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Articles 1 - 30 of 48
Full-Text Articles in Dynamic Systems
A Novel Mathematical Model Of Hiv Transmission Incorporating The Effects Of Treatment And Pre-Exposure Prophylaxis: Sensitivity Analysis And Numerical Simulations, Erick Manuel Delgado Moya
A Novel Mathematical Model Of Hiv Transmission Incorporating The Effects Of Treatment And Pre-Exposure Prophylaxis: Sensitivity Analysis And Numerical Simulations, Erick Manuel Delgado Moya
Mathematical Modelling and Numerical Simulation with Applications
Human immunodeficiency virus (HIV) continues to be a public health problem in many countries of the world, and Pre-exposure prophylaxis (PrEP) is a preventive method for HIV, which has shown great efficacy and is in use worldwide. This work presents a new mathematical model for HIV transmission incorporating PrEP use and evaluates the impact of PrEP along with its increasing use in a population. The construction of the model takes into account three forms of diagnosis: diagnosis of individuals in risky sexual contact, diagnosis after risky contact (diagnosis in the undiagnosed infected compartment), and diagnosis associated with attempting to enter …
Stability Analysis Of Thermohaline Convection With A Time-Varying Shear Flow Using The Lyapunov Method, Kalin Kochnev
Stability Analysis Of Thermohaline Convection With A Time-Varying Shear Flow Using The Lyapunov Method, Kalin Kochnev
Honors Scholar Theses
This work applies the Lyapunov method to identify instabilities and compute the growth rate of a linear time-varying system. The linear system studied describes cold fresh water on top of hot salty water with a periodically time-varying background shear flow. A time-dependent weighting matrix is employed to construct a Lyapunov function candidate. The resulting linear matrix inequalities are discretized in time using the forward Euler method. As the number of temporal discretization points increases, the growth rate predicted by the Lyapunov method or Floquet theory, used for comparison, will converge to the same value obtained from numerical simulations. Furthermore, the …
Math Meets Climate: The Energy Balance Model, Maria I. Sanchez Muniz
Math Meets Climate: The Energy Balance Model, Maria I. Sanchez Muniz
Open Educational Resources
This assignment introduces students to the mathematics of Earth’s climate through the classical energy balance model. Students analyze how incoming solar radiation, outgoing thermal radiation, and temperature-dependent albedo interact to determine Earth’s equilibrium temperature. Using analytical calculations and computational tools, students identify equilibrium states, assess their stability, and interpret the results through the lens of dynamical systems and bifurcation theory. The activity builds conceptual understanding of climate feedbacks, greenhouse effects, and tipping behavior using a transparent, one-variable model. Designed for applied mathematics and interdisciplinary STEM courses, this assignment emphasizes computation, physical interpretation, and real-world relevance. It is released as a …
Understanding Enso Through Mathematical Models, Maria I. Sanchez Muniz
Understanding Enso Through Mathematical Models, Maria I. Sanchez Muniz
Open Educational Resources
This assignment introduces students to conceptual models of the El Niño–Southern Oscillation (ENSO) and guides them through a structured investigation of their physical and mathematical foundations. Students analyze the recharge–oscillator and delayed–oscillator frameworks, explore how differential equations capture ocean–atmosphere interactions, and evaluate parameter-driven changes in oscillatory behavior. A key component of the work is the guided use of generative AI as a research tool: students employ AI models to locate peer-reviewed literature, interrogate model extensions, and refine their understanding of complex mechanisms, while synthesizing all final explanations in their own words. By blending classical climate modeling with modern AI-supported inquiry, …
(R2130) Cusum-Test For Unconditional Variance Change Detection In Bilinear Garch Models, Edoh Katchekpele, Abdou Kâ Diongue, Ben Célestin Kouassi
(R2130) Cusum-Test For Unconditional Variance Change Detection In Bilinear Garch Models, Edoh Katchekpele, Abdou Kâ Diongue, Ben Célestin Kouassi
Applications and Applied Mathematics: An International Journal (AAM)
We examine CUSUM-type test for detecting changes in unconditional variance within Bilinear GARCH models. We derive the asymptotic distribution of the test statistic under both null and alternative hypotheses and assess test effectiveness in identifying single structural breaks. Simulation studies support our theoretical results and demonstrate the practical utility of the test.
Universal Systems Simulation Via Constraint Hypergraphs With Applications To Digital Twins, John Morris
Universal Systems Simulation Via Constraint Hypergraphs With Applications To Digital Twins, John Morris
All Dissertations
The characterization of systems encompasses a variety of modeling frameworks designed to capture specific behaviors and components of various system domains. Whatever the framework, the core elements of a system representation are the information of the system and a description of how that information is related. The relations in deterministic systems are functions, which, when composed to form executable processes, can be used to simulate system data. A declarative modeling framework is one that encodes mechanisms for preparing these simulations within the model structure, allowing an external agent to form the execution processes required for a given context. To date, …
Using Compartmental Systems Of Ordinary Differential Equations And Optimal Control Theory To Compute Ideal Quantities Of Mentors For Student Populations, Timofey B. Gafurov
Using Compartmental Systems Of Ordinary Differential Equations And Optimal Control Theory To Compute Ideal Quantities Of Mentors For Student Populations, Timofey B. Gafurov
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Investigating The Basic Reproduction Number For An Avian Influenza Model, Omar Saucedo
Investigating The Basic Reproduction Number For An Avian Influenza Model, Omar Saucedo
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Computational Models For Pre-Lens Tear Film Drug Concentration Dynamics With Drug Supply From A Contact Lens And Drug Exchange During Blinking, Mazen A. Althobaiti
Computational Models For Pre-Lens Tear Film Drug Concentration Dynamics With Drug Supply From A Contact Lens And Drug Exchange During Blinking, Mazen A. Althobaiti
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
[Kyda] The Behavioral Spillover Effect: Modeling Behavioral Interdependencies In Multi-Pathogen Dynamics, Leah Lejeune, Omar Saucedo, Lauren M. Childs, Navid Ghaffarzadegan
[Kyda] The Behavioral Spillover Effect: Modeling Behavioral Interdependencies In Multi-Pathogen Dynamics, Leah Lejeune, Omar Saucedo, Lauren M. Childs, Navid Ghaffarzadegan
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Following Carbon: Pathway And Flux Representations Of Ecosystems, Caner Kazanci
Following Carbon: Pathway And Flux Representations Of Ecosystems, Caner Kazanci
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Culture Mediates Climate Opinion Change: A System Dynamics Model, Louis (Lou) Gross, Yoon Ah Shin, Sara M. Constantino, Ann Kinzig, Katherine Lacasse, Brian Beckage
Culture Mediates Climate Opinion Change: A System Dynamics Model, Louis (Lou) Gross, Yoon Ah Shin, Sara M. Constantino, Ann Kinzig, Katherine Lacasse, Brian Beckage
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
[Reev] Describing Social Movement Evolutionary Pathways Through The Conviction-Moderated Adaptive Voter Model, Arturo F. Serrano Borrero, Dylan Green, Olivia J. Chu
[Reev] Describing Social Movement Evolutionary Pathways Through The Conviction-Moderated Adaptive Voter Model, Arturo F. Serrano Borrero, Dylan Green, Olivia J. Chu
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Generalized Reciprocity In Female Norway Rats: A Mathematical Model Of Population Dynamics, Mei Q. Gordon Washington, Olivia J. Chu
Generalized Reciprocity In Female Norway Rats: A Mathematical Model Of Population Dynamics, Mei Q. Gordon Washington, Olivia J. Chu
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Reconstructing Gene Regulatory Networks From Time-Series Data In Knime, Raina Robeva
Reconstructing Gene Regulatory Networks From Time-Series Data In Knime, Raina Robeva
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Models Of Disease Transmission In Long-Term Care Facilities, Cara Sulyok
Mathematical Models Of Disease Transmission In Long-Term Care Facilities, Cara Sulyok
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling Dengue Transmission: Data Assimilation, Identifiability, Reproduction Number, And Stability Analysis, Owen Mcmann
