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Ordinary Differential Equations and Applied Dynamics Commons™
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Articles 1 - 9 of 9
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Stochastic Universal Differential Equations For Epidemiological Modeling: Uncertainty Quantification In Disease Transmission Dynamics, Alice Menaya Armah-Bonney
Stochastic Universal Differential Equations For Epidemiological Modeling: Uncertainty Quantification In Disease Transmission Dynamics, Alice Menaya Armah-Bonney
Electronic Theses and Dissertations
Epidemic forecasting requires not only predictions of expected case counts, but also quantification of uncertainty, although existing surrogate modeling frameworks for agent-based models remain fundamentally deterministic. In this thesis a Stochastic Universal Differential Equation framework is presented that extends the deterministic Universal Differential Equation approach by incorporating a learnable stochastic diffusion term, enabling calibrated probabilistic forecasts while preserving the mechanistic interpretability and computational efficiency of the deterministic baseline. In doing so, a two-phase training algorithm is introduced to ensure stable convergence and the framework is validated against the ensemble output from ExaEpi, an exascale agent-based model of a COVID-19 outbreak …
Studies Of Pathways To T2d And Interventions Through A Dynamical System Model., Rafiqul Islam
Studies Of Pathways To T2d And Interventions Through A Dynamical System Model., Rafiqul Islam
Electronic Theses and Dissertations
Existing mathematical models investigating the progression of type 2 diabetes (T2D) over time primarily focus on glucose, insulin, β-cell mass, and other related factors, while often omitting fatty acids (FA) as an explicit variable—despite FA being a major energy source for the body. There exists a complex network of dynamical interactions among glucose, insulin, FA, and β-cell mass. To gain deeper insights into the metabolic dynamics and pathophysiology of T2D, it is essential to incorporate FA into such models. In this study, we extend the classic Topp’s GIβ model by explicitly incorporating FA and exploring its interactions with glucose, insulin, …
Effects Of A Protection Zone In A Reaction-Diffusion Model With Shifting Bounded Habitat And Allee Effect., Davis Henderson
Effects Of A Protection Zone In A Reaction-Diffusion Model With Shifting Bounded Habitat And Allee Effect., Davis Henderson
Electronic Theses and Dissertations
We consider a reaction-diffusion equation that models a population in a shifting bounded habitat with a protection zone and the Allee effect. We assume that the population growth function exhibits the strong Allee effect and has a positive integral within the protection zone (indicating population persistence) and a negative integral in the surrounding patches (indicating population decay). We prove that the existence of steady-state solutions to this system depends on the length of the protection zone. It is demonstrated that there exists some value H* such that, for a protection zone of size H*, there exists a solution and, for …
A New Sir Model With Mobility., Ciana Applegate
A New Sir Model With Mobility., Ciana Applegate
Electronic Theses and Dissertations
In this paper, a mobility-based SIR model is built to understand the spread of the pandemic. A traditional SIR model used in epidemiology describes the transition of particles among states, such as susceptible, infected, and recovered states. However, the traditional model has no movement of particles. There are many variations of SIR models when it comes to the factor of mobility, the majority of studies use mobility intensity or population density as a measure of mobility. In this paper, a new dynamical SIR model, including the spatial motion of three-type particles, is constructed and the long-time behavior of the first …
A Novel Mathematical Model Of The Trojan Y-Chromosome Strategy With Optimal Control, Christopher Turner
A Novel Mathematical Model Of The Trojan Y-Chromosome Strategy With Optimal Control, Christopher Turner
Electronic Theses and Dissertations
Invasive species are a prevalent problem all over the world. Controlling and eradicating an invasive species is an even more diffcult problem. The Trojan Y Chromosome (TYC) eradication strategy is one control method. This method alters the female to male sex ratio by introducing sex reversed males called supermales. These sex reversed males can only produce male progeny. Mathematical models of this strategy have shown that a population can be driven to extinction with a continuous supply of these sex reversed males. There are many different mathematical models of this strategy, but most have serious flaws, such as negative solutions …
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Electronic Theses and Dissertations
Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …
Application Of Symplectic Integration On A Dynamical System, William Frazier
Application Of Symplectic Integration On A Dynamical System, William Frazier
Electronic Theses and Dissertations
Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic …
Spreading Speeds Along Shifting Resource Gradients In Reaction-Diffusion Models And Lattice Differential Equations., Jin Shang
Electronic Theses and Dissertations
A reaction-diffusion model and a lattice differential equation are introduced to describe the persistence and spread of a species along a shifting habitat gradient. The species is assumed to grow everywhere in space and its growth rate is assumed to be monotone and positive along the habitat region. We show that the persistence and spreading dynamics of a species are dependent on the speed of the shifting edge of the favorable habitat, c, as well as c*(∞) and c*(−∞), which are formulated in terms of the dispersal kernel and species growth rates in both directions. When …
Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker
Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker
Electronic Theses and Dissertations
Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …