D E Andreev;P V Baranov;A Milogorodskii;D Rachinskii
Totally asymmetric simple exclusion process (TASEP) modelling was shown to offer a parsimonious explanation for the experimentally confirmed ability of a single upstream open reading frames (uORFs) to upregulate downstream translation during the integrated stress response. As revealed by numerical simulations, the model predicts that reducing the density of scanning ribosomes upstream of certain uORFs increases the flow of ribosomes downstream. To gain a better insight into the mechanism which ensures the non-monotone relation between the upstream and downstream flows, in this work, we propose a phenomenological deterministic model approximating the TASEP model of the translation process. We establish the existence of a stationary solution featuring the decreasing density along the uORF for the deterministic model. Further, we find an explicit non-monotone relation between the upstream ribosome density and the downstream flow for the stationary solution in the limit of increasing uORF length and increasingly leaky initiation. The stationary distribution of the TASEP model, the stationary solution of the deterministic model and the explicit limit are compared numerically.
{"title":"A deterministic model for non-monotone relationship between translation of upstream and downstream open reading frames","authors":"D E Andreev;P V Baranov;A Milogorodskii;D Rachinskii","doi":"10.1093/imammb/dqab015","DOIUrl":"10.1093/imammb/dqab015","url":null,"abstract":"Totally asymmetric simple exclusion process (TASEP) modelling was shown to offer a parsimonious explanation for the experimentally confirmed ability of a single upstream open reading frames (uORFs) to upregulate downstream translation during the integrated stress response. As revealed by numerical simulations, the model predicts that reducing the density of scanning ribosomes upstream of certain uORFs increases the flow of ribosomes downstream. To gain a better insight into the mechanism which ensures the non-monotone relation between the upstream and downstream flows, in this work, we propose a phenomenological deterministic model approximating the TASEP model of the translation process. We establish the existence of a stationary solution featuring the decreasing density along the uORF for the deterministic model. Further, we find an explicit non-monotone relation between the upstream ribosome density and the downstream flow for the stationary solution in the limit of increasing uORF length and increasingly leaky initiation. The stationary distribution of the TASEP model, the stationary solution of the deterministic model and the explicit limit are compared numerically.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 4","pages":"490-515"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39576651","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}
Laura D'Orsi;Luciano Curcio;Fabio Cibella;Alessandro Borri;Lilach Gavish;Arik Eisenkraft;Andrea De Gaetano
A variety of mathematical models of the cardiovascular system have been suggested over several years in order to describe the time-course of a series of physiological variables (i.e. heart rate, cardiac output, arterial pressure) relevant for the compensation mechanisms to perturbations, such as severe haemorrhage. The current study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. The present work proposes a first version of a differential-algebraic equations model, the model dynamical ODE model for haemorrhage (dODEg). The model consists of 10 differential and 14 algebraic equations, incorporating 61 model parameters. This model is capable of replicating the changes in heart rate, mean arterial pressure and cardiac output after the onset of bleeding observed in four experimental animal preparations and fits well to the experimental data. By predicting the time-course of the physiological response after haemorrhage, the dODEg model presented here may be of significant value for the quantitative assessment of conventional or novel therapeutic regimens. The model may be applied to the prediction of survivability and to the determination of the urgency of evacuation towards definitive surgical treatment in the operational setting.
