Mathematical Modelling In Biology And Medicine Pdf

Special Issue "Dynamical Models of Biology and Medicine"

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Special Issue Editors

Prof. Dr. Meng Fan
E-Mail Website
Guest Editor

School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun 130024, Jilin, China
Interests: mathematical biology and medicine; functional differential equations; dynamical systems

Prof. Dr. Shengqiang Liu
E-Mail Website
Guest Editor

The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, 3026#, 2 Yi-Kuang Street, Nan-Gang District, Harbin 150080, China
Interests: mathematical epidemiology; mathematical population dynamics; dynamical system

Prof. Dr. Wanbiao Ma
E-Mail Website
Guest Editor

Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, 30 Xue Yuan Road, Beijing 100083, China
Interests: mathematical biology and medicine; mathematical models; dynamical systems

Special Issue Information

Dear Colleagues,

Mathematical and computational modeling approaches in biological and medical research are experiencing exponential growth globally. This Special Issue intends to catch a glimpse of this exciting phenomenon. Areas covered include general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling, and to nonlinear and stochastic dynamics.

Topics appropriate for this Special Issue include, but are not limited to, all areas of mathematical biology and medicine that employ dynamical (differential equation) models to describe observed nonlinear dynamics that aim to understand life science problems. To be considered by this Special Issue, a paper should be in one (or a combination) of the three categories. (a) papers developing and mathematically analyzing dynamical models that have concrete applications in biology or medicine; (b) papers devoted to mathematical theory and methods, with a clear life science motivation, whose results may lead to an improved understanding of the underlying problem; and (c) papers using numerical simulations, experiments, or both to reveal or explain some new life science phenomena, where mathematical analysis plays a useful role in the process.

All paper must contain a comprehensive introductory section and an in-depth discussion section that is closely tied to applications. The scientific importance and motivation of the paper and its conclusions should be made clear at the outset.

Prof. Dr. Yang Kuang
Prof. Dr. Meng Fan
Prof. Dr. Shengqiang Liu
Prof. Dr. Wanbiao Ma
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

• dynamical system
• mathematical biology
• mathematical medicine
• simulation
• stability
• bifurcation

Published Papers (15 papers)

Editorial

Jump to: Research

Open Access Editorial

Preface for the Special Issue on Dynamical Models of Biology and Medicine

Viewed by 908

Abstract

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally [...] Full article

Research

Jump to: Editorial

Open Access Article

Numerical Characterization of Protein Sequences Based on the Generalized Chou's Pseudo Amino Acid Composition

Cited by 9 | Viewed by 1782

Abstract

The technique of comparison and analysis of biological sequences is playing an increasingly important role in the field of Computational Biology and Bioinformatics. One of the key steps in developing the technique is to identify an appropriate manner to represent a biological sequence. [...] Read more.

The technique of comparison and analysis of biological sequences is playing an increasingly important role in the field of Computational Biology and Bioinformatics. One of the key steps in developing the technique is to identify an appropriate manner to represent a biological sequence. In this paper, on the basis of three physical–chemical properties of amino acids, a protein primary sequence is reduced into a six-letter sequence, and then a set of elements which reflect the global and local sequence-order information is extracted. Combining these elements with the frequencies of 20 native amino acids, a

$\left(21+\mathsf{\lambda }\right)$

dimensional vector is constructed to characterize the protein sequence. The utility of the proposed approach is illustrated by phylogenetic analysis and identification of DNA-binding proteins. Full article

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Open Access Article

Mathematical Models of Androgen Resistance in Prostate Cancer Patients under Intermittent Androgen Suppression Therapy

Cited by 18 | Viewed by 3052

Abstract

Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen [...] Read more.

Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). We accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). While these models are simplifications of a previously published model, they fit data with similar accuracy and improve forecasting results. Both models describe the progression of androgen resistance. Although Model 1 is simpler than the more realistic Model 2, it can fit clinical data to a greater precision. However, we found that Model 2 can forecast future PSA levels more accurately. These findings suggest that including more realistic mechanisms of androgen dynamics in a two population model may help androgen resistance timing prediction. Full article

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Open Access Article

Dynamical Systems Properties of a Mathematical Model for the Treatment of CML

Cited by 11 | Viewed by 2116

Abstract

A mathematical model for the treatment of chronic myeloid leukemia (CML) through a combination of tyrosine kinase inhibitors and immunomodulatory therapies is analyzed as a dynamical system for the case of constant drug concentrations. Equilibria and their stability are determined and it is [...] Read more.

