Non-linear Dynamics Commons^™

Accuracy Of Parameter Estimation For A Simple Gene Regulatory Network Model Is Sensitive To Network Motif, Number Of Parameters Estimated, And Magnitude And Direction Of Regulatory Relationships, Nikki C. Chun, Kam Dahlquist

Honors Thesis

A gene regulatory network (GRN) is a set of transcription factors that regulate the expression of genes encoding other transcription factors. The dynamics of a GRN explain how gene expression changes over time. GRNmap is a MATLAB software package that uses ordinary differential equations to model dynamics of small-scale GRNs. We used the program to estimate production rates, expression thresholds, and regulatory weights for each transcription factor in three related literature-derived GRNs based on yeast cold shock microarray data previously collected in the Dahlquist Lab. We noticed large differences in estimated weight values when 1-2% of the expression values were …

Dynamic Homeostasis In Relaxation And Bursting Oscillations, Christopher J. Ryzowicz

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimal Control And Bifurcation Analysis Of A Predator–Prey Model With Self-Limiting Growth And Predator Disease, Dipo Aldila, Muhammad Akmal Fasya, Bevina D. Handari, Chidozie Williams Chukwu, Olumuyiwa James Peter

Mathematical Modelling and Numerical Simulation with Applications

We propose and analyze an eco-epidemiological predator–prey model that incorporates self-limitation and disease transmission within the predator population. The model is formulated as a system of ordinary differential equations describing logistic prey growth under the interspecific interaction with the predator. On the other hand, the predator population is divided into susceptible and infected classes, whose growth is constrained by prey availability. Three biologically relevant equilibria are identified: predator extinction, disease-free coexistence, and coexistence with endemic disease. The existence and stability of these equilibria are determined by key ecological and epidemiological thresholds, including the basic reproduction number. Using numerical continuation methods, …

Optimal Control Strategies For Infectious Diseases: A Numerical Simulation Approach, M. Abu Salek, Jannatun Nayeem, Romana Yesmin, M. Haider Ali Biswas, M. Humayun Kabir

Mathematical Modelling and Numerical Simulation with Applications

Various infectious diseases, such as Tuberculosis and Hepatitis B virus (HBV), caused by Mycobacterium bacteria and hepatitis B virus, respectively, pose serious threats worldwide. This paper examines the spread of these diseases using a mathematical model that incorporates control measures, including vaccination and awareness programs. We use a system of differential equations with control variables and apply Pontryagin's principle to determine optimal control strategies. The stability of the Disease Free Equilibrium (DFE) has been analysed and demonstrated to be both locally and globally asymptotically stable when the basic reproduction number remains below unity, thereby ensuring disease elimination. Furthermore, the Endemic …

Dynamical Analysis And Optimal Control Of The Mpox Transmission Model With Stratified Susceptibility, Tuhfatul Janan, Fatmawati Fatmawati, Cicik Alfiniyah, Santi Martini, Dipo Aldila, Agus Hasan

Mathematical Modelling and Numerical Simulation with Applications

This study develops a mathematical model of Mpox transmission that combines stratified susceptibility (low-risk and high-risk groups) with vaccinated and asymptomatically infected compartments. The analysis of the model begins with examining the well-posedness, boundedness, and nonnegativity conditions for the solutions. The local stabilities of the equilibria are examined through the Jacobian matrix and phase plane analysis, while the global stabilities are provided through Lyapunov functions. The estimated parameters are verified using epidemiological data on Mpox cases in the United States, with an MAPE of 2.20% and R_0 > 1, indicating that Mpox remains endemic. Sensitivity analysis indicates that the contact rate …

Construction And Data-Driven Analysis Of A Stochastic, Individual-Based Opioid Epidemiology Network Model, Leigh Bennett Pearcy, Owen Queen, Vincent Jodoin, Suzanne Lenhart, Christopher Strickland

Mathematical Modelling and Numerical Simulation with Applications

While substance use epidemiology has been an active area of mathematical research in recent years, the social and mental processes that are involved in the development of substance use disorders have presented challenges to advancing the epidemiological theory and how they differ from the contraction of pathogenic disease. Such distinction is especially pertinent in the context of the current United States opioid epidemic and its intersection with the recent COVID-19 pandemic, as both prescription drugs and social influence play major roles in the development of opioid use disorder. In this paper, we construct a stochastic network model capturing how individual …

