Pub Date : 2018-08-16DOI: 10.1080/23737867.2018.1509026
J. Blackwood, L. Childs
ABSTRACT Mathematical models are ubiquitous in the study of the transmission dynamics of infectious diseases, In particular, the classic ‘susceptible-infectious-recovered’ (SIR) paradigm provides a modeling framework that can be adapted to describe the core transmission dynamics of a range of human and wildlife diseases. These models provide an important tool for uncovering the mechanisms generating observed disease dynamics, evaluating potential control strategies, and predicting future outbreaks. With ongoing advances in computational tools as well as access to disease incidence data, the use of such models continues to increase. Here, we provide a basic introduction to disease modeling that is primarily intended for individuals who are new to developing SIR-type models. In particular, we highlight several common issues encountered when structuring and analyzing these models.
{"title":"An introduction to compartmental modeling for the budding infectious disease modeler","authors":"J. Blackwood, L. Childs","doi":"10.1080/23737867.2018.1509026","DOIUrl":"https://doi.org/10.1080/23737867.2018.1509026","url":null,"abstract":"ABSTRACT Mathematical models are ubiquitous in the study of the transmission dynamics of infectious diseases, In particular, the classic ‘susceptible-infectious-recovered’ (SIR) paradigm provides a modeling framework that can be adapted to describe the core transmission dynamics of a range of human and wildlife diseases. These models provide an important tool for uncovering the mechanisms generating observed disease dynamics, evaluating potential control strategies, and predicting future outbreaks. With ongoing advances in computational tools as well as access to disease incidence data, the use of such models continues to increase. Here, we provide a basic introduction to disease modeling that is primarily intended for individuals who are new to developing SIR-type models. In particular, we highlight several common issues encountered when structuring and analyzing these models.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"195 - 221"},"PeriodicalIF":0.0,"publicationDate":"2018-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1509026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47307458","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}
Pub Date : 2018-08-09DOI: 10.1080/23737867.2018.1506712
E. Omondi, Rachel Waema Mbogo, L. Luboobi
ABSTRACT In this paper, we develop a mathematical model describing the dynamics of HIV transmission by incorporating sexual orientation of individuals. Equilibrium points and the basic reproduction number are derived. The basic reproduction number provides a threshold that determines whether or not the disease fades away. The model, described by non-linear ODEs, shows existence of unique disease-free and disease-persistent equilibria. Least squares curve fitting is presented to quantitatively investigate the trend of infection within each gender. The results are indicative of a higher infectivity in the female population. We further investigated the effect of the introduction of pre-exposure prophylaxis (PrEP) on the dynamics of the HIV. Our results show that the introduction of PrEP has had a positive effect on the limitation of spread of HIV. Sensitivity analysis results show that control of effective contacts can result in control of the disease across gender divide. The model provides a unique opportunity to influence policy on HIV treatment and management.
{"title":"Mathematical analysis of sex-structured population model of HIV infection in Kenya","authors":"E. Omondi, Rachel Waema Mbogo, L. Luboobi","doi":"10.1080/23737867.2018.1506712","DOIUrl":"https://doi.org/10.1080/23737867.2018.1506712","url":null,"abstract":"ABSTRACT In this paper, we develop a mathematical model describing the dynamics of HIV transmission by incorporating sexual orientation of individuals. Equilibrium points and the basic reproduction number are derived. The basic reproduction number provides a threshold that determines whether or not the disease fades away. The model, described by non-linear ODEs, shows existence of unique disease-free and disease-persistent equilibria. Least squares curve fitting is presented to quantitatively investigate the trend of infection within each gender. The results are indicative of a higher infectivity in the female population. We further investigated the effect of the introduction of pre-exposure prophylaxis (PrEP) on the dynamics of the HIV. Our results show that the introduction of PrEP has had a positive effect on the limitation of spread of HIV. Sensitivity analysis results show that control of effective contacts can result in control of the disease across gender divide. The model provides a unique opportunity to influence policy on HIV treatment and management.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"174 - 194"},"PeriodicalIF":0.0,"publicationDate":"2018-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1506712","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47777754","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}
Pub Date : 2018-07-19DOI: 10.1080/23737867.2018.1497458
J. L. Boldrini, M. Viana, S. F. dos Reis, Barbara Henning
ABSTRACT Thermoregulation in endotherms allows the maintenance of the body temperature independent of ambient temperature. Experimental data have revealed complex interactions between the physiological mechanisms of thermoregulation and environmental conditions. We derive a nonlinear partial integro-differential dynamical model based on physical first principles and fundamental physiological mechanisms to understand the role of some thermal control mechanisms in the thermoregulation process of endotherms. The model is composed of four layers representing different tissues and it incorporates six thermal feedback control mechanisms. These mechanisms are heat production due to metabolic rate and heat exchange within the body given its internal structure, and the model considers heat exchange due to conduction, heat transport by blood flow, heat exchange with the ambient through convection, radiation, and evaporation from the respiratory tract and superficial evaporation in both passive and active situations. Our model sheds new light on previous explanations about the classic metabolism-ambient temperature U-shaped curve.
