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2 pages, 187 KiB

Open AccessEditorial

Mathematical Biology: Modeling, Analysis, and Simulations

by Ricardo López-Ruiz

Mathematics 2022, 10(20), 3892; https://doi.org/10.3390/math10203892 - 20 Oct 2022

Cited by 1 | Viewed by 3568

Abstract

Mathematical biology has been an area of wide interest during the recent decades, as the modeling of complicated biological processes has enabled the creation of analytical and computational approaches to many different bio-inspired problems originating from different branches such as population dynamics, molecular [...] Read more.

Mathematical biology has been an area of wide interest during the recent decades, as the modeling of complicated biological processes has enabled the creation of analytical and computational approaches to many different bio-inspired problems originating from different branches such as population dynamics, molecular dynamics in cells, neuronal and heart diseases, the cardiovascular system, genetics, etc [...] Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

Research

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33 pages, 479 KiB

Open AccessArticle

Inferring HIV Transmission Network Determinants Using Agent-Based Models Calibrated to Multi-Data Sources

by David Niyukuri, Trust Chibawara, Peter Suwirakwenda Nyasulu and Wim Delva

Mathematics 2021, 9(21), 2645; https://doi.org/10.3390/math9212645 - 20 Oct 2021

Cited by 2 | Viewed by 2708

Abstract

(1) Background: Calibration of Simpact Cyan can help to improve estimates related to the transmission dynamics of the Human Immunodeficiency Virus (HIV). Age-mixing patterns in sexual partnerships, onward transmissions, and temporal trends of HIV incidence are determinants which can inform the design of [...] Read more.

(1) Background: Calibration of Simpact Cyan can help to improve estimates related to the transmission dynamics of the Human Immunodeficiency Virus (HIV). Age-mixing patterns in sexual partnerships, onward transmissions, and temporal trends of HIV incidence are determinants which can inform the design of efficient prevention, and linkage-to-care programs. Using an agent-based model (ABM) simulation tool, we investigated, through a simulation study, if estimates of these determinants can be obtained with high accuracy by combining summary features from different data sources. (2) Methods: With specific parameters, we generated the benchmark data, and calibrated the default model in three scenarios based on summary features for comparison. For calibration, we used Latin Hypercube Sampling approach to generate parameter values, and Approximation Bayesian Computation to choose the best fitting ones. In all calibration scenarios the mean square root error was used as a measure to depict the estimates accuracy. (3) Results: The accuracy measure showed relatively no difference between the three scenarios. Moreover, we found that in all scenarios, age and gender strata incidence trends were poorly estimated. (4) Conclusions: Using synthetic benchmarks, we showed that it is possible to infer HIV transmission dynamics using an ABM of HIV transmission. Our results suggest that any type of summary feature provides adequate information to estimate HIV transmission network determinants. However, it is advisable to check the level of accuracy of the estimates of interest using benchmark data. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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24 pages, 1823 KiB

Open AccessArticle

Modelling the Phosphorylation of Glucose by Human hexokinase I

by Vinh Q. Mai and Martin Meere

Mathematics 2021, 9(18), 2315; https://doi.org/10.3390/math9182315 - 18 Sep 2021

Cited by 3 | Viewed by 3625

Abstract

In this paper, we develop a comprehensive mathematical model to describe the phosphorylation of glucose by the enzyme hexokinase I. Glucose phosphorylation is the first step of the glycolytic pathway, and as such, it is carefully regulated in cells. Hexokinase I phosphorylates [...] Read more.