{"title":"A mathematical model of cardiovascular dynamics for the diagnosis and prognosis of hemorrhagic shock","authors":"Laura D'Orsi;Luciano Curcio;Fabio Cibella;Alessandro Borri;Lilach Gavish;Arik Eisenkraft;Andrea De Gaetano","doi":"10.1093/imammb/dqab011","DOIUrl":"10.1093/imammb/dqab011","url":null,"abstract":"A variety of mathematical models of the cardiovascular system have been suggested over several years in order to describe the time-course of a series of physiological variables (i.e. heart rate, cardiac output, arterial pressure) relevant for the compensation mechanisms to perturbations, such as severe haemorrhage. The current study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. The present work proposes a first version of a differential-algebraic equations model, the model dynamical ODE model for haemorrhage (dODEg). The model consists of 10 differential and 14 algebraic equations, incorporating 61 model parameters. This model is capable of replicating the changes in heart rate, mean arterial pressure and cardiac output after the onset of bleeding observed in four experimental animal preparations and fits well to the experimental data. By predicting the time-course of the physiological response after haemorrhage, the dODEg model presented here may be of significant value for the quantitative assessment of conventional or novel therapeutic regimens. The model may be applied to the prediction of survivability and to the determination of the urgency of evacuation towards definitive surgical treatment in the operational setting.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 4","pages":"417-441"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39416172","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}
Formulating accurate and robust classification strategies is a key challenge of developing diagnostic and antibody tests. Methods that do not explicitly account for disease prevalence and uncertainty therein can lead to significant classification errors. We present a novel method that leverages optimal decision theory to address this problem. As a preliminary step, we develop an analysis that uses an assumed prevalence and conditional probability models of diagnostic measurement outcomes to define optimal (in the sense of minimizing rates of false positives and false negatives) classification domains. Critically, we demonstrate how this strategy can be generalized to a setting in which the prevalence is unknown by either (i) defining a third class of hold-out samples that require further testing or (ii) using an adaptive algorithm to estimate prevalence prior to defining classification domains. We also provide examples for a recently published SARS-CoV-2 serology test and discuss how measurement uncertainty (e.g. associated with instrumentation) can be incorporated into the analysis. We find that our new strategy decreases classification error by up to a decade relative to more traditional methods based on confidence intervals. Moreover, it establishes a theoretical foundation for generalizing techniques such as receiver operating characteristics by connecting them to the broader field of optimization.
{"title":"Classification under uncertainty: data analysis for diagnostic antibody testing","authors":"Paul N Patrone;Anthony J Kearsley","doi":"10.1093/imammb/dqab007","DOIUrl":"10.1093/imammb/dqab007","url":null,"abstract":"Formulating accurate and robust classification strategies is a key challenge of developing diagnostic and antibody tests. Methods that do not explicitly account for disease prevalence and uncertainty therein can lead to significant classification errors. We present a novel method that leverages optimal decision theory to address this problem. As a preliminary step, we develop an analysis that uses an assumed prevalence and conditional probability models of diagnostic measurement outcomes to define optimal (in the sense of minimizing rates of false positives and false negatives) classification domains. Critically, we demonstrate how this strategy can be generalized to a setting in which the prevalence is unknown by either (i) defining a third class of hold-out samples that require further testing or (ii) using an adaptive algorithm to estimate prevalence prior to defining classification domains. We also provide examples for a recently published SARS-CoV-2 serology test and discuss how measurement uncertainty (e.g. associated with instrumentation) can be incorporated into the analysis. We find that our new strategy decreases classification error by up to a decade relative to more traditional methods based on confidence intervals. Moreover, it establishes a theoretical foundation for generalizing techniques such as receiver operating characteristics by connecting them to the broader field of optimization.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 3","pages":"396-416"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016811/9579095/09579102.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39307448","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}
There is a gradual telomere shortening due to the inability of the replication machinery to copy the very ends of chromosomes. Additionally, other factors such as high levels of oxidation (free radicals or reactive oxygen species (ROS)), e.g. due to cumulated stress, inflammation or tobacco smoke, accelerate telomere shortening. In humans, the average telomere length is about 10–15 kb at birth and telomeres shorten at a pace of 70 bp per year. However, when cells are exposed to ROS, telomere attrition happens at a faster pace, generating a wide variety of telomere size distribution in different length percentiles, which are different to what is expected just by age. In this work, the generational age of a cell is associated with its telomere length (TL), from certain maximum to the minimal TL that allows replication. In order to study the accumulation of aged granulosa cells in human follicles, from preantral to preovulatory size, a mathematical model is proposed, regarding different degrees of accelerated telomere shortening, which reflect the action of ROS in addition to the telomere shortening that happens after cell division. In cases of cells with TL shorter than cells with average TL, with low telomerase activity and accelerated telomere shortening, the mathematical model predicts an aged outcome in preovulatory follicles. The model provides a plausible explanation for what has been observed in oocytes from older women, which have been exposed to ROS for a longer period of time and have bad outcomes after in vitro fertilization.
