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Dynamic Models of Biology and Medicine, Volume III

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Applied Biosciences and Bioengineering".

Deadline for manuscript submissions: 20 December 2024 | Viewed by 19382

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Prof. Dr. Yang Kuang

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School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
Interests: mathematical and computational biology and medicine; delay differential equations; mathematical models; applied mathematics
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Dr. Kevin Flores

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North Carolina State University, Raleigh, NC, USA
Interests: applied mathematics; inverse problems; mathematical biology; precision medicine; machine learning
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Dr. Erica Rutter

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North Carolina State University/ University of California – Merced, Raleigh, NC, USA
Interests: mathematical biology; mathematical oncology; machine learning
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Special Issue Information

Dear Colleagues,

Mathematical and computational modeling approaches in biological and medical research are experiencing exponential growth globally. This Special Issue aims 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 dynamic (differential equation) models to describe observed nonlinear dynamics that aim to understand life science problems. To be considered for this Special Issue, a paper should be in one (or a combination) of the following three categories: (a) Papers developing and mathematically analyzing dynamic 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 papers 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
Dr. Kevin Flores
Dr. Erica Rutter
Guest Editors

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Keywords

dynamic system
mathematical biology
mathematical medicine
simulation
stability
bifurcation

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Published Papers (11 papers)

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23 pages, 787 KiB

Open AccessArticle

Study of an Epidemiological Model for Plant Virus Diseases with Periodic Coefficients

by Aníbal Coronel, Fernando Huancas and Stefan Berres

Appl. Sci. 2024, 14(1), 399; https://doi.org/10.3390/app14010399 - 31 Dec 2023

Cited by 1 | Viewed by 1442

Abstract

In the present article, we research the existence of the positive periodic solutions for a mathematical model that describes the propagation dynamics of a pathogen living within a vector population over a plant population. We propose a generalized compartment model of the susceptible–infected–susceptible (SIS) type. This model is derived primarily based on four assumptions: (i) the plant population is subdivided into healthy plants, which are susceptible to virus infection, and infected plants; (ii) the vector population is categorized into non-infectious and infectious vectors; (iii) the dynamics of pathogen propagation follow the standard susceptible–infected–susceptible pattern; and (iv) the rates of pathogen propagation are time-dependent functions. The main contribution of this paper is the introduction of a sufficient condition for the existence of positive periodic solutions in the model. The proof of our main results relies on a priori estimates of system solutions and the application of coincidence degree theory. Additionally, we present some numerical examples that demonstrate the periodic behavior of the system. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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16 pages, 2430 KiB

Open AccessArticle

Rich Dynamics of a General Producer–Grazer Interaction Model under Shared Multiple Resource Limitations

by Tin Phan, James J. Elser and Yang Kuang

Appl. Sci. 2023, 13(7), 4150; https://doi.org/10.3390/app13074150 - 24 Mar 2023

Cited by 2 | Viewed by 1611

Abstract

Organism growth is often determined by multiple resources interdependently. However, growth models based on the Droop cell quota framework have historically been built using threshold formulations, which means they intrinsically involve single-resource limitations. In addition, it is a daunting task to study the global dynamics of these models mathematically, since they employ minimum functions that are non-smooth (not differentiable). To provide an approach to encompass interactions of multiple resources, we propose a multiple-resource limitation growth function based on the Droop cell quota concept and incorporate it into an existing producer–grazer model. The formulation of the producer’s growth rate is based on cell growth process time-tracking, while the grazer’s growth rate is constructed based on optimal limiting nutrient allocation in cell transcription and translation phases. We show that the proposed model captures a wide range of experimental observations, such as the paradox of enrichment, the paradox of energy enrichment, and the paradox of nutrient enrichment. Together, our proposed formulation and the existing threshold formulation provide bounds on the expected growth of an organism. Moreover, the proposed model is mathematically more tractable, since it does not use the minimum functions as in other stoichiometric models. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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12 pages, 1970 KiB

Open AccessArticle

Serotonin Signaling in the Enteric Nervous System and Connection to Autism Spectrum Disorder: A Translational Mathematical Model

by Irina Kareva

Appl. Sci. 2023, 13(5), 2970; https://doi.org/10.3390/app13052970 - 25 Feb 2023

Viewed by 1737

Abstract

While the causes of autism spectrum disorder (ASD) remain unclear, some studies have shown that serotonin-mediated effects on the enteric nervous system (ENS) correlate with an ASD-like behavioral phenotype in mice. Introduced here is a mathematical model of interactions between gut serotonin and its impact on the ENS. The model was used to identify three key factors that affect ENS size, namely, serotonin production, its clearance, and its ability to act as a growth factor for the ENS. The model was used to reproduce experimentally reported results from a mouse model by Margolis et al. (2016), which connected serotonin-mediated ENS hypoplasia to an ASD phenotype. The proposed mathematical model was used to scale the quantified relationship from mice to humans to show how the combination of these three factors can translate to a quantifiable metric that could potentially be correlated to the ASD spectrum. A detailed discussion of how ENS hypoplasia could mechanistically affect CNS activity concludes this paper. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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21 pages, 4488 KiB