Modeling Synaptic Dysfunction As Neural Contagion: A Graph-Based Sedr Framework For Simulating Signal Spread, Michelle Marfo, Dr. Padmanabhan Seshaiyer, Alonso Ogueda-Oliva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Immune Dysregulation In Covid-19: Mathematical Modeling Of The Within-Host Dynamics, Pagnapech Ngoun, Nicolas Alvarez, Ayesh Awad, Hwayeon Ryu

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Kadel] Robust Basins, Fragile Attractors: A New View On Boolean Network Dynamics, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Metapopulation Model For Oyster Restoration, Leah Shaw

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Understanding The Spread Of Black Sigatoka Disease: A Deterministic And Stochastic Modeling Approach, Bernard Asamoah Afful, Luis F. Gordillo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Balancing Stability And Complexity In Boolean Models Of Biological Networks, Venkata Sai Narayana Bavisetty

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Dynamics And Optimal Intervention Strategies In A Shigellosis Transmission Model, Mehmet Gümüs, Shewafera Wondimagegnhu Teklu, Kemal Türk

Mathematical Modelling and Numerical Simulation with Applications

This research explores how water treatment contributes to limiting the transmission of Shigellosis, an infection caused by bacteria from the Shigella genus. A mathematical framework is formulated to evaluate the influence of protective strategies and water purification on the spread of the disease. To confirm the model's biological relevance, its well-posedness is investigated. The basic reproduction number $(\mathfrak{R}_0)$, a critical indicator of disease behavior, is derived using the matrix operator method. Findings indicate that if $\mathfrak{R}_01$, the infection persists, with the endemic equilibrium exhibiting local asymptotic stability. A comprehensive cost-effectiveness analysis reveals that combining environmental protection with water treatment represents …

Coarse-Graining Spiking Reservoirs: Reducing Reservoir Size While Preserving Critical Dynamics, Tucker X. Mastin, Christof Teuscher

Northeast Journal of Complex Systems (NEJCS)

We propose an extension of renormalization into the domain of spiking neural networks, thereby providing a novel framework for coarse-graining neural networks without disrupting their critical properties. The proposed coarse-graining technique merges neurons and synaptic connections based on a graph-theoretic distance derived from synaptic weight strength and is configured to effectively prune the reservoir size while preserving the scale-free spiking dynamics indicative of criticality. Criticality in spiking neural networks may provide information-theoretic advantages by optimizing information processing and sensitivity to input. Using time-series prediction benchmarks, we demonstrate that networks operating at criticality exhibit up to 32% higher prediction accuracy before …

Evolutionary Dynamics Of Artificial Agents: Exploration And Learning In Games, Brian Mintz

Dartmouth College Ph.D Dissertations

The natural world abounds with examples of complex behavior in humans and many other species. Evolutionary game theory is a powerful mathematical framework to understand the origins of many such behaviors like cooperation. Since these behaviors are often selected against initially, understanding why they are so widespread has been a longstanding question. Rather than assuming agents' rationality, like in traditional game theory, this approach studies the mutation and selection of strategies themselves. However most behavior is neither perfectly rational nor entirely determined by genetics. This dissertation works to bridge the gap between these two perspectives by analyzing models where individuals …

Stability Insights From Modeling Chronic Myelogenous Leukemia, Giovani Thai

Master's Theses

This thesis centers around a model for chronic myelogenous leukemia (CML) as it behaves under imatinib treatment, a common medication for CML patients, and the anti-leukemia immune response. The dynamics are represented with a system of nonlinear delay-differential equations first constructed by Kim et al. in 2008, capturing population changes of T-cells and various CML growth stages. We investigate stability in both the clinical and mathematical sense. Through numerical simulations, we computationally incorporate a supplementary treatment plan to determine its effectiveness in aiding immune response and medication in achieving remission and full elimination. The primary goal is to conduct a …

Individual And Collective Properties Of Tunable Photochemical Belousov-Zhabotinsky Micro-Reactors, Kudakwashe Benedict Shumba

Graduate Theses, Dissertations, and Problem Reports (ETD)

Cell-like model chemical systems are powerful tools that can be used to explore the role of intercellular coupling on population level behaviors in communities of biological cells. Firstly, we present a new method for fabricating such micro-reactors using the photosensitive Belousov–Zhabotinsky (BZ) reaction system employed in silica microparticles. These BZ micro-reactors have a tunable response to photochemical coupling, varying from a fully excitatory response to a fully inhibitory response. Their response can be tuned through variations in either the reactive mixture or, on an individual micro-reactor level, by changes in the synthesis temperature used during the fabrication of the silica …

Mathematical Modelling Of Disease Outbreak, Favour Christian, Matthew Molloy

SURE Journal: Science Undergraduate Research Experience Journal

Establishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study was to investigate the significance of the many criteria linked to a zombie virus spread. The zombie framework provides an accessible and relatively simple representation of the nature of infectious disease spread, allowing for tractable assumptions and the development of more complex situations.