In this paper, we develop a comprehensive mathematical model to describe the phosphorylation of glucose by the enzyme hexokinase I. Glucose phosphorylation is the first step of the glycolytic pathway, and as such, it is carefully regulated in cells. Hexokinase I phosphorylates glucose to produce glucose-6-phosphate, and the cell regulates the phosphorylation rate by inhibiting the action of this enzyme. The cell uses three inhibitory processes to regulate the enzyme: an allosteric product inhibitory process, a competitive product inhibitory process, and a competitive inhibitory process. Surprisingly, the cellular regulation of hexokinase I is not yet fully resolved, and so, in this study, we developed a detailed mathematical model to help unpack the behaviour. Numerical simulations of the model produced results that were consistent with the experimentally determined behaviour of hexokinase I. In addition, the simulations provided biological insights into the abstruse enzymatic behaviour, such as the dependence of the phosphorylation rate on the concentration of inorganic phosphate or the concentration of the product glucose-6-phosphate. A global sensitivity analysis of the model was implemented to help identify the key mechanisms of hexokinase I regulation. The sensitivity analysis also enabled the development of a simpler model that produced an output that was very close to that of the full model. Finally, the potential utility of the model in assisting experimental studies is briefly indicated. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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23 pages, 728 KiB

Open AccessArticle

An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors

by Fatima Sulayman, Farah Aini Abdullah and Mohd Hafiz Mohd

Mathematics 2021, 9(4), 327; https://doi.org/10.3390/math9040327 - 7 Feb 2021

Cited by 29 | Viewed by 4574

Abstract

This study extends a deterministic mathematical model for the dynamics of tuberculosis transmission to examine the impact of an imperfect vaccine and other exogenous factors, such as re-infection among treated individuals and exogenous re-infection. The qualitative behaviors of the model are investigated, covering [...] Read more.

This study extends a deterministic mathematical model for the dynamics of tuberculosis transmission to examine the impact of an imperfect vaccine and other exogenous factors, such as re-infection among treated individuals and exogenous re-infection. The qualitative behaviors of the model are investigated, covering many distinct aspects of the transmission of the disease. The proposed model is observed to show a backward bifurcation, even when

R v < 1

. As such, we assume that diminishing

R v

to less than unity is not effective for the elimination of tuberculosis. Furthermore, the results reveal that an imperfect tuberculosis vaccine is always effective at reducing the spread of infectious diseases within the population, though the general effect increases with the increase in effectiveness and coverage. In particular, it is shown that a limited portion of people being vaccinated at steady-state and vaccine efficacy assume a equivalent role in decreasing disease burden. From the numerical simulation, it is shown that using an imperfect vaccine lead to effective control of tuberculosis in a population, provided that the efficacy of the vaccine and its coverage are reasonably high. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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22 pages, 380 KiB

Open AccessArticle

Using Copula to Model Dependence When Testing Multiple Hypotheses in DNA Microarray Experiments: A Bayesian Approximation

by Elisa C. J. Maria, Isabel Salazar, Luis Sanz and Miguel A. Gómez-Villegas

Mathematics 2020, 8(9), 1514; https://doi.org/10.3390/math8091514 - 4 Sep 2020

Cited by 2 | Viewed by 2324

Abstract

Many experiments require simultaneously testing many hypotheses. This is particularly relevant in the context of DNA microarray experiments, where it is common to analyze many genes to determine which of them are differentially expressed under two conditions. Another important problem in this context [...] Read more.

Many experiments require simultaneously testing many hypotheses. This is particularly relevant in the context of DNA microarray experiments, where it is common to analyze many genes to determine which of them are differentially expressed under two conditions. Another important problem in this context is how to model the dependence at the level of gene expression. In this paper, we propose a Bayesian procedure for simultaneously testing multiple hypotheses, modeling the dependence through copula functions, where all available information, both objective and subjective, can be used. The approach has the advantage that it can be used with different dependency structures. Simulated data analysis was performed to examine the performance of the proposed approach. The results show that our procedure captures the dependence appropriately classifying adequately a high percentage of true and false null hypotheses when choosing a prior distribution beta skewed to the right for the initial probability of each null hypothesis, resulting in a very powerful procedure. The procedure is also illustrated with real data. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