Modeling Dengue Transmission: Data Assimilation, Identifiability, Reproduction Number, And Stability Analysis, Owen Mcmann
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Can We End The Hiv Epidemic In The U.S.? Linking Clinical And National Surveillance Data Through Multiscale Modeling From Patients To Populations, Necibe Tuncer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
[Lele] Measles And Mandates– What Will Happen If Florida Repeals The Mmr Vaccine Mandate?, Alice Oveson, Abba Gumel
[Lele] Measles And Mandates– What Will Happen If Florida Repeals The Mmr Vaccine Mandate?, Alice Oveson, Abba Gumel
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Representing Ewe-Lamb Contact Dynamics In An Agent-Based Model Of Enzootic Abortion Of Ewes, Kelly R. Buch, Cara J. Sulyok
Representing Ewe-Lamb Contact Dynamics In An Agent-Based Model Of Enzootic Abortion Of Ewes, Kelly R. Buch, Cara J. Sulyok
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Metapopulation Model For Oyster Restoration, Leah Shaw
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
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.
Using Compartmental Systems Of Ordinary Differential Equations And Optimal Control Theory To Compute Ideal Quantities Of Mentors For Student Populations, Timofey B. Gafurov
Using Compartmental Systems Of Ordinary Differential Equations And Optimal Control Theory To Compute Ideal Quantities Of Mentors For Student Populations, Timofey B. Gafurov
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Optimal Location And Sizing Of Facts Devices To Improve Voltage Profiles On A 132 Kv Mwanza-Musoma-Nyamongo Transmission Line, Peter Makolo
Optimal Location And Sizing Of Facts Devices To Improve Voltage Profiles On A 132 Kv Mwanza-Musoma-Nyamongo Transmission Line, Peter Makolo
Tanzania Journal of Engineering and Technology (TJET)
Recently, utility companies have desired to supply quality, stable and reliable power to customers, and ensure they meet the demand. Flexible AC Transmission Systems (FACTS) dynamic compensator devices such as Static Synchronous Compensator (STATCOM), Static VAr Compensator (SVC) and Unified Power Flow Controller (UPFC) are an impeccable choice, however, cost is one of the limiting factors following these technologies. In addition, using FACTS devices in the system requires a detailed steady state, dynamic and optimisation analysis to effectively meet the purpose and ensure reduced cost. This paper proposes using an optimised FACTS device to improve voltage profile, power transfer, system …
(Si15-121) Analyzing Seitr Tuberculosis Transmission Model Using Caputo–Fabrizio Fractional Derivative With Diverse Contact Rates, S. S. Sumaiya Banu, T. Gunasekar, S. Manikandan, Kamalendra Kumar, M. Suba
(Si15-121) Analyzing Seitr Tuberculosis Transmission Model Using Caputo–Fabrizio Fractional Derivative With Diverse Contact Rates, S. S. Sumaiya Banu, T. Gunasekar, S. Manikandan, Kamalendra Kumar, M. Suba
Applications and Applied Mathematics: An International Journal (AAM)
In the modern age, tuberculosis remains a pressing global health concern. Our study introduces and evaluates the SEITR pandemic TB transmission model, dividing the population into five compartments to explore distinct characteristics relevant to our investigation. Additionally, we delve into the application of fractional calculus. Through the Laplace transform method, we derive series solutions for all compartments, ensuring their existence and uniqueness. We also investigate the reproduction number of the tuberculosis epidemic model, examining how varying contact rates impact disease spread. We apply the predictor-corrector method for the Caputo-Fabrizio fractional derivative to verify the accuracy of our approach. This accurately …
Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response, Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro
Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response, Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro
Mathematical Modelling and Numerical Simulation with Applications
