitates, hypopyons and Krukenberg spindles.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 1","pages":"31-60"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"22090071","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":"Modelling the transmission dynamics of Ross River virus in Southwestern Australia.","authors":"Y H Choi,&nbsp;C Comiskey,&nbsp;M D A Lindsay,&nbsp;J A Cross,&nbsp;M Anderson","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>During the 1995-1996 Australian financial year, over 1300 notifications of Ross River (RR) virus disease were notified in humans from Southwestern Australia. Due to the mild symptoms of the disease, it is difficult to diagnose and subclinical infections are common. However, these subclinical infections do give rise to immunity. For planning and control, it is important for public health authorities to estimate the true number of people who have contracted the disease and to assess the impact of key epidemiological parameters. A mathematical model was developed to describe the transmission of RR virus between its hosts (humans and kangaroos) and its vectors (mosquitoes). For this model, the threshold conditions and relative removal rates were calculated and interpreted. Finally, a computer program was written to simulate the model in order to estimate the total number, both clinical and sub clinical human infections given known and hypothetical epidemiological parameter values. Within this simulation sensitivity of the results to changes in the parameters were examined. The analysis of the threshold conditions conformed well to established principles of arboviral transmission and control. It was observed that conditions which can prevent an outbreak occuring include reducing the number of susceptibles in host and vector populations, reducing the infection rates between hosts and vectors and shortening the duration of viraemia. Results on the sensitivity analysis showed that some parameters such as the extrinsic incubation period, mosquito mortality rate in winter and the proportion of Western Grey Kangaroos in the marsupial population have little effect on human incidence. However, the transmission rate between hosts and vectors, vector-mortality rate in summer and the proportion of infectious vectors among infected vectors have pronounced effects. The simulation results on the ratio of clinical to subclinical human infections predicted a minimum ratio of 1:2 and a maximum ratio of 1:65, which is consistent with data obtained during previous sero-epidemiological studies.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 1","pages":"61-74"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"22090072","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":"Asymmetric growth of models of avascular solid tumours: exploiting symmetries.","authors":"H. Byrne, P. Matthews","doi":"10.1093/IMAMMB/19.1.1","DOIUrl":"https://doi.org/10.1093/IMAMMB/19.1.1","url":null,"abstract":"In this paper a mathematical model of avascular tumour growth is studied. Attention focuses on the stability of radially symmetric model solutions to perturbations involving spherical harmonics Ylm (theta, phi). Linear theory is used to identify bifurcation points at which the radially symmetric steady state loses stability. The first modes to become unstable are shown to correspond to the l = 2 spherical harmonics. Results from group theory and weakly nonlinear analysis indicate the structure of the l = 2 bifurcation point is a transcritical bifurcation in which all nontrivial solution branches are unstable. By proceeding to third order and focusing on a special set of parameter values for which the quadratic terms are negligible, it is shown that the system's behaviour in a neighbourhood of the l = 2 bifurcation point is governed by a subcritical bifurcation. In consequence, the nontrivial asymmetric solution branches in a neighbourhood of the bifurcation point are unstable. The branches of asymmetric solutions bound the domain of attraction of the radially symmetric tumour configuration where it is locally stable. The analytical results that are derived lead us to conjecture that any stable asymmetric tumour structures will involve spherical harmonics of order l > or = 3.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 1 1","pages":"1-29"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/19.1.1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182678","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}