21 pages, 1502 KiB

Open AccessArticle

Software-Automatized Individual Lactation Model Fitting, Peak and Persistence and Bayesian Criteria Comparison for Milk Yield Genetic Studies in Murciano-Granadina Goats

by María Gabriela Pizarro Inostroza, Francisco Javier Navas González, Vincenzo Landi, José Manuel León Jurado, Juan Vicente Delgado Bermejo, Javier Fernández Álvarez and María del Amparo Martínez Martínez

Mathematics 2020, 8(9), 1505; https://doi.org/10.3390/math8091505 - 4 Sep 2020

Cited by 16 | Viewed by 3076

Abstract

SPSS model syntax was defined and used to evaluate the individual performance of 49 linear and non-linear models to fit the lactation curve of 159 Murciano-Granadina goats selected for genotyping analyses. Lactation curve shape, peak and persistence were evaluated for each model using [...] Read more.

SPSS model syntax was defined and used to evaluate the individual performance of 49 linear and non-linear models to fit the lactation curve of 159 Murciano-Granadina goats selected for genotyping analyses. Lactation curve shape, peak and persistence were evaluated for each model using 3107 milk yield controls with an average of 3.78 ± 2.05 lactations per goat. Best fit (Adjusted R²) values (0.47) were reached by the five-parameter logarithmic model of Ali and Schaeffer. Three main possibilities were detected: non-fitting (did not converge), standard (Adjusted R² over 75%) and atypical curves (Adjusted R² below 75%). All the goats fitted for 38 models. The ability to fit different possible functional forms for each goat, which progressively increased with the number of parameters comprised in each model, translated into a higher sensitivity to explaining curve shape individual variability. However, for models for which all goats fitted, only moderate increases in explanatory and predictive potential (AIC, AICc or BIC) were found. The Ali and Schaeffer model reported the best fitting results to study the genetic variability behind goat milk yield and perhaps enhance the evaluation of curve parameters as trustable future selection criteria to face the future challenges offered by the goat dairy industry. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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17 pages, 5116 KiB

Open AccessArticle

Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations

by Roberto Barrio, M. Angeles Martínez, Lucía Pérez and Esther Pueyo

Mathematics 2020, 8(6), 880; https://doi.org/10.3390/math8060880 - 1 Jun 2020

Cited by 15 | Viewed by 3179

Abstract

In this study, we teased out the dynamical mechanisms underlying the generation of arrhythmogenic early afterdepolarizations (EADs) in a three-variable model of a mammalian ventricular cell. Based on recently published studies, we consider a 1-fast, 2-slow variable decomposition of the system describing the [...] Read more.

In this study, we teased out the dynamical mechanisms underlying the generation of arrhythmogenic early afterdepolarizations (EADs) in a three-variable model of a mammalian ventricular cell. Based on recently published studies, we consider a 1-fast, 2-slow variable decomposition of the system describing the cellular action potential. We use sweeping techniques, such as the spike-counting method, and bifurcation and continuation methods to identify parametric regions with EADs. We show the existence of isolas of periodic orbits organizing the different EAD patterns and we provide a preliminary classification of our fast–slow decomposition according to the involved dynamical phenomena. This investigation represents a basis for further studies into the organization of EAD patterns in the parameter space and the involved bifurcations. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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19 pages, 3078 KiB

Open AccessArticle

Algorithmic Analysis of Vesselness and Blobness for Detecting Retinopathies Based on Fractional Gaussian Filters

by Maria de Jesus Estudillo-Ayala, Hugo Aguirre-Ramos, Juan Gabriel Avina-Cervantes, Jorge Mario Cruz-Duarte, Ivan Cruz-Aceves and Jose Ruiz-Pinales

Mathematics 2020, 8(5), 744; https://doi.org/10.3390/math8050744 - 8 May 2020

Cited by 3 | Viewed by 2857

Abstract

All around the world, partial or total blindness has become a direct consequence of diabetes and hypertension. Visual disorders related to these diseases require automatic and specialized methods to detect early malformations, artifacts, or irregular structures for helping specialists in the diagnosis. This [...] Read more.

All around the world, partial or total blindness has become a direct consequence of diabetes and hypertension. Visual disorders related to these diseases require automatic and specialized methods to detect early malformations, artifacts, or irregular structures for helping specialists in the diagnosis. This study presents an innovative methodology for detecting and evaluating retinopathies, particularly microaneurysm and hemorrhages. The method is based on a multidirectional Fractional-Order Gaussian Filters tuned by the Differential Evolution algorithm. The contrast of the microaneurysms and hemorrhages, regarding the background, is improved substantially. After that, these structures are extracted using the Kittler thresholding method under additional considerations. Then, candidate lesions are detected by removing the blood vessels and fovea pixels in the resulting image. Finally, candidate lesions are classified according to its size, shape, and intensity properties via Support Vector Machines with a radial basis function kernel. The proposed method is evaluated by using the publicly available database MESSIDOR for detecting microaneurysms. The numerical results are summarized by the averaged binary metrics of accuracy, sensitivity, and specificity giving the performance values of 0.9995, 0.7820 and 0.9998, respectively. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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14 pages, 1498 KiB

Open AccessArticle

Searching for Complexity in the Human Pupillary Light Reflex

by Rosário D. Laureano, Diana Mendes, Clara Grácio and Fátima Laureano

Mathematics 2020, 8(3), 394; https://doi.org/10.3390/math8030394 - 11 Mar 2020

Cited by 3 | Viewed by 3120

Abstract

This article aims to examine the dynamical characteristics of the pupillary light reflex and to provide a contribution towards their explanation based on the nonlinear theory of dynamical systems. To introduce the necessary concepts, terminology, and relevant features of the pupillary light reflex [...] Read more.

This article aims to examine the dynamical characteristics of the pupillary light reflex and to provide a contribution towards their explanation based on the nonlinear theory of dynamical systems. To introduce the necessary concepts, terminology, and relevant features of the pupillary light reflex and its associated delay, we start with an overview of the human eye anatomy and physiology with emphasis on the iris, pupil, and retina. We also present the most highly regarded models for pupil dynamics found in the current scientific literature. Then we consider the model developed by Longtin and Milton, which models the human pupillary light reflex, defined by a nonlinear differential equation with delay, and present our study carried out on the qualitative and quantitative dynamic behavior of that neurophysiological control system. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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18 pages, 859 KiB

Open AccessArticle

A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

by Lorand Gabriel Parajdi, Radu Precup, Eduard Alexandru Bonci and Ciprian Tomuleasa

Mathematics 2020, 8(3), 376; https://doi.org/10.3390/math8030376 - 8 Mar 2020

Cited by 8 | Viewed by 4737

Abstract

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing [...] Read more.

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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33 pages, 8740 KiB

Open AccessArticle

Kinematics in Biology: Symbolic Dynamics Approach

by Carlos Correia Ramos

Mathematics 2020, 8(3), 339; https://doi.org/10.3390/math8030339 - 4 Mar 2020

Cited by 1 | Viewed by 4123

Abstract

Motion in biology is studied through a descriptive geometrical method. We consider a deterministic discrete dynamical system used to simulate and classify a variety of types of movements which can be seen as templates and building blocks of more complex trajectories. The dynamical [...] Read more.