Open AccessArticle

Understanding Neutrophil Dynamics during COVID-19 Infection

by Quiyana M. Murphy and Stanca M. Ciupe

Appl. Sci. 2023, 13(4), 2409; https://doi.org/10.3390/app13042409 - 13 Feb 2023

Viewed by 1255

Abstract

Infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) results in varied clinical outcomes, with virus-induced chronic inflammation and tissue injury being associated with enhanced disease pathogenesis. To determine the role of tissue damage on immune populations recruitment and function, a mathematical model of innate immunity following SARS-CoV-2 infection has been proposed. The model was fitted to published longitudinal immune marker data from patients with mild and severe COVID-19 disease and key parameters were estimated for each clinical outcome. Analytical, bifurcation, and numerical investigations were conducted to determine the effect of parameters and initial conditions on long-term dynamics. The results were used to suggest changes needed to achieve immune resolution. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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15 pages, 2939 KiB

Open AccessArticle

GAN Training Acceleration Using Fréchet Descriptor-Based Coreset

by Yanzhe Xu, Teresa Wu, Jennifer R. Charlton and Kevin M. Bennett

Appl. Sci. 2022, 12(15), 7599; https://doi.org/10.3390/app12157599 - 28 Jul 2022

Cited by 2 | Viewed by 1533

Abstract

Generative Adversarial Networks (GANs) are a class of deep learning models being applied to image processing. GANs have demonstrated state-of-the-art performance in applications such as image generation and image-to-image translation, just to name a few. However, with this success comes the realization that the training of GANs takes a long time and is often limited by available computing resources. In this research, we propose to construct a Coreset using Fréchet Descriptor Distances (FDD-Coreset) to accelerate the training of GAN for blob identification. We first propose a Fréchet Descriptor Distance (FDD) to measure the difference between each pair of blob images based on the statistics derived from blob distribution. The Coreset is then employed using our proposed FDD metric to select samples from the entire dataset for GAN training. A 3D-simulated dataset of blobs and a 3D MRI dataset of human kidneys are studied. Using computation time and eight performance metrics, the GAN trained on the FDD-Coreset is compared against the model trained on the entire dataset and an Inception and Euclidean Distance-based Coreset (IED-Coreset). We conclude that the FDD-Coreset not only significantly reduces the training time, but also achieves higher denoising performance and maintains approximate performance of blob identification compared with training on the entire dataset. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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16 pages, 4523 KiB

Open AccessArticle

Combining Androgen Deprivation and Immunotherapy in Prostate Cancer Treatment: A Mechanistic Approach

by Johnna Barnaby and Harsh Vardhan Jain

Appl. Sci. 2022, 12(14), 6954; https://doi.org/10.3390/app12146954 - 9 Jul 2022

Cited by 1 | Viewed by 1837

Abstract

Due to its initial dependence on testosterone, prostate cancer patients are initially treated with androgen deprivation therapy, a form of chemical castration. However, in many cases, the cancer develops resistance to this treatment. Sipuleucel-T (Provenge), is the first live cell vaccine approved for treating patients with advanced, hormonally refractive prostate cancer. However, it has shown limited survival benefit. Recently, it has been proposed that combining Provenge with androgen deprivation may result in a better treatment outcome. Here, we develop a nonlinear dynamical systems model with a view to predicting the therapeutic potential of such a combination. Our model accounts for the mechanism of action of Provenge and the immune system response elicited by androgen deprivation. We use data from mouse xenograft experiments to calibrate and validate our model. The validated model is then used to explain the limited clinical success of Provenge, and predict optimal scheduling that maximizes the anti-tumor potential of Provenge combined with androgen deprivation. In particular, we demonstrate that the two treatments should be given concurrently, rather than sequentially, as is current practice. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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21 pages, 707 KiB

Open AccessArticle

Hierarchy Establishment from Nonlinear Social Interactions and Metabolic Costs: An Application to Harpegnathos saltator

by Carlos Bustamante-Orellana, Dingyong Bai, Jordy Cevallos-Chavez, Yun Kang, Benjamin Pyenson and Congbo Xie

Appl. Sci. 2022, 12(9), 4239; https://doi.org/10.3390/app12094239 - 22 Apr 2022

Viewed by 1512

Abstract

Social hierarchies are ubiquitous in social groups such as human societies and social insect colonies; however, the factors that maintain these hierarchies are less clear. Motivated by the shared reproductive hierarchy of the ant species Harpegnathos saltator, we have developed simple compartmental nonlinear differential equations to explore how key life-history and metabolic rate parameters may impact and determine its colony size and the length of its shared hierarchy. Our modeling approach incorporates nonlinear social interactions and metabolic theory. The results from the proposed model, which were linked with limited data, show that: (1) the proportion of reproductive individuals decreases over colony growth; (2) an increase in mortality rates can diminish colony size but may also increase the proportion of reproductive individuals; and (3) the metabolic rates have a major impact in the colony size and structure of a shared hierarchy. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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15 pages, 1236 KiB

