{"title":"On a branching model of division-within-division.","authors":"P. O'neill","doi":"10.1093/IMAMMB/16.4.395","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.4.395","url":null,"abstract":"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.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4 1","pages":"395-405"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.4.395","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61179731","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":"Multihost, multiparasite systems: an application of bifurcation theory.","authors":"J. Greenman, P. Hudson","doi":"10.1093/IMAMMB/16.4.333","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.4.333","url":null,"abstract":"The local analysis of multihost multiparasite models has been hampered by algebraic intractability. There have been two responses to this difficulty: extensive numerical investigation, and simplification to a level where analytical techniques work. In this paper we describe another approach, based on bifurcation theory, in which the qualitative properties of the model equilibrium structure are realized on an array of maps drawn in parameter space. This approach is described in the context of two models: the basic two-host shared microparasite S-I model and the single-host two-microparasite S-I (susceptible-infective) model. The procedure involved does not require model simplification through a reduction in dimensionality. It can handle intraspecific as well as parasite-mediated competition and, in the second model, single-host parasite coexistence. The map arrays provide a concise catalogue of the possible modes of behaviour of a system and an explanation for changes in that behaviour. In particular, the reasons why the conjectures made about the behaviour of the first of these models do not hold throughout parameter space are immediately clear from the map structure, as are the conditions for collusive and competitive behaviour between the two types of parasite in the second model.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4 1","pages":"333-67"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.4.333","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61179448","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}
J. Mena-Lorca, J. Velasco-Hernández, C. Castillo-Chavez
{"title":"Density-dependent dynamics and superinfection in an epidemic model.","authors":"J. Mena-Lorca, J. Velasco-Hernández, C. Castillo-Chavez","doi":"10.1093/IMAMMB/16.4.307","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.4.307","url":null,"abstract":"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.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4 1","pages":"307-17"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.4.307","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61179573","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":"Multihost, multiparasite systems: an application of bifurcation theory.","authors":"J V Greenman, P J Hudson","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The local analysis of multihost multiparasite models has been hampered by algebraic intractability. There have been two responses to this difficulty: extensive numerical investigation, and simplification to a level where analytical techniques work. In this paper we describe another approach, based on bifurcation theory, in which the qualitative properties of the model equilibrium structure are realized on an array of maps drawn in parameter space. This approach is described in the context of two models: the basic two-host shared microparasite S-I model and the single-host two-microparasite S-I (susceptible-infective) model. The procedure involved does not require model simplification through a reduction in dimensionality. It can handle intraspecific as well as parasite-mediated competition and, in the second model, single-host parasite coexistence. The map arrays provide a concise catalogue of the possible modes of behaviour of a system and an explanation for changes in that behaviour. In particular, the reasons why the conjectures made about the behaviour of the first of these models do not hold throughout parameter space are immediately clear from the map structure, as are the conditions for collusive and competitive behaviour between the two types of parasite in the second model.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4","pages":"333-67"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21523744","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 Kermack-McKendrick model applied to an infectious disease in a natural population.","authors":"M. Roberts","doi":"10.1093/IMAMMB/16.4.319","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.4.319","url":null,"abstract":"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.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 4 1","pages":"319-32"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.4.319","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61179852","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 mathematical model of the ecology of Lyme disease.","authors":"T. Porco","doi":"10.1093/IMAMMB/16.3.261","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.3.261","url":null,"abstract":"A mathematical model of enzootic Lyme-disease transmission in a natural focus is presented. This model is based on the life history of the vector tick Ixodes scapularis Say and the primary reservoir host Peromyscus leucopus. Using this model, the threshold condition for the disease to be able to invade a nonenzootic region is determined as a function of the various possible transmission chains operating throughout the year. These expressions show that the transmission chain in which ticks acquire the disease from mice in the fall and transmit it back to mice as nymphs in the spring is the most important chain (contributing approximately 87% of the elasticity of the threshold for the parameter choices examined). Equilibrium disease levels were examined under the assumption of a constant tick population; these levels were determined as a function of tick and mouse density, the vertical transmission rate, the infectivity of mice, and the survivorship parameters of the ticks and of the tick-host contact rates. Vertical transmission has a disproportionately large effect, since unfed infected larval ticks have two opportunities to feed on mice, rather than only one opportunity (as for a newly infected unfed nymph). Finally, a global sensitivity analysis based on Latin hypercube sampling is performed, in which is shown the importance of quantifying the natural history of infection in mice, and of elucidating the contribution of other hosts for I. scapularis than mice.