{"title":"A mathematical model for thermoregulation in endotherms including heat transport by blood flow and thermal feedback control mechanisms: changes in coat, metabolic rate, blood fluxes, ventilation and sweating rates","authors":"J. L. Boldrini, M. Viana, S. F. dos Reis, Barbara Henning","doi":"10.1080/23737867.2018.1497458","DOIUrl":"https://doi.org/10.1080/23737867.2018.1497458","url":null,"abstract":"ABSTRACT Thermoregulation in endotherms allows the maintenance of the body temperature independent of ambient temperature. Experimental data have revealed complex interactions between the physiological mechanisms of thermoregulation and environmental conditions. We derive a nonlinear partial integro-differential dynamical model based on physical first principles and fundamental physiological mechanisms to understand the role of some thermal control mechanisms in the thermoregulation process of endotherms. The model is composed of four layers representing different tissues and it incorporates six thermal feedback control mechanisms. These mechanisms are heat production due to metabolic rate and heat exchange within the body given its internal structure, and the model considers heat exchange due to conduction, heat transport by blood flow, heat exchange with the ambient through convection, radiation, and evaporation from the respiratory tract and superficial evaporation in both passive and active situations. Our model sheds new light on previous explanations about the classic metabolism-ambient temperature U-shaped curve.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"129 - 173"},"PeriodicalIF":0.0,"publicationDate":"2018-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1497458","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43857189","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}
Pub Date : 2018-06-30DOI: 10.1080/23737867.2018.1440978
Elpiniki Nikolopoulou, Lauren R. Johnson, Duane Harris, J. Nagy, E. Stites, Y. Kuang
Abstract The use of immune checkpoint inhibitors is becoming more commonplace in clinical trials across the nation. Two important factors in the tumour-immune response are the checkpoint protein programmed death-1 (PD-1) and its ligand PD-L1. We propose a mathematical tumour-immune model using a system of ordinary differential equations to study dynamics with and without the use of anti-PD-1. A sensitivity analysis is conducted, and series of simulations are performed to investigate the effects of intermittent and continuous treatments on the tumour-immune dynamics. We consider the system without the anti-PD-1 drug to conduct a mathematical analysis to determine the stability of the tumour-free and tumorous equilibria. Through simulations, we found that a normally functioning immune system may control tumour. We observe treatment with anti-PD-1 alone may not be sufficient to eradicate tumour cells. Therefore, it may be beneficial to combine single agent treatments with additional therapies to obtain a better antitumour response.
{"title":"Tumour-immune dynamics with an immune checkpoint inhibitor","authors":"Elpiniki Nikolopoulou, Lauren R. Johnson, Duane Harris, J. Nagy, E. Stites, Y. Kuang","doi":"10.1080/23737867.2018.1440978","DOIUrl":"https://doi.org/10.1080/23737867.2018.1440978","url":null,"abstract":"Abstract The use of immune checkpoint inhibitors is becoming more commonplace in clinical trials across the nation. Two important factors in the tumour-immune response are the checkpoint protein programmed death-1 (PD-1) and its ligand PD-L1. We propose a mathematical tumour-immune model using a system of ordinary differential equations to study dynamics with and without the use of anti-PD-1. A sensitivity analysis is conducted, and series of simulations are performed to investigate the effects of intermittent and continuous treatments on the tumour-immune dynamics. We consider the system without the anti-PD-1 drug to conduct a mathematical analysis to determine the stability of the tumour-free and tumorous equilibria. Through simulations, we found that a normally functioning immune system may control tumour. We observe treatment with anti-PD-1 alone may not be sufficient to eradicate tumour cells. Therefore, it may be beneficial to combine single agent treatments with additional therapies to obtain a better antitumour response.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"S137 - S159"},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1440978","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48005006","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}
Pub Date : 2018-06-12DOI: 10.1080/23737867.2018.1483003
A. Eladdadi, L. Pillis, P. Kim
While incredible efforts have been made over the past decades to decipher the complexity of tumour–immune interactions, there is still a growing need for innovative quantitative modelling approaches that account for the complexity of tumour–immune dynamics. Mathematical modelling can shed light on the multifaceted processes implicated in this new type of therapy, such as the dynamics of immune activation and regulation, immune responses against tumour, tumour suppression of immune cells, the impact of the tumour environment, tumour escape mechanisms and recent advances in cancer therapies.