Motion in biology is studied through a descriptive geometrical method. We consider a deterministic discrete dynamical system used to simulate and classify a variety of types of movements which can be seen as templates and building blocks of more complex trajectories. The dynamical system is determined by the iteration of a bimodal interval map dependent on two parameters, up to scaling, generalizing a previous work. The characterization of the trajectories uses the classifying tools from symbolic dynamics—kneading sequences, topological entropy and growth number. We consider also the isentropic trajectories, trajectories with constant topological entropy, which are related with the possible existence of a constant drift. We introduce the concepts of pure and mixed bimodal trajectories which give much more flexibility to the model, maintaining it simple. We discuss several procedures that may allow the use of the model to characterize empirical data. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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14 pages, 982 KiB

Open AccessArticle

The Effect of a Linear Tuning between the Antigenic Stimulations of CD4⁺ T Cells and CD4⁺ Tregs

by Aliyu A. Yusuf, Isabel P. Figueiredo, Atefeh Afsar, Nigel J. Burroughs, Alberto A. Pinto and Bruno M. P. M. Oliveira

Mathematics 2020, 8(2), 293; https://doi.org/10.3390/math8020293 - 21 Feb 2020

Cited by 6 | Viewed by 2742

Abstract

We study the equilibria of an Ordinary Differencial Equation (ODE) system where CD4

^{+}

effector or helper T cells and Regulatory T cells (Tregs) are present. T cells trigger an immune response in the presence of their specific antigen. Regulatory T cells (Tregs) [...] Read more.

We study the equilibria of an Ordinary Differencial Equation (ODE) system where CD4

^{+}

effector or helper T cells and Regulatory T cells (Tregs) are present. T cells trigger an immune response in the presence of their specific antigen. Regulatory T cells (Tregs) play a role in limiting auto-immune diseases due to their immune-suppressive ability. Here, we present explicit exact formulas that give the relationship between the concentration of T cells, the concentration of Tregs, and the antigenic stimulation of T cells, when the system is at equilibria, stable or unstable. We found a parameter region of bistability, limited by two thresholds of antigenic stimulation of T cells (hysteresis). Moreover, there are values of the slope parameter of the tuning for which an isola-center bifurcation appears, and, for some other values, there is a transcritical bifurcation. We also present time evolutions of the ODE system. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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11 pages, 1327 KiB

Open AccessArticle

On the Necessary Conditions for Non-Equivalent Solutions of the Rotlet-Induced Stokes Flow in a Sphere: Towards a Minimal Model for Fluid Flow in the Kupffer’s Vesicle

by Yunay Hernández-Pereira, Adán O. Guerrero, Juan Manuel Rendón-Mancha and Idan Tuval

Mathematics 2020, 8(1), 1; https://doi.org/10.3390/math8010001 - 18 Dec 2019

Cited by 3 | Viewed by 2845

Abstract

The emergence of left–right (LR) asymmetry in vertebrates is a prime example of a highly conserved fundamental process in developmental biology. Details of how symmetry breaking is established in different organisms are, however, still not fully understood. In the zebrafish (Danio rerio [...] Read more.

The emergence of left–right (LR) asymmetry in vertebrates is a prime example of a highly conserved fundamental process in developmental biology. Details of how symmetry breaking is established in different organisms are, however, still not fully understood. In the zebrafish (Danio rerio), it is known that a cilia-mediated vortical flow exists within its LR organizer, the so-called Kupffer’s vesicle (KV), and that it is directly involved in early LR determination. However, the flow exhibits spatio-temporal complexity; moreover, its conversion to asymmetric development has proved difficult to resolve despite a number of recent experimental advances and numerical efforts. In this paper, we provide further theoretical insight into the essence of flow generation by putting together a minimal biophysical model which reduces to a set of singular solutions satisfying the imposed boundary conditions; one that is informed by our current understanding of the fluid flow in the KV, that satisfies the requirements for left–right symmetry breaking, but which is also amenable to extensive parametric analysis. Our work is a step forward in this direction. By finding the general conditions for the solution to the fluid mechanics of a singular rotlet within a rigid sphere, we have enlarged the set of available solutions in a way that can be easily extended to more complex configurations. These general conditions define a suitable set for which to apply the superposition principle to the linear Stokes problem and, hence, by which to construct a continuous set of solutions that correspond to spherically constrained vortical flows generated by arbitrarily displaced infinitesimal rotations around any three-dimensional axis. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations)

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