{"title":"Mathematical modelling of ageing acceleration of the human follicle due to oxidative stress and other factors","authors":"A M Portillo;C Peláez","doi":"10.1093/imammb/dqab004","DOIUrl":"10.1093/imammb/dqab004","url":null,"abstract":"There is a gradual telomere shortening due to the inability of the replication machinery to copy the very ends of chromosomes. Additionally, other factors such as high levels of oxidation (free radicals or reactive oxygen species (ROS)), e.g. due to cumulated stress, inflammation or tobacco smoke, accelerate telomere shortening. In humans, the average telomere length is about 10–15 kb at birth and telomeres shorten at a pace of 70 bp per year. However, when cells are exposed to ROS, telomere attrition happens at a faster pace, generating a wide variety of telomere size distribution in different length percentiles, which are different to what is expected just by age. In this work, the generational age of a cell is associated with its telomere length (TL), from certain maximum to the minimal TL that allows replication. In order to study the accumulation of aged granulosa cells in human follicles, from preantral to preovulatory size, a mathematical model is proposed, regarding different degrees of accelerated telomere shortening, which reflect the action of ROS in addition to the telomere shortening that happens after cell division. In cases of cells with TL shorter than cells with average TL, with low telomerase activity and accelerated telomere shortening, the mathematical model predicts an aged outcome in preovulatory follicles. The model provides a plausible explanation for what has been observed in oocytes from older women, which have been exposed to ROS for a longer period of time and have bad outcomes after in vitro fertilization.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 3","pages":"273-291"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqab004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25532334","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}
The collection of 3D cell tracking data from live images of micro-tissues is a recent innovation made possible due to advances in imaging techniques. As such there is increased interest in studying cell motility in 3D in vitro model systems but a lack of rigorous methodology for analysing the resulting data sets. One such instance of the use of these in vitro models is in the study of cancerous tumours. Growing multicellular tumour spheroids in vitro allows for modelling of the tumour microenvironment and the study of tumour cell behaviours, such as migration, which improves understanding of these cells and in turn could potentially improve cancer treatments. In this paper, we present a workflow for the rigorous analysis of 3D cell tracking data, based on the persistent random walk model, but adaptable to other biologically informed mathematical models. We use statistical measures to assess the fit of the model to the motility data and to estimate model parameters and provide confidence intervals for those parameters, to allow for parametrization of the model taking correlation in the data into account. We use in silico simulations to validate the workflow in 3D before testing our method on cell tracking data taken from in vitro experiments on glioblastoma tumour cells, a brain cancer with a very poor prognosis. The presented approach is intended to be accessible to both modellers and experimentalists alike in that it provides tools for uncovering features of the data set that may suggest amendments to future experiments or modelling attempts.