A mathematical model for the treatment of chronic myeloid leukemia (CML) through a combination of tyrosine kinase inhibitors and immunomodulatory therapies is analyzed as a dynamical system for the case of constant drug concentrations. Equilibria and their stability are determined and it is shown that, depending on the parameter values, the model exhibits a variety of behaviors which resemble the chronic, accelerated and blast phases typical of the disease. This work provides qualitative insights into the system which should be useful for understanding the interaction between CML and the therapies considered here. Full article

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Open Access Article

Chronic Inflammation in the Epidermis: A Mathematical Model

Cited by 2 | Viewed by 3623

Abstract

The epidermal tissue is the outmost component of the skin that plays an important role as a first barrier system in preventing the invasion of various environmental agents, such as bacteria. Recent studies have identified the importance of microbial competition between harmful and [...] Read more.

The epidermal tissue is the outmost component of the skin that plays an important role as a first barrier system in preventing the invasion of various environmental agents, such as bacteria. Recent studies have identified the importance of microbial competition between harmful and beneficial bacteria and the diversity of the skin surface on our health. We develop mathematical models (M1 and M2 models) for the inflammation process using ordinary differential equations and delay differential equations. In this paper, we study microbial community dynamics via transcription factors, protease and extracellular cytokines. We investigate possible mechanisms to induce community composition shift and analyze the vigorous competition dynamics between harmful and beneficial bacteria through immune activities. We found that the activation of proteases from the transcription factor within a cell plays a significant role in the regulation of bacterial persistence in the M1 model. The competition model (M2) predicts that different cytokine clearance levels may lead to a harmful bacteria persisting system, a bad bacteria-free state and the co-existence of harmful and good bacterial populations in Type I dynamics, while a bi-stable system without co-existence is illustrated in the Type II dynamics. This illustrates a possible phenotypic switch among harmful and good bacterial populations in a microenvironment. We also found that large time delays in the activation of immune responses on the dynamics of those bacterial populations lead to the onset of oscillations in harmful bacteria and immune activities. The mathematical model suggests possible annihilation of time-delay-driven oscillations by therapeutic drugs. Full article

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Open Access Article

Global Dynamics of Modeling Flocculation of Microorganism

Cited by 10 | Viewed by 2113

Abstract

From a biological perspective, a dynamic model describing the cultivation and flocculation of a microorganism that uses two different kinds of nutrients (carbon source and nitrogen source) is proposed. For the proposed model, there always exists a boundary equilibrium, i.e., [...] Read more.

From a biological perspective, a dynamic model describing the cultivation and flocculation of a microorganism that uses two different kinds of nutrients (carbon source and nitrogen source) is proposed. For the proposed model, there always exists a boundary equilibrium, i.e.,

$Rhodopseudomonaspalustris$

-free equilibrium. Furthermore, under additional conditions, the model also has five positive equilibria at most, i.e., the equilibria for which carbon source, nitrogen source,

$Rhodopseudomonaspalustris$

and flocculants are coexistent. The phenomena of backward and forward bifurcations are extensively discussed by using center manifold theory. The global stability of the boundary equilibrium of the proposed model is deeply investigated. Moreover, the local stability of the positive equilibrium and the uniform persistence of the proposed model are discussed. Under additional conditions, the global stability of the positive equilibrium is studied. Some control strategies are given by the theoretical analysis. Finally, some numerical simulations are performed to confirm the correctness of the theoretical results. Full article

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Open Access Article

Optimal Control of Drug Therapy in a Hepatitis B Model

Cited by 17 | Viewed by 2788

Abstract

Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects that make them unsuitable for long-term administration. To address the trade-off between [...] Read more.

Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects that make them unsuitable for long-term administration. To address the trade-off between the positive and negative effects of the combination therapy, we investigated an optimal control problem for a delay differential equation model of immune responses to hepatitis virus B infection. Our optimal control problem investigates the interplay between virological and immunomodulatory effects of therapy, the control of viremia and the administration of the minimal dosage over a short period of time. Our numerical results show that the high drug levels that induce immune modulation rather than suppression of virological factors are essential for the clearance of hepatitis B virus. Full article

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Open Access Article

Altered Mechano-Electrochemical Behavior of Articular Cartilage in Populations with Obesity

Cited by 4 | Viewed by 2174

Abstract

Obesity, one of the major problems in modern society, adversely affects people's health and increases the risk of suffering degeneration in supportive tissues such as cartilage, which loses its ability to support and distribute loads. However, no specific research regarding obesity-associated alterations in [...] Read more.

