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

{"title":"Multiple dose vaccination against childhood diseases: high coverage with the first dose remains crucial for eradication.","authors":"A C Paulo,&nbsp;M C Gomes,&nbsp;A C Casinhas,&nbsp;A Horta,&nbsp;T Domingos","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The high vaccination coverage required to eradicate communicable diseases like measles, mumps and rubella, with a single dose of vaccine, has prompted many countries to introduce a second dose. In this paper we investigate the conditions to eradicate childhood diseases with multiple doses of vaccine by obtaining explicit analytical solutions to the classical compartment model that assumes an age-independent force of infection and conceptualizes the host population as divided into maternally protected (P), susceptibles (S), latents (E), infectious (I), and removed (R). The solutions allow a quantitative discussion of the long-term impact of vaccination schedules with an arbitrary number of doses of vaccine. It becomes possible to determine the effect of the number of doses, ages at vaccination, and coverage rates of vaccines against childhood diseases. In an example with a two-dose vaccination schedule against measles, we show that, in spite of a second dose, a high (> 90%) immunization coverage in the first dose is still crucial to achieve eradication. With a high first-dose coverage, however, eradication is relatively insensitive to the age of the second dose and requires only moderate coverage rates in the latter.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 3","pages":"201-12"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21927846","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":"Variability in centred house-of-cards mutation models.","authors":"S Mahdi,&nbsp;S Lessard","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Convergence of variability in phenotypic models with balance between selection and mutation is analysed. The mutation assumed occurs with weak probability and brings down the evolutionary process built up by selection around the mean in the population. Gaussian approximations are used.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 3","pages":"185-200"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21927844","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":"Behaviour change and treatment of core groups: its effect on the spread of HIV/AIDS.","authors":"Y H Hsieh,&nbsp;K Cooke","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>A general model is considered for treatment and behaviour change of the Human Immunodeficiency Virus (HIV) infected in a highly sexually active core group of female commercial sex workers (CSWs) and a 'bridge population' of young unpartnered males. In this model, the spread of HIV/AIDS in the community is carried out mainly through the sexual interaction between the core group and the bridge population which acts as a bridge for the spread of disease to the general population. We will consider the effect of treatment of the infected and/or the subsequent behaviour change when targeted toward the core group and the bridge population. Analytical results will be given for a strategy which targets treatment and behaviour change at either the core group or the bridge population. Numerical examples are also provided to illustrate the biological significance of the treatment/behaviour change and its effect on the threshold parameter values. The results show that if the contact rates and transmission probabilities of the treated individuals are sufficiently reduced, the treatment/behaviour change can eradicate the disease provided that the level of treatment in the infected population is sufficiently high. However, an ill-planned treatment program which fails to meet the required reductions in contact rate or transmission probability could have a detrimental effect on the spread of the epidemic.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 3","pages":"213-41"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21927847","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":"Higher-dimensional separation principle for the analysis of relaxation oscillations in nonlinear systems: application to a model of HIV infection.","authors":"Y Lenbury,&nbsp;R Ouncharoen,&nbsp;N Tumrasvin","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>In this paper, geometric and singular perturbation arguments are utilized to develop a separation condition for the identification of limit cycles in higher-dimensional (n > or = 4) dynamical systems characterized by highly diversified time responses, in which there exists an (n - 3)-dimensional subsystem which quickly reaches a quasi-steady state. The condition, which has been used up to now to analyze relaxation oscillation in slow-fast systems, is extended to accommodate dynamical systems in which more state variables are involved in a special manner which still allows for the use of singular perturbation techniques. Application is then made to a model of human immunodeficiency virus infection in T helper (TH) cell clones with limiting resting TH cell supply.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 3","pages":"243-61"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21927848","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":"Stochastic models for systems of interacting ion channels.","authors":"F G Ball,&nbsp;R K Milne,&nbsp;G F Yeo","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>We consider a variety of Markov based models for systems of ion channels exhibiting dependence between channels. It is shown how many useful properties which may be calculated for an aggregated single-channel model, or a system of independent channels, can be extended to various types of interacting channel systems. Key structure and results from the theory of aggregated Markov processes are summarized in a convenient matrix form. These are then applied to the superposition of independent and dependent channels, including a patch of channels in a random environment, and a system of channels with spatial interactions. Calculations based on the resultant matrix expressions and intensity arguments can be implemented straightforwardly in a matrix-oriented package such as Matlab. The role of reversibility is also studied. A number of examples illustrate the strengths of the methods and enable numerical comparisons between the different types of systems.