Mathematical medicine and biology : a journal of the IMA最新文献

{"title":"Aggregation and asymptotic analysis of an SI-epidemic model for heterogeneous populations","authors":"V. M. Veliov;A. Widder","doi":"10.1093/imammb/dqv018","DOIUrl":"10.1093/imammb/dqv018","url":null,"abstract":"The paper investigates a version of a simple epidemiological model involving only susceptible and infected individuals, where the heterogeneity of the population with respect to susceptibility/infectiousness is taken into account. A comprehensive analysis of the asymptotic behaviour of the disease is given, based on an explicit aggregation of the model. The results are compared with those of a homogeneous version of the model to highlight the influence of the heterogeneity on the asymptotics. Moreover, the performed analysis reveals in which cases incomplete information about the heterogeneity of the population is sufficient in order to determine the long-run outcome of the disease. Numerical simulation is used to emphasize that, for a given level of prevalence, the evolution of the disease under the influence of heterogeneity may in the long run qualitatively differ from the one ‘predicted’ by the homogeneous model. Furthermore, it is shown that, in a closed population, the indicator for the survival of the population is in the presence of heterogeneity distinct from the basic reproduction number.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 3","pages":"295-318"},"PeriodicalIF":0.0,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33333819","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":"Computed tear film and osmolarity dynamics on an eye-shaped domain","authors":"Longfei Li;Richard J. Braun;Tobin A. Driscoll;William D. Henshaw;Jeffrey W. Banks;P. Ewen King-Smith","doi":"10.1093/imammb/dqv013","DOIUrl":"10.1093/imammb/dqv013","url":null,"abstract":"The concentration of ions, or osmolarity, in the tear film is a key variable in understanding dry eye symptoms and disease. In this manuscript, we derive a mathematical model that couples osmolarity (treated as a single solute) and fluid dynamics within the tear film on a 2D eye-shaped domain. The model includes the physical effects of evaporation, surface tension, viscosity, ocular surface wettability, osmolarity, osmosis and tear fluid supply and drainage. The governing system of coupled non-linear partial differential equations is solved using the Overture computational framework, together with a hybrid time-stepping scheme, using a variable step backward differentiation formula and a Runge–Kutta–Chebyshev method that were added to the framework. The results of our numerical simulations provide new insight into the osmolarity distribution over the ocular surface during the interblink.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 2","pages":"123-157"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33225542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exploring the benefits of antibody immune response in HIV-1 infection using a discrete model","authors":"S. P. Showa;F. Nyabadza;S. D. Hove-Musekwa;G. Magombedze","doi":"10.1093/imammb/dqv014","DOIUrl":"10.1093/imammb/dqv014","url":null,"abstract":"The role of antibodies in HIV-1 infection is investigated using a discrete-time mathematical model that considers cell-free and cell-associated transmission of the virus. Model analysis shows that the effect of each type of antibody is dependent on the stage of the infection. Neutralizing antibodies are efficient in controlling the viral levels in the early days after seroconversion and antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication are efficient when the infection becomes established. Model simulations show that antibodies that inhibit viral replication are more effective in controlling the infection than those that recruit Natural Killer T cells after infection establishment. The model was fitted to subjects of the Tsedimoso study conducted in Botswana and conclusions similar to elasticity analysis results were obtained. Model fitting results predicted that neutralizing antibodies are more efficient in controlling the viral levels than antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication in the early days after seroconversion.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 2","pages":"189-210"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33240226","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":"Back matter","authors":"","doi":"","DOIUrl":"https://doi.org/","url":null,"abstract":"","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 2","pages":"1-2"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016811/8189260/08189267.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50351792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal fractionation in radiotherapy with multiple normal tissues","authors":"Fatemeh Saberian;Archis Ghate;Minsun Kim","doi":"10.1093/imammb/dqv015","DOIUrl":"10.1093/imammb/dqv015","url":null,"abstract":"The goal in radiotherapy is to maximize the biological effect (BE) of radiation on the tumour while limiting its toxic effects on healthy anatomies. Treatment is administered over several sessions to give the normal tissue time to recover as it has better damage-repair capabilities than tumour cells. This is termed fractionation. A key problem in radiotherapy involves finding an optimal number of treatment sessions (fractions) and the corresponding dosing schedule. A major limitation of existing mathematically rigorous work on this problem is that it includes only a single normal tissue. Since essentially no anatomical region of interest includes only one normal tissue, these models may incorrectly identify the optimal number of fractions and the corresponding dosing schedule. We present a formulation of the optimal fractionation problem that includes multiple normal tissues. Our model can tackle any combination of maximum dose, mean dose and dose-volume type constraints for serial and parallel normal tissues as this is characteristic of most treatment protocols. We also allow for a spatially heterogeneous dose distribution within each normal tissue. Furthermore, we do not a priori assume that the doses are invariant across fractions. Finally, our model uses a spatially optimized treatment plan as input and hence can be seamlessly combined with any treatment planning system. Our formulation is a mixed-integer, non-convex, quadratically constrained quadratic programming problem. In order to simplify this computationally challenging problem without loss of optimality, we establish sufficient conditions under which equal-dosage or single-dosage fractionation is optimal. Based on the prevalent estimates of tumour and normal tissue model parameters, these conditions are expected to hold in many types of commonly studied tumours, such as those similar to head-and-neck and prostate cancers. This motivates a simple reformulation of our problem that leads to a closed-form formula for the dose per fraction. We then establish that the tumour-BE is quasiconcave in the number of fractions; this ultimately helps in identifying the optimal number of fractions. We perform extensive numerical experiments using 10 head-and-neck and prostate test cases to uncover several clinically relevant insights.