In this paper, the complexity of the dynamic behavior of the interaction between prey and predator is studied. The predator-prey relationship involves Allee effects and Monod-Haldane functional response. The constructed model has been shown to have validity in several respects, including the existence and uniqueness of the solution, as well as its non-negativity and boundedness. Three equilibrium points, namely trivial, axial, and coexistence points, are found, including their global dynamics using the Lyapunov function together with the LaSalle's invariance principle. The effect of the predation conversion rate causes changes in the dynamic behavior of predators and prey, which is characterized …
Synergistic Modeling Of Hydrogel Gelation Via Time-Delay Dynamics And Machine Learning Algorithms, Mine Babaoglu, Dipesh ., Pankaj Kumar, Jagjit Singh Dhatterwal, Mansoor Alsulami
Synergistic Modeling Of Hydrogel Gelation Via Time-Delay Dynamics And Machine Learning Algorithms, Mine Babaoglu, Dipesh ., Pankaj Kumar, Jagjit Singh Dhatterwal, Mansoor Alsulami
Mathematical Modelling and Numerical Simulation with Applications
This paper presents an integrated framework in which delay differential equation (DDE) modeling and machine learning (ML) approaches are coupled to study hydrogel formation kinetics, with emphasis on delayed crosslinker addition. Conventional mechanistic models disclose many physical and kinetic complexities of reacting mixtures; they seldom depict the nonlinear and time-evolving complexities inherent in developing polymer networks. To address this, a mathematical model is developed that examines how the insertion of crosslinkers affects system stability and equilibrium. Analytical and numerical results show that delays nearing critical levels cause bifurcation behavior with substantial implications on gelation kinetics. Sophisticated machine learning systems, including …
Fuzzy Logic-Based Decision Support System For Adoption Of Industry 4.0 Predictive Maintenance By Manufacturing Industries, Fred E. Peter
Fuzzy Logic-Based Decision Support System For Adoption Of Industry 4.0 Predictive Maintenance By Manufacturing Industries, Fred E. Peter
Tanzania Journal of Engineering and Technology (TJET)
In the context of Industry 4.0, predictive maintenance enhances operational efficiency by optimizing processes, minimizing downtime, and improving cost-effectiveness. However, implementing predictive maintenance requires a systematic approach due to its complexity. This study collected expert input from 15 food and beverage manufacturing industries located in Dar es Salaam, Tanzania, using a purposive sampling technique. Six representatives were selected from each industry, and their opinions were analyzed using MATLAB 7.6 through a fuzzy logic inference system. The analysis focused on key factors influencing Industry 4.0 technology adoption for predictive maintenance, including adoption intention (strategic decision, equipment data, perceived benefit) and perceived …
Assessment Of Maintenance Performance Level Of Selected Hydropower Plants In Tanzania, Mahamudu H. Mtebwa
Assessment Of Maintenance Performance Level Of Selected Hydropower Plants In Tanzania, Mahamudu H. Mtebwa
Tanzania Journal of Engineering and Technology (TJET)
Despite significant progress in increasing electricity access to over 78%, electricity reliability in Tanzania remains a concern, with frequent power outages reported. Maintenance issues in hydropower plants have been identified as a critical factor contributing to this problem. However, the specific maintenance performance levels have not been fully assessed. This study conducts a comprehensive evaluation of the maintenance performance of four key hydropower plants: Kidatu (204 MW), Kihansi (180 MW), Mtera (80 MW), and New Pangani Falls (68 MW). Data collected from staff surveys and maintenance records between 2018 and 2022 were used in the study. Although staff demonstrated a …
Coarse-Graining Spiking Reservoirs: Reducing Reservoir Size While Preserving Critical Dynamics, Tucker X. Mastin, Christof Teuscher
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 …