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Ordinary Differential Equations and Applied Dynamics Commons™
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- Epidemiology (2)
- Bifurcation (1)
- Chemical chaotic reactor (1)
- Compartmental Model (1)
- Disease Modeling (1)
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- Equilibria (1)
- Hopf Bifurcation (1)
- Hopf normal form (1)
- Incidence rate (1)
- Linear analysis (1)
- Lyapunov function, limit cycle (1)
- Mathematical modeling (1)
- Method of multiple scales (1)
- Mosquito-borne disease (1)
- Nonlinear Schrödinger Equation, Integrable Systems, Inverse Scattering Transform, Solitons, Differential Equations, Random Nonlinear Waves (1)
- Ordinary differential equations (1)
- SIR model (1)
- Wolbachia (1)
Articles 1 - 5 of 5
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
A Mathematical Modeling Approach To Investigate The Impacts Of Post-Infection Mortality And Partial Immunity On Disease Endemicity, Brendan M. Shrader
A Mathematical Modeling Approach To Investigate The Impacts Of Post-Infection Mortality And Partial Immunity On Disease Endemicity, Brendan M. Shrader
Honors Undergraduate Theses
A number of infectious diseases cause post-infection conditions or complications, such as COVID- 19, Q fever, and Polio. These conditions result in recovered individuals having a higher mortality rate than susceptibles, and this can impact disease dynamics. An existing mass-action model in the literature that incorporated post-infection mortality was shown to have limit cycles, or persistent oscillations, in the infected population. To better understand what causes these limit cycles, we develop and analyze a new epidemiological model with standard incidence. We show standard results, including the existence, uniqueness, and stability of the disease-free and endemic equilibria, and we rule out …
The Inverse Scattering Transform For The Nonlinear Schrödinger Equation, Ivan Casas-Rocha
The Inverse Scattering Transform For The Nonlinear Schrödinger Equation, Ivan Casas-Rocha
Honors Undergraduate Theses
The Nonlinear Schrödinger (NLS) Equation, iψt + 1/2 ψxx ± |ψ|2ψ = 0, is a nonlinear partial differential equation which is used to model several physical phenomena including nonlinear effects inside optical fibers and the formation of rogue waves in shallow water. It is particu- larly difficult to study solutions to this equation due to the nonlinearity, and the nonlinearity leads to incredibly interesting solutions not found in linear PDEs such as solitons. In this thesis, we highlight two methods of obtaining solutions to the (NLS) equation: the Inverse Scattering Transform and the Dressing Method. Furthermore, …
Estimating Modeling Parameters For Covid-19 Spread On Campus, Aviel S. Crigger
Estimating Modeling Parameters For Covid-19 Spread On Campus, Aviel S. Crigger
Honors Undergraduate Theses
Understanding the true burden of community transmission of communicable diseases like COVID-19 is crucial for effective public health response. Clinical cases, while important, only represent a fraction of the actual disease prevalence within a population. In this thesis, we investigate methods to estimate parameters that link clinical cases to the true disease prevalence using a modified compartmental model known as SICR (Susceptible, Infected, Cases, Recovered). We employ Bayesian inference and ensemble Markov chain Monte Carlo (MCMC) simulations to analyze clinical case data provided by the University of Central Florida Health Center from 2020 to 2022. Our goal is to estimate …
Mathematical Models Of Mosquito Populations, Hanna Reed
Mathematical Models Of Mosquito Populations, Hanna Reed
Honors Undergraduate Theses
The intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquito-borne diseases, such as dengue. We develop another ODE model to investigate the invasion of Wolbachia in a mosquito population. In a biologically feasible situation, we determine three coexisting …
Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona
Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona
Honors Undergraduate Theses
Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis of …