A Mathematical Modelling Study of Chemotactic Dynamics in Cell Cultures: The Impact of Spatio-temporal Heterogeneity
Bull Math Biol. 2023 Sep 8;85(10):98. doi: 10.1007/s11538-023-01194-9.ABSTRACTAs motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell chemotaxis waves in heterogeneous fields of chemoattractant from the underlying partial differential equation models. In particular, such chemotactic waves are not in general translationally invariant travelling waves, but possess a spatial variation that evolves in time, and may even oscillate back and forth in ...
Source: Bulletin of Mathematical Biology - September 8, 2023 Category: Bioinformatics Authors: Jacobo Ayensa-Jim énez Mohamed H Doweidar Manuel Doblar é Eamonn A Gaffney Source Type: research
A Mathematical Modelling Study of Chemotactic Dynamics in Cell Cultures: The Impact of Spatio-temporal Heterogeneity
Bull Math Biol. 2023 Sep 8;85(10):98. doi: 10.1007/s11538-023-01194-9.ABSTRACTAs motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell chemotaxis waves in heterogeneous fields of chemoattractant from the underlying partial differential equation models. In particular, such chemotactic waves are not in general translationally invariant travelling waves, but possess a spatial variation that evolves in time, and may even oscillate back and forth in ...
Source: Bulletin of Mathematical Biology - September 8, 2023 Category: Bioinformatics Authors: Jacobo Ayensa-Jim énez Mohamed H Doweidar Manuel Doblar é Eamonn A Gaffney Source Type: research
Getting Jab or Regular Test: Observations from an Impulsive Epidemic COVID-19 Model
This study proposes a population-based model that can accommodate different personal decision choices, such as getting vaccinated or undergoing regular tests, as well as vaccine efficacies and uncertainties in epidemic transmission. The model, formulated as impulsive differential equations, uses time instants to represent the reporting date for the test result of an unvaccinated individual. By employing well-accepted indices to measure transmission risk, including the basic reproduction number, the peak time, the final size, and the number of severe infections, the study shows that an optimal testing frequency is highly se...
Source: Bulletin of Mathematical Biology - September 7, 2023 Category: Bioinformatics Authors: Kaihui Liu Zhenguo Bai Daihai He Yijun Lou Source Type: research
Getting Jab or Regular Test: Observations from an Impulsive Epidemic COVID-19 Model
This study proposes a population-based model that can accommodate different personal decision choices, such as getting vaccinated or undergoing regular tests, as well as vaccine efficacies and uncertainties in epidemic transmission. The model, formulated as impulsive differential equations, uses time instants to represent the reporting date for the test result of an unvaccinated individual. By employing well-accepted indices to measure transmission risk, including the basic reproduction number, the peak time, the final size, and the number of severe infections, the study shows that an optimal testing frequency is highly se...
Source: Bulletin of Mathematical Biology - September 7, 2023 Category: Bioinformatics Authors: Kaihui Liu Zhenguo Bai Daihai He Yijun Lou Source Type: research
Modelling the Effect of Matrix Metalloproteinases in Dermal Wound Healing
Bull Math Biol. 2023 Sep 5;85(10):96. doi: 10.1007/s11538-023-01195-8.ABSTRACTWith over 2 million people in the UK suffering from chronic wounds, understanding the biochemistry and pharmacology that underpins these wounds and wound healing is of high importance. Chronic wounds are characterised by high levels of matrix metalloproteinases (MMPs), which are necessary for the modification of healthy tissue in the healing process. Overexposure of MMPs, however, adversely affects healing of the wound by causing further destruction of the surrounding extracellular matrix. In this work, we propose a mathematical model that focuse...
Source: Bulletin of Mathematical Biology - September 5, 2023 Category: Bioinformatics Authors: Sonia Dari Nabil T Fadai Reuben D O'Dea Source Type: research
Modelling the Effect of Matrix Metalloproteinases in Dermal Wound Healing
Bull Math Biol. 2023 Sep 5;85(10):96. doi: 10.1007/s11538-023-01195-8.ABSTRACTWith over 2 million people in the UK suffering from chronic wounds, understanding the biochemistry and pharmacology that underpins these wounds and wound healing is of high importance. Chronic wounds are characterised by high levels of matrix metalloproteinases (MMPs), which are necessary for the modification of healthy tissue in the healing process. Overexposure of MMPs, however, adversely affects healing of the wound by causing further destruction of the surrounding extracellular matrix. In this work, we propose a mathematical model that focuse...
Source: Bulletin of Mathematical Biology - September 5, 2023 Category: Bioinformatics Authors: Sonia Dari Nabil T Fadai Reuben D O'Dea Source Type: research
Pretty Darn Good Control: When are Approximate Solutions Better than Approximate Models
Bull Math Biol. 2023 Sep 4;85(10):95. doi: 10.1007/s11538-023-01198-5.ABSTRACTExisting methods for optimal control struggle to deal with the complexity commonly encountered in real-world systems, including dimensionality, process error, model bias and data heterogeneity. Instead of tackling these system complexities directly, researchers have typically sought to simplify models to fit optimal control methods. But when is the optimal solution to an approximate, stylized model better than an approximate solution to a more accurate model? While this question has largely gone unanswered owing to the difficulty of finding even ...
Source: Bulletin of Mathematical Biology - September 4, 2023 Category: Bioinformatics Authors: Felipe Montealegre-Mora Marcus Lapeyrolerie Melissa Chapman Abigail G Keller Carl Boettiger Source Type: research
Pretty Darn Good Control: When are Approximate Solutions Better than Approximate Models
Bull Math Biol. 2023 Sep 4;85(10):95. doi: 10.1007/s11538-023-01198-5.ABSTRACTExisting methods for optimal control struggle to deal with the complexity commonly encountered in real-world systems, including dimensionality, process error, model bias and data heterogeneity. Instead of tackling these system complexities directly, researchers have typically sought to simplify models to fit optimal control methods. But when is the optimal solution to an approximate, stylized model better than an approximate solution to a more accurate model? While this question has largely gone unanswered owing to the difficulty of finding even ...
Source: Bulletin of Mathematical Biology - September 4, 2023 Category: Bioinformatics Authors: Felipe Montealegre-Mora Marcus Lapeyrolerie Melissa Chapman Abigail G Keller Carl Boettiger Source Type: research
Probability Distribution of Tree Age for the Simple Birth-Death Process, with Applications to Distributions of Number of Ancestral Lineages and Divergence Times for Pairs of Taxa in a Yule Tree
Bull Math Biol. 2023 Sep 1;85(10):94. doi: 10.1007/s11538-023-01196-7.ABSTRACTIn this contribution, a general expression is derived for the probability density of the time to the most recent common ancestor (TMRCA) of a simple birth-death tree, a widely used stochastic null-model of biological speciation and extinction, conditioned on the constant birth and death rates and number of extant lineages. This density is contrasted with a previous result which was obtained using a uniform prior for the time of origin. The new distribution is applied to two problems of phylogenetic interest. First, that of the probability of the ...
Source: Bulletin of Mathematical Biology - September 1, 2023 Category: Bioinformatics Authors: Willem H Mulder Source Type: research
Modeling the Role of Immune Cell Conversion in the Tumor-Immune Microenvironment
Bull Math Biol. 2023 Sep 1;85(10):93. doi: 10.1007/s11538-023-01201-z.ABSTRACTTumors develop in a complex physical, biochemical, and cellular milieu, referred to as the tumor microenvironment. Of special interest is the set of immune cells that reciprocally interact with the tumor, the tumor-immune microenvironment (TIME). The diversity of cell types and cell-cell interactions in the TIME has led researchers to apply concepts from ecology to describe the dynamics. However, while tumor cells are known to induce immune cells to switch from anti-tumor to pro-tumor phenotypes, this type of ecological interaction has been large...
Source: Bulletin of Mathematical Biology - September 1, 2023 Category: Bioinformatics Authors: Alexander S Moffett Youyuan Deng Herbert Levine Source Type: research
Probability Distribution of Tree Age for the Simple Birth-Death Process, with Applications to Distributions of Number of Ancestral Lineages and Divergence Times for Pairs of Taxa in a Yule Tree
Bull Math Biol. 2023 Sep 1;85(10):94. doi: 10.1007/s11538-023-01196-7.ABSTRACTIn this contribution, a general expression is derived for the probability density of the time to the most recent common ancestor (TMRCA) of a simple birth-death tree, a widely used stochastic null-model of biological speciation and extinction, conditioned on the constant birth and death rates and number of extant lineages. This density is contrasted with a previous result which was obtained using a uniform prior for the time of origin. The new distribution is applied to two problems of phylogenetic interest. First, that of the probability of the ...
Source: Bulletin of Mathematical Biology - September 1, 2023 Category: Bioinformatics Authors: Willem H Mulder Source Type: research
Modeling the Role of Immune Cell Conversion in the Tumor-Immune Microenvironment
Bull Math Biol. 2023 Sep 1;85(10):93. doi: 10.1007/s11538-023-01201-z.ABSTRACTTumors develop in a complex physical, biochemical, and cellular milieu, referred to as the tumor microenvironment. Of special interest is the set of immune cells that reciprocally interact with the tumor, the tumor-immune microenvironment (TIME). The diversity of cell types and cell-cell interactions in the TIME has led researchers to apply concepts from ecology to describe the dynamics. However, while tumor cells are known to induce immune cells to switch from anti-tumor to pro-tumor phenotypes, this type of ecological interaction has been large...
Source: Bulletin of Mathematical Biology - September 1, 2023 Category: Bioinformatics Authors: Alexander S Moffett Youyuan Deng Herbert Levine Source Type: research
Probability Distribution of Tree Age for the Simple Birth-Death Process, with Applications to Distributions of Number of Ancestral Lineages and Divergence Times for Pairs of Taxa in a Yule Tree
Bull Math Biol. 2023 Sep 1;85(10):94. doi: 10.1007/s11538-023-01196-7.ABSTRACTIn this contribution, a general expression is derived for the probability density of the time to the most recent common ancestor (TMRCA) of a simple birth-death tree, a widely used stochastic null-model of biological speciation and extinction, conditioned on the constant birth and death rates and number of extant lineages. This density is contrasted with a previous result which was obtained using a uniform prior for the time of origin. The new distribution is applied to two problems of phylogenetic interest. First, that of the probability of the ...
Source: Bulletin of Mathematical Biology - September 1, 2023 Category: Bioinformatics Authors: Willem H Mulder Source Type: research
Modeling the Role of Immune Cell Conversion in the Tumor-Immune Microenvironment
Bull Math Biol. 2023 Sep 1;85(10):93. doi: 10.1007/s11538-023-01201-z.ABSTRACTTumors develop in a complex physical, biochemical, and cellular milieu, referred to as the tumor microenvironment. Of special interest is the set of immune cells that reciprocally interact with the tumor, the tumor-immune microenvironment (TIME). The diversity of cell types and cell-cell interactions in the TIME has led researchers to apply concepts from ecology to describe the dynamics. However, while tumor cells are known to induce immune cells to switch from anti-tumor to pro-tumor phenotypes, this type of ecological interaction has been large...
Source: Bulletin of Mathematical Biology - September 1, 2023 Category: Bioinformatics Authors: Alexander S Moffett Youyuan Deng Herbert Levine Source Type: research
A Continuation Technique for Maximum Likelihood Estimators in Biological Models
Bull Math Biol. 2023 Aug 31;85(10):90. doi: 10.1007/s11538-023-01200-0.ABSTRACTEstimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if modelling is performed simultaneously with the calibration experiments, or during an on-going public health crisis as in the case of the COVID-19 pandemic. Consequently, the optimal parameter set, or maximal likelihood estimator (MLE), is a function of the experimental data set. Here, we develop a numerical t...
Source: Bulletin of Mathematical Biology - August 31, 2023 Category: Bioinformatics Authors: Tyler Cassidy Source Type: research