{"title":"Modelling tumour–immune dynamics, disease progression and treatment","authors":"A. Eladdadi, L. Pillis, P. Kim","doi":"10.1080/23737867.2018.1483003","DOIUrl":"https://doi.org/10.1080/23737867.2018.1483003","url":null,"abstract":"While incredible efforts have been made over the past decades to decipher the complexity of tumour–immune interactions, there is still a growing need for innovative quantitative modelling approaches that account for the complexity of tumour–immune dynamics. Mathematical modelling can shed light on the multifaceted processes implicated in this new type of therapy, such as the dynamics of immune activation and regulation, immune responses against tumour, tumour suppression of immune cells, the impact of the tumour environment, tumour escape mechanisms and recent advances in cancer therapies.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"S1 - S5"},"PeriodicalIF":0.0,"publicationDate":"2018-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1483003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45857915","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}
Pub Date : 2018-05-14DOI: 10.1080/23737867.2018.1468725
M. Ch-Chaoui, A. Eladdadi, K. Mokni
Abstract In this paper, we present a mathematical model at the cellular level of the tumour–immune competition mediated by the cytokines. The model consists of a system of nonlinear differential equations describing the intracellular interactions between the tumour and the immune cells in the presence of the cytokines. A detailed phenomenological description of the model based on the kinetic theory for active particle approach is carried out to formulate the model. Well-posedness is presented to establish local and global existence. Numerical simulations are addressed to show how initial conditions and model parameters influence the output of the model. Under a suitable choice of the model’s key parameters and the cytokines’ initial activation levels, the simulation results show that the activated immune system is able to achieve a total elimination of the cancer cells.
{"title":"Activation of the immune response by cytokines and its effect on tumour cells: a mathematical model","authors":"M. Ch-Chaoui, A. Eladdadi, K. Mokni","doi":"10.1080/23737867.2018.1468725","DOIUrl":"https://doi.org/10.1080/23737867.2018.1468725","url":null,"abstract":"Abstract In this paper, we present a mathematical model at the cellular level of the tumour–immune competition mediated by the cytokines. The model consists of a system of nonlinear differential equations describing the intracellular interactions between the tumour and the immune cells in the presence of the cytokines. A detailed phenomenological description of the model based on the kinetic theory for active particle approach is carried out to formulate the model. Well-posedness is presented to establish local and global existence. Numerical simulations are addressed to show how initial conditions and model parameters influence the output of the model. Under a suitable choice of the model’s key parameters and the cytokines’ initial activation levels, the simulation results show that the activated immune system is able to achieve a total elimination of the cancer cells.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"S178 - S200"},"PeriodicalIF":0.0,"publicationDate":"2018-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1468725","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49481959","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}
Pub Date : 2018-05-14DOI: 10.1080/23737867.2018.1465863
Heidi J. Dritschel, S. Waters, A. Roller, H. Byrne
Abstract We develop a mathematical model to examine the role of helper and cytotoxic T cells in an anti-tumour immune response. The model comprises three ordinary differential equations describing the dynamics of the tumour cells, the helper and the cytotoxic T cells, and implicitly accounts for immunosuppressive effects. The aim is to investigate how the anti-tumour immune response varies with the level of infiltrating helper and cytotoxic T cells. Through a combination of analytical studies and numerical simulations, our model exemplifies the three Es of immunoediting: elimination, equilibrium and escape. Specifically, it reveals that the three Es of immunoediting depend highly on the infiltration rates of the helper and cytotoxic T cells. The model’s results indicate that both the helper and cytotoxic T cells play a key role in tumour elimination. They also show that combination therapies that boost the immune system and block tumour-induced immunosuppression may have a synergistic effect in reducing tumour growth.