{"title":"A mathematical framework for modelling 3D cell motility: applications to glioblastoma cell migration","authors":"M Scott;K Żychaluk;R N Bearon","doi":"10.1093/imammb/dqab009","DOIUrl":"10.1093/imammb/dqab009","url":null,"abstract":"The collection of 3D cell tracking data from live images of micro-tissues is a recent innovation made possible due to advances in imaging techniques. As such there is increased interest in studying cell motility in 3D in vitro model systems but a lack of rigorous methodology for analysing the resulting data sets. One such instance of the use of these in vitro models is in the study of cancerous tumours. Growing multicellular tumour spheroids in vitro allows for modelling of the tumour microenvironment and the study of tumour cell behaviours, such as migration, which improves understanding of these cells and in turn could potentially improve cancer treatments. In this paper, we present a workflow for the rigorous analysis of 3D cell tracking data, based on the persistent random walk model, but adaptable to other biologically informed mathematical models. We use statistical measures to assess the fit of the model to the motility data and to estimate model parameters and provide confidence intervals for those parameters, to allow for parametrization of the model taking correlation in the data into account. We use in silico simulations to validate the workflow in 3D before testing our method on cell tracking data taken from in vitro experiments on glioblastoma tumour cells, a brain cancer with a very poor prognosis. The presented approach is intended to be accessible to both modellers and experimentalists alike in that it provides tools for uncovering features of the data set that may suggest amendments to future experiments or modelling attempts.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 3","pages":"333-354"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39143759","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}
Peter Mortensen;Hao Gao;Godfrey Smith;Radostin D Simitev
The analytical theory of our earlier study (Mortensen et al., 2021, Math. Med. Biol., 38, 106–131) is extended to address the outstanding cases of fibroblast barrier distribution and myocyte strait distribution. In particular, closed-form approximations to the resting membrane potential and to the critical parameter values for propagation are derived for these two non-uniform fibroblast distributions and are in good agreement with numerical estimates.
我们早期研究的分析理论(Mortensen et al.， 2021, Math。地中海,杂志。， 38, 106-131)扩展到解决成纤维细胞屏障分布和肌细胞海峡分布的突出案例。特别是，对于这两种非均匀成纤维细胞分布，导出了静息膜电位和繁殖关键参数值的封闭近似，并与数值估计很好地一致。
{"title":"Addendum: Action potential propagation and block in a model of atrial tissue with myocyte–fibroblast coupling","authors":"Peter Mortensen;Hao Gao;Godfrey Smith;Radostin D Simitev","doi":"10.1093/imammb/dqab005","DOIUrl":"10.1093/imammb/dqab005","url":null,"abstract":"The analytical theory of our earlier study (Mortensen et al., 2021, Math. Med. Biol., 38, 106–131) is extended to address the outstanding cases of fibroblast barrier distribution and myocyte strait distribution. In particular, closed-form approximations to the resting membrane potential and to the critical parameter values for propagation are derived for these two non-uniform fibroblast distributions and are in good agreement with numerical estimates.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 3","pages":"292-298"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016811/9579095/09579097.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38958678","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}
Daniel M Anderson;Maria Corsaro;Jonathan Horton;Tim Reid;Padmanabhan Seshaiyer
We develop a lubrication theory-based mathematical model that describes the dynamics of a tear film during blinking and contact lens (CL) wear. The model extends previous work on pre-corneal tear film dynamics during blinking by coupling the partial differential equation for tear film thickness to a dynamic model for CL motion. We explore different models for eyelid motion and also account for possible voluntary and involuntary globe (eyeball) rotation that may accompany blinking. Boundary conditions for mass flux at the eyelids are also adapted to account for the presence and motion of the CL. Our predictions for CL motion compare reasonably with existing data. Away from the eyelids the pre-lens tear film (PrLTF) is shifted, relative to its pre-corneal counterpart, in the direction of CL motion. Near the eyelids, the inflow/outflow of fluid under the eyelids also influences the PrLTF profile. We also compare our PrLTF dynamics to existing in vivo tear film thickness measurements.