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 3 1","pages":"261-96"},"PeriodicalIF":0.0,"publicationDate":"1999-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.3.261","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61179377","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 population model applied to HIV transmission considering protection and treatment.","authors":"H. Yang, W. C. Ferreira","doi":"10.1093/IMAMMB/16.3.237","DOIUrl":"https://doi.org/10.1093/IMAMMB/16.3.237","url":null,"abstract":"An epidemiological population model is proposed to assess the impact of protection and/or treatment strategies applied to HIV infection. Sex-education campaigns are the available protection strategy, and drug (or association of drugs) administration is the treatment strategy considered. In this model we assumed recruitment and differential mortality rates for the homosexual population. In addition to the classical threshold contact rate related to the establishment of the disease, we obtained a threshold input rate.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 3 1","pages":"O: 099 M: I: 515"},"PeriodicalIF":0.0,"publicationDate":"1999-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/16.3.237","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61179052","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 population model applied to HIV transmission considering protection and treatment.","authors":"H M Yang, W C Ferreira Júnior","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>An epidemiological population model is proposed to assess the impact of protection and/or treatment strategies applied to HIV infection. Sex-education campaigns are the available protection strategy, and drug (or association of drugs) administration is the treatment strategy considered. In this model we assumed recruitment and differential mortality rates for the homosexual population. In addition to the classical threshold contact rate related to the establishment of the disease, we obtained a threshold input rate.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 3","pages":"O: 099 M: I: 515"},"PeriodicalIF":0.0,"publicationDate":"1999-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21382405","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 mathematical model of the ecology of Lyme disease.","authors":"T C Porco","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>A mathematical model of enzootic Lyme-disease transmission in a natural focus is presented. This model is based on the life history of the vector tick Ixodes scapularis Say and the primary reservoir host Peromyscus leucopus. Using this model, the threshold condition for the disease to be able to invade a nonenzootic region is determined as a function of the various possible transmission chains operating throughout the year. These expressions show that the transmission chain in which ticks acquire the disease from mice in the fall and transmit it back to mice as nymphs in the spring is the most important chain (contributing approximately 87% of the elasticity of the threshold for the parameter choices examined). Equilibrium disease levels were examined under the assumption of a constant tick population; these levels were determined as a function of tick and mouse density, the vertical transmission rate, the infectivity of mice, and the survivorship parameters of the ticks and of the tick-host contact rates. Vertical transmission has a disproportionately large effect, since unfed infected larval ticks have two opportunities to feed on mice, rather than only one opportunity (as for a newly infected unfed nymph). Finally, a global sensitivity analysis based on Latin hypercube sampling is performed, in which is shown the importance of quantifying the natural history of infection in mice, and of elucidating the contribution of other hosts for I. scapularis than mice.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 3","pages":"261-96"},"PeriodicalIF":0.0,"publicationDate":"1999-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21382406","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}
L A Kelly, G Gibson, G Gettinby, W Donachie, J C Low
{"title":"The use of dummy data points when fitting bacterial growth curves.","authors":"L A Kelly, G Gibson, G Gettinby, W Donachie, J C Low","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>We consider the problem of fitting mathematical models for bacterial growth and decline to experimental data. Using models which represent the phases of the growth and decline cycle in a piecewise manner, we describe how least-squares fitting can lead to potentially misleading parameter estimates. We show how these difficulties can be overcome by extending a data set to include hypothetical observations (dummy data points) which reflect biological beliefs, and the resulting stabilization of parameter estimates is analysed mathematically. The techniques are illustrated using real and simulated data sets.</p>","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"16 2","pages":"155-70"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"21266810","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}