Obesity, one of the major problems in modern society, adversely affects people's health and increases the risk of suffering degeneration in supportive tissues such as cartilage, which loses its ability to support and distribute loads. However, no specific research regarding obesity-associated alterations in the mechano-electrochemical cartilage environment has been developed. Such studies could help us to understand the first signs of cartilage degeneration when body weight increases and to establish preventive treatments to avoid cartilage deterioration. In this work, a previous mechano-electrochemical computational model has been further developed and employed to analyze and quantify the effects of obesity on the articular cartilage of the femoral hip. A comparison between the obtained results of the healthy and osteoarthritic cartilage has been made. It shows that behavioral patterns of cartilage, such as ion fluxes and cation distribution, have considerable similarities with those obtained for the early stages of osteoarthritis. Thus, an increment in the outgoing ion fluxes is produced, resulting in lower cation concentrations in all the cartilage layers. These results suggest that people with obesity, i.e. a body mass index greater than 30 kg/m², should undergo preventive treatments for osteoarthritis to avoid homeostatic alterations and, subsequent, tissue deterioration. Full article

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Open Access Article

The Spotting Distribution of Wildfires

Cited by 19 | Viewed by 3535

Abstract

In wildfire science, spotting refers to non-local creation of new fires, due to downwind ignition of brands launched from a primary fire. Spotting is often mentioned as being one of the most difficult problems for wildfire management, because of its unpredictable nature. Since [...] Read more.

In wildfire science, spotting refers to non-local creation of new fires, due to downwind ignition of brands launched from a primary fire. Spotting is often mentioned as being one of the most difficult problems for wildfire management, because of its unpredictable nature. Since spotting is a stochastic process, it makes sense to talk about a probability distribution for spotting, which we call the spotting distribution. Given a location ahead of the fire front, we would like to know how likely is it to observe a spot fire at that location in the next few minutes. The aim of this paper is to introduce a detailed procedure to find the spotting distribution. Most prior modelling has focused on the maximum spotting distance, or on physical subprocesses. We will use mathematical modelling, which is based on detailed physical processes, to derive a spotting distribution. We discuss the use and measurement of this spotting distribution in fire spread, fire management and fire breaching. The appendix of this paper contains a comprehensive review of the relevant underlying physical sub-processes of fire plumes, launching fire brands, wind transport, falling and terminal velocity, combustion during transport, and ignition upon landing. Full article

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Open Access Article

Validation of a Mathematical Model for Green Algae (Raphidocelis Subcapitata) Growth and Implications for a Coupled Dynamical System with Daphnia Magna

Cited by 11 | Viewed by 2640

Abstract

Toxicity testing in populations probes for responses in demographic variables to anthropogenic or natural chemical changes in the environment. Importantly, these tests are primarily performed on species in isolation of adjacent tropic levels in their ecosystem. The development and validation of coupled species [...] Read more.

Toxicity testing in populations probes for responses in demographic variables to anthropogenic or natural chemical changes in the environment. Importantly, these tests are primarily performed on species in isolation of adjacent tropic levels in their ecosystem. The development and validation of coupled species models may aid in predicting adverse outcomes at the ecosystems level. Here, we aim to validate a model for the population dynamics of the green algae Raphidocelis subcapitata, a planktonic species that is often used as a primary food source in toxicity experiments for the fresh water crustacean Daphnia magna. We collected longitudinal data from three replicate population experiments of R. subcapitata. We used this data with statistical model comparison tests and uncertainty quantification techniques to compare the performance of four models: the Logistic model, the Bernoulli model, the Gompertz model, and a discretization of the Logistic model. Overall, our results suggest that the logistic model is the most accurate continuous model for R. subcapitata population growth. We then implement the numerical discretization showing how the continuous logistic model for algae can be coupled to a previously validated discrete-time population model for D. magna. Full article

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Open Access Article

A Simple Predator-Prey Population Model with Rich Dynamics

Cited by 10 | Viewed by 4108

Abstract

A non-smooth switched harvest on predators is introduced into a simple predator-prey model with logistical growth of the prey and a bilinear functional response. If the density of the predator is below a switched value, the harvesting rate is linear; otherwise, it is [...] Read more.

A non-smooth switched harvest on predators is introduced into a simple predator-prey model with logistical growth of the prey and a bilinear functional response. If the density of the predator is below a switched value, the harvesting rate is linear; otherwise, it is constant. The model links the well studied predator-prey model with constant harvesting to that with a proportional harvesting rate. It is shown that when the net reproductive number for the predator is greater than unity, the system is permanent and there may exist multiple positive equilibria due to the effects of the switched harvest, a saddle-node bifurcation, a limit cycle, and the coexistence of a stable equilibrium and a unstable circled inside limit cycle and a stable circled outside limit cycle. When the net reproductive number is less than unity, a backward bifurcation from a positive equilibrium occurs, which implies that the stable predator-extinct equilibrium may coexist with two coexistence equilibria. In this situation, reducing the net reproductive number to less than unity is not enough to enable the predator to go extinct. Numerical simulations are provided to illustrate the theoretical results. It seems that the model possesses new complex dynamics compared to the existing harvesting models. Full article

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Open Access Article

Mathematical Modeling of Bacteria Communication in Continuous Cultures

Cited by 4 | Viewed by 2912

Abstract

Quorum sensing is a bacterial cell-to-cell communication mechanism and is based on gene regulatory networks, which control and regulate the production of signaling molecules in the environment. In the past years, mathematical modeling of quorum sensing has provided an understanding of key components [...] Read more.

Quorum sensing is a bacterial cell-to-cell communication mechanism and is based on gene regulatory networks, which control and regulate the production of signaling molecules in the environment. In the past years, mathematical modeling of quorum sensing has provided an understanding of key components of such networks, including several feedback loops involved. This paper presents a simple system of delay differential equations (DDEs) for quorum sensing of Pseudomonas putida with one positive feedback plus one (delayed) negative feedback mechanism. Results are shown concerning fundamental properties of solutions, such as existence, uniqueness, and non-negativity; the last feature is crucial for mathematical models in biology and is often violated when working with DDEs. The qualitative behavior of solutions is investigated, especially the stationary states and their stability. It is shown that for a certain choice of parameter values, the system presents stability switches with respect to the delay. On the other hand, when the delay is set to zero, a Hopf bifurcation might occur with respect to one of the negative feedback parameters. Model parameters are fitted to experimental data, indicating that the delay system is sufficient to explain and predict the biological observations. Full article

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Open Access Article

Dynamics of a Stochastic Intraguild Predation Model

Cited by 3 | Viewed by 1875

Abstract

Intraguild predation (IGP) is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation [...] Read more.

Intraguild predation (IGP) is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation model. We analyze stochastic persistence and extinction of the stochastic IGP model containing five cases and establish the sufficient criteria for global asymptotic stability of the positive solutions. This study shows that it is possible for the coexistence of three species under the influence of environmental noise, and that the noise may have a positive effect for IGP species. A stationary distribution of the stochastic IGP model is established and it has the ergodic property, suggesting that the time average of population size with the development of time is equal to the stationary distribution in space. Finally, we show that our results may be extended to two well-known biological systems: food chains and exploitative competition. Full article

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Open Access Article

Novel Graphical Representation and Numerical Characterization of DNA Sequences

Cited by 8 | Viewed by 2792

Abstract

Modern sequencing technique has provided a wealth of data on DNA sequences, which has made the analysis and comparison of sequences a very important but difficult task. In this paper, by regarding the dinucleotide as a 2-combination of the multiset { ∞ · [...] Read more.

Modern sequencing technique has provided a wealth of data on DNA sequences, which has made the analysis and comparison of sequences a very important but difficult task. In this paper, by regarding the dinucleotide as a 2-combination of the multiset { ∞ · A , ∞ · G , ∞ · C , ∞ · T } , a novel 3-D graphical representation of a DNA sequence is proposed, and its projections on planes (x,y), (y,z) and (x,z) are also discussed. In addition, based on the idea of "piecewise function", a cell-based descriptor vector is constructed to numerically characterize the DNA sequence. The utility of our approach is illustrated by the examination of phylogenetic analysis on four datasets. Full article

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Open Access Article

A Liquid-Solid Coupling Hemodynamic Model with Microcirculation Load

Cited by 3 | Viewed by 2017

Abstract

From the aspect of human circulation system structure, a complete hemodynamic model requires consideration of the influence of microcirculation load effect. This paper selected the seepage in porous media as the simulant of microcirculation load. On the basis of a bi-directional liquid-solid coupling [...] Read more.

From the aspect of human circulation system structure, a complete hemodynamic model requires consideration of the influence of microcirculation load effect. This paper selected the seepage in porous media as the simulant of microcirculation load. On the basis of a bi-directional liquid-solid coupling tube model, we built a liquid-solid-porous media seepage coupling model. The simulation parameters accorded with the physiological reality. Inlet condition was set as transient single-pulse velocity, and outlet as free outlet. The pressure in the tube was kept at the state of dynamic stability in the range of 80–120 mmHg. The model was able to simulate the entire propagating process of pulse wave. The pulse wave velocity simulated was 6.25 m/s, which accorded with the physiological reality. The complex pressure wave shape produced by reflections of pressure wave was also observed. After the model changed the cardiac cycle length, the pressure change according with actual human physiology was simulated successfully. The model in this paper is well-developed and reliable. It demonstrates the importance of microcirculation load in hemodynamic model. Moreover the properties of the model provide a possibility for the simulation of dynamic adjustment process of human circulation system, which indicates a promising prospect in clinical application. Full article

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Mathematical Modelling In Biology And Medicine Pdf

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