{"title":"Tear film dynamics with blinking and contact lens motion","authors":"Daniel M Anderson;Maria Corsaro;Jonathan Horton;Tim Reid;Padmanabhan Seshaiyer","doi":"10.1093/imammb/dqab010","DOIUrl":"10.1093/imammb/dqab010","url":null,"abstract":"We develop a lubrication theory-based mathematical model that describes the dynamics of a tear film during blinking and contact lens (CL) wear. The model extends previous work on pre-corneal tear film dynamics during blinking by coupling the partial differential equation for tear film thickness to a dynamic model for CL motion. We explore different models for eyelid motion and also account for possible voluntary and involuntary globe (eyeball) rotation that may accompany blinking. Boundary conditions for mass flux at the eyelids are also adapted to account for the presence and motion of the CL. Our predictions for CL motion compare reasonably with existing data. Away from the eyelids the pre-lens tear film (PrLTF) is shifted, relative to its pre-corneal counterpart, in the direction of CL motion. Near the eyelids, the inflow/outflow of fluid under the eyelids also influences the PrLTF profile. We also compare our PrLTF dynamics to existing in vivo tear film thickness measurements.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 3","pages":"355-395"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39204057","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}
The goal of patient-specific treatment of diseases requires a connection between clinical observations with models that are able to accurately predict the disease progression. Even when realistic models are available, it is very difficult to parameterize them and often parameter estimates that are made using early time course data prove to be highly inaccurate. Inaccuracies can cause different predictions, especially when the progression depends sensitively on the parameters. In this study, we apply a Bayesian data assimilation method, where the data are incorporated sequentially, to a model of the autoimmune disease alopecia areata that is characterized by distinct spatial patterns of hair loss. Using synthetic data as simulated clinical observations, we show that our method is relatively robust with respect to variations in parameter estimates. Moreover, we compare convergence rates for parameters with different sensitivities, varying observational times and varying levels of noise. We find that this method works better for sparse observations, sensitive parameters and noisy observations. Taken together, we find that our data assimilation, in conjunction with our biologically inspired model, provides directions for individualized diagnosis and treatments.
{"title":"Data assimilation of synthetic data as a novel strategy for predicting disease progression in alopecia areata","authors":"NG Cogan;Feng Bao;Ralf Paus;Atanaska Dobreva","doi":"10.1093/imammb/dqab008","DOIUrl":"10.1093/imammb/dqab008","url":null,"abstract":"The goal of patient-specific treatment of diseases requires a connection between clinical observations with models that are able to accurately predict the disease progression. Even when realistic models are available, it is very difficult to parameterize them and often parameter estimates that are made using early time course data prove to be highly inaccurate. Inaccuracies can cause different predictions, especially when the progression depends sensitively on the parameters. In this study, we apply a Bayesian data assimilation method, where the data are incorporated sequentially, to a model of the autoimmune disease alopecia areata that is characterized by distinct spatial patterns of hair loss. Using synthetic data as simulated clinical observations, we show that our method is relatively robust with respect to variations in parameter estimates. Moreover, we compare convergence rates for parameters with different sensitivities, varying observational times and varying levels of noise. We find that this method works better for sparse observations, sensitive parameters and noisy observations. Taken together, we find that our data assimilation, in conjunction with our biologically inspired model, provides directions for individualized diagnosis and treatments.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 3","pages":"314-332"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39078946","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}
A James;M J Plank;R N Binny;A Lustig;K Hannah;S C Hendy;N Steyn
We use a stochastic branching process model, structured by age and level of healthcare access, to look at the heterogeneous spread of COVID-19 within a population. We examine the effect of control scenarios targeted at particular groups, such as school closures or social distancing by older people. Although we currently lack detailed empirical data about contact and infection rates between age groups and groups with different levels of healthcare access within New Zealand, these scenarios illustrate how such evidence could be used to inform specific interventions. We find that an increase in the transmission rates among children from reopening schools is unlikely to significantly increase the number of cases, unless this is accompanied by a change in adult behaviour. We also find that there is a risk of undetected outbreaks occurring in communities that have low access to healthcare and that are socially isolated from more privileged communities. The greater the degree of inequity and extent of social segregation, the longer it will take before any outbreaks are detected. A well-established evidence for health inequities, particularly in accessing primary healthcare and testing, indicates that Māori and Pacific peoples are at a higher risk of undetected outbreaks in Aotearoa New Zealand. This highlights the importance of ensuring that community needs for access to healthcare, including early proactive testing, rapid contact tracing and the ability to isolate, are being met equitably. Finally, these scenarios illustrate how information concerning contact and infection rates across different demographic groups may be useful in informing specific policy interventions.