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 3","pages":"263-93"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21927851","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":"Three-stage AIDS incubation period: a best case scenario using addict-needle interaction assumptions.","authors":"D Greenhalgh,&nbsp;F Lewis","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>In this paper we extend the 'needles that kill' model discussed in Kaplan & O'Keefe (1993) to allow addicts to progress through three-stages of variable infectivity prior to the onset of full-blown AIDS, and where the class of infectious needles is split into three according to the different levels of infectivity in addicts. Given the structure of this model we are required to make assumptions regarding the interaction of addicts and needles of different infectivity levels. We deliberately choose these assumptions so that our model serves as a lower bound for the prevalence of HIV under the assumption of a three-stage AIDS incubation period. We find that there is a critical threshold parameter R0 which determines the behaviour of the model. If R0 > 1 then there is a unique endemic equilibrium which is locally stable if, as is realistic, the timescale on which addicts inject is much shorter than that of the other epidemiological and demographic processes. Simulations indicate that if R0 > 1, then provided that disease is initially present in at least one addict or needle then it will tend to the endemic equilibrium. In addition, we derive conditions which guarantee this. We also find that under calibration the long-term prevalence of disease in the 'needles that kill' model is the same as in our three-stage model.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 2","pages":"95-118"},"PeriodicalIF":0.0,"publicationDate":"2000-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21827755","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":"Prediction of a glucose appearance function from foods using deconvolution.","authors":"T L Yates,&nbsp;L R Fletcher","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The glycaemic response of an insulin-treated diabetic patient goes through many transitory phases, leading to a steady state glycaemic profile following a change in either insulin regimen or diet. Most models attempting to model the glucose and insulin relationship try to model the effect of oral or injected glucose rather than that from the digestion of food. However, it is clear that a better understanding of the glycaemic response would arise from consideration of intestinal absorption from the gut. It is assumed that this type of absorption can be modelled by a so-called glucose appearance function (systemic appearance of glucose via glucose absorption from the gut) predicting the glucose load from the food. Much research has been carried out in the areas of hepatic balance, insulin absorption and insulin independent/dependent utilization. However, little is known about intestinal absorption patterns or their corresponding glucose appearance profiles. The strategy under investigation herein is to use deconvolution or backward engineering. By starting with specific results i.e. blood glucose and insulin therapy, it is possible to work backwards to predict the glucose forcing functions responsible for the outcome. Assuming compartmental consistency, this will allow a clearer insight into the true gut absorption process. If successful, the same strategy can be applied to more recent glucose and insulin models to further our understanding of the food to blood glucose problem. This paper investigates the Lehmann-Deutsch modified model of glucose and insulin interaction, created from the model proposed by Berger-Rodbard. The model attempts to simulate the steady state glycaemic and plasma insulin responses, independent of the initial values from which the simulation is started. Glucose enters the model via both intestinal absorption and hepatic glucose production. We considered a 70 kg male insulin-dependent diabetic patient with corresponding hepatic and insulin sensitivity parameters of 0.6 and 0.3 respectively. Net hepatic glucose balance was modelled piecewise by linear and symmetric functions. A first-order Euler method with step size of 15 minutes was employed. For the simulation, only Actrapid and NPH injections were considered. The injection of insulin and the glucose flux to the gut were started simultaneously to avoid any delay associated with gastric emptying. The systemic appearance of glucose was compared from two view points, not only to assess the strategic principle, but also to assess the suitability of the modifications made by Lehmann and Deutsch. The first is a forward prediction using the compartmental structure. This analysis involves the rate of gastric emptying without time delay. The second is a backward prediction from experimentally observed blood glucose profiles. Investigations involved porridge, white rice and banana containing the same carbohydrate content (25 g). Results obtained from the first analysis were de","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 2","pages":"169-84"},"PeriodicalIF":0.0,"publicationDate":"2000-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21827759","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 role of the central chemoreceptor in causing periodic breathing.","authors":"A C Fowler,&nbsp;G P Kalamangalam","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>In a previous publication (Fowler et al., 1993), we reduced the classical cardiorespiratory control model of (Grodins et al., 1967) to a much simpler form, which we then used to study the phenomenon of periodic breathing. In particular, cardiac output was assumed constant, and a single (constant) delay representing arterial blood transport time between lung and brain was included in the model. In this paper we extend this earlier work, both by allowing for the variability in transport delays, due to the dependence of cardiac output on blood gas concentrations, and also by including further delays in the system. In addition, we extensively discuss the physiological implications of parameter variations in the model; several novel mechanisms for periodic breathing in clinical situations are proposed. The results are discussed in the light of recent observational studies.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 2","pages":"147-67"},"PeriodicalIF":0.0,"publicationDate":"2000-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21827758","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":"Estimating vaccine coverage by using computer algebra.","authors":"D Altmann,&nbsp;K Altmann","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The approach of N Gay for estimating the coverage of a multivalent vaccine from antibody prevalence data in certain age cohorts is complemented by using computer aided elimination theory of variables. Hereby, Gay's usage of numerical approximation can be replaced by exact formulae which are surprisingly nice, too.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 2","pages":"137-46"},"PeriodicalIF":0.0,"publicationDate":"2000-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21827757","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":"Stability analysis of a general age-dependent vaccination model for a vertically transmitted disease under the proportionate mixing assumption.","authors":"M el-Doma","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>An SIR epidemic model of a general age-dependent vaccination of a vertically as well as horizontally transmitted disease is investigated when the total population is in steady state. We assume proportionate mixing and age-dependent fertility, mortality and removal rates. We determine the steady states and examine their stabilities.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"17 2","pages":"119-36"},"PeriodicalIF":0.0,"publicationDate":"2000-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21827756","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}