{"title":"A mathematical model of cytotoxic and helper T cell interactions in a tumour microenvironment","authors":"Heidi J. Dritschel, S. Waters, A. Roller, H. Byrne","doi":"10.1080/23737867.2018.1465863","DOIUrl":"https://doi.org/10.1080/23737867.2018.1465863","url":null,"abstract":"Abstract We develop a mathematical model to examine the role of helper and cytotoxic T cells in an anti-tumour immune response. The model comprises three ordinary differential equations describing the dynamics of the tumour cells, the helper and the cytotoxic T cells, and implicitly accounts for immunosuppressive effects. The aim is to investigate how the anti-tumour immune response varies with the level of infiltrating helper and cytotoxic T cells. Through a combination of analytical studies and numerical simulations, our model exemplifies the three Es of immunoediting: elimination, equilibrium and escape. Specifically, it reveals that the three Es of immunoediting depend highly on the infiltration rates of the helper and cytotoxic T cells. The model’s results indicate that both the helper and cytotoxic T cells play a key role in tumour elimination. They also show that combination therapies that boost the immune system and block tumour-induced immunosuppression may have a synergistic effect in reducing tumour growth.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"S36 - S68"},"PeriodicalIF":0.0,"publicationDate":"2018-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1465863","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44582252","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}
Pub Date : 2018-05-14DOI: 10.1080/23737867.2018.1465862
E. Piretto, M. Delitala, M. Ferraro
Abstract Treatment of cancer relies increasingly on combination therapies to overcome cancer resistance, but the design of successful combined protocols is still an open problem. In order to provide some indications on the effectiveness of medical treatments, results from in silico experiments are presented based on a mathematical model comprising two cancer populations competing for resources and with different susceptibilities to the action of immune system cells and therapies. The focus is on the effects of therapies that affect the rate of cancer growth, as in case of chemotherapy, used alone or in combination with immunotherapy, which boost the action of the immune system. Simulations show that a standard dose chemotherapy is effective when the sensitive clone has a marked competitive advantage, whereas combination of immuno- and chemotherapy works better in all the other cases. These results stress the importance to take into account competitive interactions among cancer clones to decide which therapeutic strategy should be adopted. Next the analysis is extended to protocols involving a drug holiday, i.e. periods in which no drug is administered. Finally, the model has been adapted to investigate combination therapies for non-small cell lung cancer: simulation results show that administration of standard dose of Erlotinib (a tyrosine kinase inhibitor), alone, has quite the same effect as a low-dose combination therapy, but the latter produces a slower increase of resistant cells.
{"title":"How combination therapies shape drug resistance in heterogeneous tumoral populations","authors":"E. Piretto, M. Delitala, M. Ferraro","doi":"10.1080/23737867.2018.1465862","DOIUrl":"https://doi.org/10.1080/23737867.2018.1465862","url":null,"abstract":"Abstract Treatment of cancer relies increasingly on combination therapies to overcome cancer resistance, but the design of successful combined protocols is still an open problem. In order to provide some indications on the effectiveness of medical treatments, results from in silico experiments are presented based on a mathematical model comprising two cancer populations competing for resources and with different susceptibilities to the action of immune system cells and therapies. The focus is on the effects of therapies that affect the rate of cancer growth, as in case of chemotherapy, used alone or in combination with immunotherapy, which boost the action of the immune system. Simulations show that a standard dose chemotherapy is effective when the sensitive clone has a marked competitive advantage, whereas combination of immuno- and chemotherapy works better in all the other cases. These results stress the importance to take into account competitive interactions among cancer clones to decide which therapeutic strategy should be adopted. Next the analysis is extended to protocols involving a drug holiday, i.e. periods in which no drug is administered. Finally, the model has been adapted to investigate combination therapies for non-small cell lung cancer: simulation results show that administration of standard dose of Erlotinib (a tyrosine kinase inhibitor), alone, has quite the same effect as a low-dose combination therapy, but the latter produces a slower increase of resistant cells.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"S160 - S177"},"PeriodicalIF":0.0,"publicationDate":"2018-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1465862","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45974149","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}
Pub Date : 2018-05-11DOI: 10.1080/23737867.2018.1456366
Luke Morgan, Gregory Moses, T. Young
Abstract We investigate the possibility that slow metabolic, cell-cycle-related oscillations in yeast and associated temporal clustering of cells within the cell cycle could be due to an interplay between near-critical metabolism and cell cycle checkpoints. We construct a dynamical model of the cell cycles of a large culture of cells that incorporates checkpoint gating and metabolic mode switching that are triggered by resource thresholds. We investigate the model analytically and prove that there exist open sets of parameter values for which the model possesses stable periodic solutions that exhibit metabolic oscillations with cell cycle clustering. Simulations of the model give evidence that such solutions exist for large sets of parameter values. This demonstrates that checkpoint gating coupled with critical resources can be a robust mechanism for producing the phenomena observed in experiments.