{"title":"A structured model for COVID-19 spread: modelling age and healthcare inequities","authors":"A James;M J Plank;R N Binny;A Lustig;K Hannah;S C Hendy;N Steyn","doi":"10.1093/imammb/dqab006","DOIUrl":"10.1093/imammb/dqab006","url":null,"abstract":"We use a stochastic branching process model, structured by age and level of healthcare access, to look at the heterogeneous spread of COVID-19 within a population. We examine the effect of control scenarios targeted at particular groups, such as school closures or social distancing by older people. Although we currently lack detailed empirical data about contact and infection rates between age groups and groups with different levels of healthcare access within New Zealand, these scenarios illustrate how such evidence could be used to inform specific interventions. We find that an increase in the transmission rates among children from reopening schools is unlikely to significantly increase the number of cases, unless this is accompanied by a change in adult behaviour. We also find that there is a risk of undetected outbreaks occurring in communities that have low access to healthcare and that are socially isolated from more privileged communities. The greater the degree of inequity and extent of social segregation, the longer it will take before any outbreaks are detected. A well-established evidence for health inequities, particularly in accessing primary healthcare and testing, indicates that Māori and Pacific peoples are at a higher risk of undetected outbreaks in Aotearoa New Zealand. This highlights the importance of ensuring that community needs for access to healthcare, including early proactive testing, rapid contact tracing and the ability to isolate, are being met equitably. Finally, these scenarios illustrate how information concerning contact and infection rates across different demographic groups may be useful in informing specific policy interventions.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 3","pages":"299-313"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqab006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39004967","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}
Blebs are cell protrusions generated by local membrane–cortex detachments followed by expansion of the plasma membrane. Blebs are formed by some migrating cells, e.g. primordial germ cells of the zebrafish. While blebs occur randomly at each part of the membrane in unpolarized cells, a polarization process guarantees the occurrence of blebs at a preferential site and thereby facilitates migration toward a specified direction. Little is known about the factors involved in the controlled and directed bleb generation, yet recent studies revealed the influence of an intracellular flow and the stabilizing role of the membrane–cortex linker molecule Ezrin. Based on this information, we develop and analyse a coupled bulk-surface model describing a potential cellular mechanism by which a bleb could be induced at a controlled site. The model rests upon intracellular Darcy flow and a diffusion–advection–reaction system, describing the temporal evolution from a homogeneous to a strongly anisotropic Ezrin distribution. We prove the well-posedness of the mathematical model and show that simulations qualitatively correspond to experimental observations, suggesting that indeed the interaction of an intracellular flow with membrane proteins can be the cause of the Ezrin redistribution accompanying bleb formation.
{"title":"A mathematical model for bleb regulation in zebrafish primordial germ cells","authors":"Carolin Dirks;Paul Striewski;Benedikt Wirth;Anne Aalto;Adan Olguin-Olguin","doi":"10.1093/imammb/dqab002","DOIUrl":"10.1093/imammb/dqab002","url":null,"abstract":"Blebs are cell protrusions generated by local membrane–cortex detachments followed by expansion of the plasma membrane. Blebs are formed by some migrating cells, e.g. primordial germ cells of the zebrafish. While blebs occur randomly at each part of the membrane in unpolarized cells, a polarization process guarantees the occurrence of blebs at a preferential site and thereby facilitates migration toward a specified direction. Little is known about the factors involved in the controlled and directed bleb generation, yet recent studies revealed the influence of an intracellular flow and the stabilizing role of the membrane–cortex linker molecule Ezrin. Based on this information, we develop and analyse a coupled bulk-surface model describing a potential cellular mechanism by which a bleb could be induced at a controlled site. The model rests upon intracellular Darcy flow and a diffusion–advection–reaction system, describing the temporal evolution from a homogeneous to a strongly anisotropic Ezrin distribution. We prove the well-posedness of the mathematical model and show that simulations qualitatively correspond to experimental observations, suggesting that indeed the interaction of an intracellular flow with membrane proteins can be the cause of the Ezrin redistribution accompanying bleb formation.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 2","pages":"218-254"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqab002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9303904","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}
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