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 2","pages":"211-252"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33189257","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":"Improving Bacillus Calmette-Guérin (BCG) immunotherapy for bladder cancer by adding interleukin 2 (IL-2): a mathematical model","authors":"Svetlana Bunimovich-Mendrazitsky;Sarel Halachmi;Natalie Kronik","doi":"10.1093/imammb/dqv007","DOIUrl":"10.1093/imammb/dqv007","url":null,"abstract":"One of the treatments offered to non-invasive bladder cancer patients is BCG instillations, using a well-established, time-honoured protocol. Some of the patients, however, do not respond to this protocol. To examine possible changes in the protocol, we provide a platform for in silico testing of alternative protocols for BCG instillations and combinations with IL-2, to be used by urologists in planning new treatment strategies for subpopulations of bladder cancer patients who may benefit from a personalized protocol. We use a systems biology approach to describe the BCG-tumour-immune interplay and translate it into a set of mathematical differential equations. The variables of the equation set are the number of tumour cells, bacteria cells, immune cells, and cytokines participating in the tumour-immune response. Relevant parameters that describe the system's dynamics are taken from a variety of independent literature, unrelated to the clinical trial results assessed by the model predictions. Model simulations use a clinically relevant range of initial tumour sizes (tumour volume) and tumour growth rates (tumour grade), representative of a virtual population of fifty patients. Our model successfully retrieved previous clinical results for BCG induction treatment and BCG maintenance therapy with a complete response (CR) rate of 82%. Furthermore, we designed alternative maintenance protocols, using IL-2 combinations with BCG, which improved success rates up to 86% and 100% of the patients, albeit without considering possible side effects. We have shown our simulation platform to be reliable by demonstrating its ability to retrieve published clinical trial results. We used this platform to predict the outcome of treatment combinations. Our results suggest that the subpopulation of non-responsive patients may benefit from an intensified combined BCG IL-2 maintenance treatment.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 2","pages":"159-188"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33229472","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":"Front matter","authors":"","doi":"","DOIUrl":"https://doi.org/","url":null,"abstract":"","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 2","pages":"1-2"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016811/8189260/08189265.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50425688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Revisiting a two-patch SIS model with infection during transport","authors":"Julien Arino;Chengjun Sun;Wei Yang","doi":"10.1093/imammb/dqv001","DOIUrl":"10.1093/imammb/dqv001","url":null,"abstract":"We incorporate parameter heterogeneity in a two-patch susceptible-infectious-susceptible (SIS) epidemic model with infection during transport and prove that the disease-free and endemic equilibria are globally asymptotically stable when the basic reproduction number \u0000<tex>$mathscr {R}_0 &lt; 1$</tex>\u0000 and \u0000<tex>$mathscr {R}_0&gt;1$</tex>\u0000, respectively. We find that infection during transport increases the possibility that the disease persists in both patches and amplifies prevalence when disease is present. We then study the effect of a perfect unilateral exit screening programme. Finally, we compare numerically the effects of using different incidence functions for infection within and while travelling between patches, and find that using mass action incidence to model infection during transport has the effect of maintaining disease prevalence at a higher level compared with when standard incidence is used.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 1","pages":"29-55"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33051958","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":"Front matter","authors":"","doi":"","DOIUrl":"https://doi.org/","url":null,"abstract":"","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 1","pages":"1-2"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016811/8225294/08225300.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67867564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modelling cholesterol effects on the dynamics of the hypothalamic–pituitary–adrenal (HPA) axis","authors":"Vladimir M. Marković;Željko Čupić;Stevan Maćešić;Stevan Maćešić;Vladana Vukojević;Ljiljana Kolar-Anić","doi":"10.1093/imammb/dqu020","DOIUrl":"10.1093/imammb/dqu020","url":null,"abstract":"A mathematical model of the hypothalamic–pituitary–adrenal (HPA) axis with cholesterol as a dynamical variable was derived to investigate the effects of cholesterol, the primary precursor of all steroid hormones, on the ultradian and circadian HPA axis activity. To develop the model, the parameter space was systematically examined by stoichiometric network analysis to identify conditions for ultradian oscillations, determine conditions under which dynamic transitions, i.e. bifurcations occur and identify bifurcation types. The bifurcations were further characterized using numerical simulations. Model predictions agree well with empirical findings reported in the literature, indicating that cholesterol levels may critically affect the global dynamics of the HPA axis. The proposed model provides a base for better understanding of experimental observations, it may be used as a tool for designing experiments and offers useful insights into the characteristics of basic dynamic regulatory mechanisms that, when impaired, may lead to the development of some modern-lifestyle-associated diseases.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 1","pages":"1-28"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqu020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32761440","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}