{"title":"Coupling of the cell cycle and metabolism in yeast cell-cycle-related oscillations via resource criticality and checkpoint gating","authors":"Luke Morgan, Gregory Moses, T. Young","doi":"10.1080/23737867.2018.1456366","DOIUrl":"https://doi.org/10.1080/23737867.2018.1456366","url":null,"abstract":"Abstract We investigate the possibility that slow metabolic, cell-cycle-related oscillations in yeast and associated temporal clustering of cells within the cell cycle could be due to an interplay between near-critical metabolism and cell cycle checkpoints. We construct a dynamical model of the cell cycles of a large culture of cells that incorporates checkpoint gating and metabolic mode switching that are triggered by resource thresholds. We investigate the model analytically and prove that there exist open sets of parameter values for which the model possesses stable periodic solutions that exhibit metabolic oscillations with cell cycle clustering. Simulations of the model give evidence that such solutions exist for large sets of parameter values. This demonstrates that checkpoint gating coupled with critical resources can be a robust mechanism for producing the phenomena observed in experiments.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"113 - 128"},"PeriodicalIF":0.0,"publicationDate":"2018-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1456366","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45720696","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}
Pub Date : 2018-04-30DOI: 10.1080/23737867.2018.1463183
Frank H. Lynch, G. North, B. S. Page, Cullen J. Faulwell
Abstract We describe a hybrid numerical method to solve a boundary value problem where an unknown parameter of the model is chosen to satisfy an additional boundary condition. After the solution of the differential equation is approximated using a one-step method, a secant method is used to update the value of the unknown parameter. The model is a generalization of a model first used to describe water flow through roots, which was later used to describe water flow through the tank bromeliad Guzmania lingulata. In both cases, identification of the unknown parameter represents the decomposition of overall plant conductance into components in the radial and axial directions. We describe convergence of the one-step and secant portions of the method in a base case corresponding to previous applications of the model and in an intermediate case corresponding to a first approximation of the geometry of the leaf. We demonstrate that in the more general case, which better represents the geometry of G. lingulata, the one-step method also converges as expected. Finally, we discuss the implications of including a better description of the geometry of the leaf in context of radial conductance and show that our modeling of the leaf geometry increases the component of the overall leaf conductance in the radial direction by as much as 25%.
{"title":"Analysis of a hybrid numerical method – decomposing leaf hydraulic conductance","authors":"Frank H. Lynch, G. North, B. S. Page, Cullen J. Faulwell","doi":"10.1080/23737867.2018.1463183","DOIUrl":"https://doi.org/10.1080/23737867.2018.1463183","url":null,"abstract":"Abstract We describe a hybrid numerical method to solve a boundary value problem where an unknown parameter of the model is chosen to satisfy an additional boundary condition. After the solution of the differential equation is approximated using a one-step method, a secant method is used to update the value of the unknown parameter. The model is a generalization of a model first used to describe water flow through roots, which was later used to describe water flow through the tank bromeliad Guzmania lingulata. In both cases, identification of the unknown parameter represents the decomposition of overall plant conductance into components in the radial and axial directions. We describe convergence of the one-step and secant portions of the method in a base case corresponding to previous applications of the model and in an intermediate case corresponding to a first approximation of the geometry of the leaf. We demonstrate that in the more general case, which better represents the geometry of G. lingulata, the one-step method also converges as expected. Finally, we discuss the implications of including a better description of the geometry of the leaf in context of radial conductance and show that our modeling of the leaf geometry increases the component of the overall leaf conductance in the radial direction by as much as 25%.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"5 1","pages":"112 - 98"},"PeriodicalIF":0.0,"publicationDate":"2018-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2018.1463183","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48668985","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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