The models are designed around a zombie outbreak in which the zombie virus is spread through a …

Modelling Saccharomyces Cerevisiae For The Production Of Fermented Beverages, Paul A. Valle Dr., Yolocuauhtli Salazar Dr., Luis N. Coria Dr., Oscar N. Soto Dr., Jesus B. Paez Dr.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Model Of Oocyte Population Dynamics For Fish Oogenesis, Louis Fostier, Frédérique Clément, Romain Yvinec, Violette Thermes

Biology and Medicine Through Mathematics Conference

No abstract provided.

Information Feedback Delays Within Epidemic Models And Their Effect On Model Dynamics., Maria K. Bouka, Christopher Strickland Dr

Biology and Medicine Through Mathematics Conference

No abstract provided.

Leveraging Redundancy As A Link Between Spreading Dynamics On And Of Networks, Felipe Xavier Costa

Electronic Theses & Dissertations (2024 - present)

A constant quest in network science has been in the development of methods to identify the most relevant components in a dynamical system solely via the interaction structure amongst its subsystems. This information allows the development of control and intervention strategies in biochemical signaling and epidemic spreading. We highlight the relevant components in heterogeneous dynamical system by their patterns of redundancy, which can connect how dynamics affect network topology and which pathways are necessary to spreading phenomena on networks. In order to measure the redundancies in a large class of empirical systems, we develop the backbone of directed networks methodology, …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Using A Coupled Integral Projection Model To Investigate Interspecific Competition During An Invasion: An Application To Silver Carp (Hypophthalmichthys Molitrix) And Gizzard Shad (Dorosoma Cepedianum), James Peirce

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Kadelka: Modularizing The Control Search For Biological Systems, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Kadelka: Canalization Reduces The Nonlinearity Of Regulation In Biological Networks, Claus Kadelka, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Exploring The Presence Of Nonlinear Deterministic Dynamics In Commodity Prices, Sagar Dahal

Department of Agricultural Economics: Dissertations, Theses, and Student Research

Determining whether commodity prices (and volatility) are driven by linear stochastic processes or low-dimensional nonlinear deterministic dynamics (“chaos”) is crucial for policymaking, forecasting, production, storage, investment, risk management, and hedging decisions. Previous studies that used Lyapunov exponents and correlation dimensions to identify chaotic structures in price series may be unreliable in practical applications because these methods rely on asymptotic properties that require large, noiseless data which is often not available. We applied nonlinear time series analysis approaches to empirically detect the underlying market dynamics using the daily futures prices of ten agricultural commodities. We used phase space reconstruction to reconstruct …

Pathogen Emergence As Complex Biological Invasion: Lessons From Dynamical Systems Modeling, Sudam Surasinghe, Marisabel Rodriguez, Victor Meszaros, Jane Molofsky, Salvador Almagro-Moreno, Brandon Ogbunugafor

Northeast Journal of Complex Systems (NEJCS)

Infectious disease emergence has become the target of cross-disciplinary efforts
that aim to understand and predict the shape of outbreaks. The many challenges
involved with the prediction of disease emergence events is a characteristic that in-
fectious diseases share with biological invasions in many subfields of ecology (e.g.,
how certain plants are able to successfully invade a new niche). Like infectious
diseases, biological invasions by plants and animals involve interactions between
agents (pathogens and plants in their respective cases) and a recipient niche. In
this study, we examine the problem of pathogen emergence through the lens of a
framework first …

Deep Hybrid Modeling Of Neuronal Dynamics Using Generative Adversarial Networks, Soheil Saghafi

Dissertations

Mechanistic modeling and machine learning methods are powerful techniques for approximating biological systems and making accurate predictions from data. However, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. This dissertation constructs Deep Hybrid Models that address these shortcomings by combining deep learning with mechanistic modeling. In particular, this dissertation uses Generative Adversarial Networks (GANs) to provide an inverse mapping of data to mechanistic models and identifies the distributions of mechanistic model parameters coherent to the data.

Chapter 1 provides background information on …

Computing Brain Networks With Complex Dynamics, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.