IMA journal of mathematics applied in medicine and biology最新文献_第9页

Hopf bifurcation in epidemic models with a time delay in vaccination. 具有接种时滞的流行病模型的Hopf分岔。

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-06-01

Q J Khan, D Greenhalgh

引用次数: 0

Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation. 血管肿瘤生长的数学模型。II:模拟生长饱和度。

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-06-01

J P Ward, J R King

{"title":"Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation.","authors":"J P Ward, J R King","doi":"","DOIUrl":"","url":null,"abstract":"We build on our earlier mathematical model (Ward & King, 1997, IMA J. Appl. Math Appl. Med. Biol., 14, 39-69) by incorporating two necrotic depletion mechanisms, which results in a model that can predict all the main phases of avascular-tumour growth and heterogeneity. The model assumes a continuum of live cells which, depending on the concentration of a generic nutrient, may reproduce or die, generating local volume changes and thus producing movement described by a velocity field. The necrotic material is viewed as basic cellular material (i.e. as a generic mix of proteins, DNA, etc.) which is able to diffuse and is utilized by living cells as raw material to construct new cells during mitosis. Numerical solution of the resulting system of partial differential equations shows that growth ultimately tends either to a steady-state (growth saturation) or becomes linear. Both the travelling-wave and steady-state limits of the model are therefore derived and studied. The analysis demonstrates that, except in a very special case, passage of cellular material across the tumour surface is necessary for growth saturation to occur. Using numerical techniques, the domains of existence of the large-time solutions are explored in parameter space. For a particular limit, asymptotic analysis makes explicit the main phases of growth and gives the location of the bifurcation between the long-time outcomes.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 2","pages":"171-211"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21266811","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 two-type model for the Cuban national programme on HIV/AIDS. 古巴国家艾滋病毒/艾滋病方案的两种模式。

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-06-01

R Lounes, H de Arazoza

引用次数: 0

Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation. 血管肿瘤生长的数学模型。II:模拟生长饱和度。

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-06-01 DOI: 10.1093/IMAMMB/16.2.171

John P. Ward, John R. King

{"title":"Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation.","authors":"John P. Ward, John R. King","doi":"10.1093/IMAMMB/16.2.171","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.2.171","url":null,"abstract":"We build on our earlier mathematical model (Ward & King, 1997, IMA J. Appl. Math Appl. Med. Biol., 14, 39-69) by incorporating two necrotic depletion mechanisms, which results in a model that can predict all the main phases of avascular-tumour growth and heterogeneity. The model assumes a continuum of live cells which, depending on the concentration of a generic nutrient, may reproduce or die, generating local volume changes and thus producing movement described by a velocity field. The necrotic material is viewed as basic cellular material (i.e. as a generic mix of proteins, DNA, etc.) which is able to diffuse and is utilized by living cells as raw material to construct new cells during mitosis. Numerical solution of the resulting system of partial differential equations shows that growth ultimately tends either to a steady-state (growth saturation) or becomes linear. Both the travelling-wave and steady-state limits of the model are therefore derived and studied. The analysis demonstrates that, except in a very special case, passage of cellular material across the tumour surface is necessary for growth saturation to occur. Using numerical techniques, the domains of existence of the large-time solutions are explored in parameter space. For a particular limit, asymptotic analysis makes explicit the main phases of growth and gives the location of the bifurcation between the long-time outcomes.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 2 1","pages":"171-211"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.2.171","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61178964","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: 217

The use of dummy data points when fitting bacterial growth curves. 拟合细菌生长曲线时使用虚拟数据点。

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-06-01 DOI: 10.1093/IMAMMB/16.2.155

L. Kelly, G. Gibson, G. Gettinby, W. Donachie, J. Low

引用次数: 1

Hopf bifurcation in epidemic models with a time delay in vaccination. 具有接种时滞的流行病模型的Hopf分岔。

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-06-01 DOI: 10.1093/IMAMMB/16.2.113