Open AccessArticle

A Mathematical Study of COVID-19 Spread by Vaccination Status in Virginia

by Matthew D. Johnston, Bruce Pell and Patrick Nelson

Appl. Sci. 2022, 12(3), 1723; https://doi.org/10.3390/app12031723 - 8 Feb 2022

Cited by 6 | Viewed by 2649

Abstract

We introduce a novel n-stage vaccination model and corresponding system of differential equations that stratify a population according to their vaccination status. The model is an extension of the classical SIR-type models commonly used for time-course simulations of infectious disease spread and allows for the mitigation effects of vaccination to be uncoupled from other factors, such as changes in social behavior and the prevalence of virus variants. We fit the model to the Virginia Department of Health data on new COVID-19 cases, hospitalizations, and deaths broken down by vaccination status. The model suggests that, from 23 January through 11 September, fully vaccinated individuals were 89.8% less likely to become infected with COVID-19 and that the B.1.617.2 (Delta) variant is 2.08 times more transmissible than previously circulating strains of COVID-19. We project the model trajectories into the future to predict the impact of booster shots. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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14 pages, 378 KiB

Open AccessArticle

Global Dynamics of a Stochastic Viral Infection Model with Latently Infected Cells

by Chinnathambi Rajivganthi and Fathalla A. Rihan

Appl. Sci. 2021, 11(21), 10484; https://doi.org/10.3390/app112110484 - 8 Nov 2021

Cited by 4 | Viewed by 2010

Abstract

In this paper, we study the global dynamics of a stochastic viral infection model with humoral immunity and Holling type II response functions. The existence and uniqueness of non-negative global solutions are derived. Stationary ergodic distribution of positive solutions is investigated. The solution fluctuates around the equilibrium of the deterministic case, resulting in the disease persisting stochastically. The extinction conditions are also determined. To verify the accuracy of the results, numerical simulations were carried out using the Euler–Maruyama scheme. White noise’s intensity plays a key role in treating viral infectious diseases. The small intensity of white noises can maintain the existence of a stationary distribution, while the large intensity of white noises is beneficial to the extinction of the virus. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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19 pages, 471 KiB

Open AccessFeature PaperArticle

Global Dynamics and Implications of an HBV Model with Proliferating Infected Hepatocytes

by Sarah Hews, Steffen Eikenberry, John D. Nagy, Tin Phan and Yang Kuang

Appl. Sci. 2021, 11(17), 8176; https://doi.org/10.3390/app11178176 - 3 Sep 2021

Cited by 3 | Viewed by 2151

Abstract

Chronic hepatitis B (HBV) infection is a major cause of human suffering, and a number of mathematical models have examined the within-host dynamics of the disease. Most previous models assumed that infected hepatocytes do not proliferate; however, the effect of HBV infection on hepatocyte proliferation is controversial, with conflicting data showing both induction and inhibition of proliferation. With a family of ordinary differential equation (ODE) models, we explored the dynamical impact of proliferation among HBV-infected hepatocytes. Here, we show that infected hepatocyte proliferation in this class of models generates a threshold that divides the dynamics into two categories. Sufficiently compromised proliferation in infected cells produces complex dynamics characterized by oscillating viral loads, whereas higher proliferation generates straightforward dynamics that always results in chronic infection, sometimes with liver failure. A global stability result of the liver failure state was included as it is unique to this class of models. Finally, the model analysis motivated a testable biological hypothesis: Healthy hepatocytes are present in chronic HBV infection if and only if the proliferation of infected hepatocytes is severely impaired. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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10 pages, 2365 KiB

Open AccessProtocol

Towards a System Dynamics Model on Risk Factors of Knee Osteoarthritis: A Study Protocol for the DYNAMIKOS Model

by Charis Tsarbou, Nikolaos I. Liveris, George Papageorgiou, Joanna Kvist, Elias Tsepis, Evdokia Billis, John Gliatis and Sofia A. Xergia

Appl. Sci. 2024, 14(22), 10691; https://doi.org/10.3390/app142210691 - 19 Nov 2024

Viewed by 355

Abstract

(1) Background: Osteoarthritis (OA) is a serious chronic disease mostly affecting the knee joint. Despite the many efforts for developing strategies to predict and control Knee Osteoarthritis (KOA), the disease is on the rise. This paper describes the process for the creation of a simulation model, the Dynamic Knee Osteoarthritis Simulation (DYNAMIKOS) model, that captures the complex interrelationships of the risk factors for the development of KOA; (2) Methods: The DYNAMIKOS model will be based on the System Dynamics approach. The first step will be to develop a Causal Loop Diagram (CLD) model for the risk factors involved incorporating a series of Group Modeling Building (GMB) workshops with experts and stakeholders. Using data from a representative sample of KOA patients, the statistical approaches Exploratory Factor Analysis, Confirmatory Factor Analysis, and Structural Equation Modeling (SEM) will be carried out. (3) Results: This study will develop a simulation System Dynamics model for the risk factors of KOA based on the results of CLD and SEM; (4) Conclusions: The proposed DYNAMIKOS model could be used for effectively analyzing the complex interrelationships among the multiple factors that constitute the spread of KOA. In this way, plausible prevention strategies could be implemented for effectively managing and leading the potential eradication of KOA. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume III)

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