Q. J. Khan, David G. Greenhalgh

{"title":"Hopf bifurcation in epidemic models with a time delay in vaccination.","authors":"Q. J. Khan, David G. Greenhalgh","doi":"10.1093/IMAMMB/16.2.113","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.2.113","url":null,"abstract":"Two SIR models for the spread of infectious diseases which were originally suggested by Greenhalgh & Das (1995, Theor. Popul. Biol. 47, 129-179; 1995, Mathematical Population Dynamics: Analysis of Heterogeneity, pp. 79-101, Winnipeg: Wuerz Publishing) are considered but with a time delay in the vaccination term. This reflects the fact that real vaccines do not immediately confer permanent immunity. The population is divided into susceptible, infectious, and immune classes. The contact rate is constant in model I but it depends on the population size in model II. The death rate depends on the population size in both models. There is an additional mortality due to the disease, and susceptibles are vaccinated and may become permanently immune after a lapse of some time. Using the time delay as a bifurcation parameter, necessary and sufficient conditions for Hopf bifurcation to occur are derived. Numerical results indicate that that for diseases in human populations Hopf bifurcation is unlikely to occur at realistic parameter values if the death rate is a concave function of the population size.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 2 1","pages":"113-42"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.2.113","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61178691","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: 36

A two-type model for the Cuban national programme on HIV/AIDS. 古巴国家艾滋病毒/艾滋病方案的两种模式。

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-06-01 DOI: 10.1093/IMAMMB/16.2.143

R. Lounes, H. de Arazoza

引用次数: 24

Dynamics of Japanese encephalitis--a study in mathematical epidemiology. 日本脑炎的动态——数学流行病学研究。

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-03-01

A K Ghosh, P K Tapaswi

{"title":"Dynamics of Japanese encephalitis--a study in mathematical epidemiology.","authors":"A K Ghosh, P K Tapaswi","doi":"","DOIUrl":"","url":null,"abstract":"An S-->I-->R-->S (susceptible-infective-recovered-susceptible) epidemiological model coupling the dynamics of the spread of Japanese encephalitis (JE) in two populations, human and reservoir animals (pigs, cattle, equines, birds, etc.) through a vector population (a particular species of mosquitos, Culex vishnui, Culex tritaeniorhynchus, etc.) is discussed. We assume that there is a constant recruitment rate of the susceptibles into both the populations, whereas the death rates are proportional to the population sizes, which are hence variables. We also assume that the human population is regulated by the disease. Conditions for the existence of a unique endemic equilibrium were found, and the endemicity of the disease is discussed. The threshold values determine whether the disease dies out or approaches an endemic equilibrium. The persistence of disease and disease-related death can lead to a new equilibrium population size. The criteria for eradication of the disease have been worked out. The analytical results corresponding to the solutions of our system are verified by numerical analysis and computer simulation. The dynamics of disease transmission of JE during 1948-1956 in Japan were also investigated with the help of available data.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 1","pages":"1-27"},"PeriodicalIF":0.0,"publicationDate":"1999-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21205179","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 and simulation of chemotherapy of haematological and gynaecological cancers 血液学和妇科癌症化疗的建模和模拟

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-03-01 DOI: 10.1093/IMAMMB/16.1.39

Nani Fk, Oğuztöreli Mn

{"title":"Modelling and simulation of chemotherapy of haematological and gynaecological cancers","authors":"Nani Fk, Oğuztöreli Mn","doi":"10.1093/IMAMMB/16.1.39","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.1.39","url":null,"abstract":"In this paper elaborate mathematical models and investigative computer simulations for the chemotherapy of haematological and gynaecological cancers are presented. The pharmacodynamics of the actions of the antineoplastic drugs are described by multicompartmental models with the associated model equations taking into account the drug dosage, type of delivery, route of delivery, the intercompartmental drug-transition constants, degradation parameters, and leakage coefficients. The cell-cycle phase-specific six-compartmental cytokinetic tumour growth model presented here incorporates the cell-cycle phase residence time, time lags associated with drug-induced cell-kill, or progression delays due to repair of cell damage. Investigative computer simulations are performed depicting the effects of cell-cycle phase-specific antineoplastic drugs on haematological and gynaecological cancer cells. The computer simulations are performed under various clinically plausible parametric configurations to elucidate the effects of certain critical variables such as tumour cell burden, mode of antineoplastic drug delivery, tumour cell loss and cell-cycle cytokinetic parameters.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 1","pages":"39-91"},"PeriodicalIF":0.0,"publicationDate":"1999-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.1.39","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61178829","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

Delay effect in a model for virus replication. 病毒复制模型中的延迟效应。

IMA journal of mathematics applied in medicine and biology Pub Date : 1999-03-01

J Tam

引用次数: 0