Ordinary Differential Equations and Applied Dynamics Commons^™

Data-Driven Exploration Of Coarse-Grained Equations: Harnessing Machine Learning, Elham Kianiharchegani

Electronic Thesis and Dissertation Repository

In scientific research, understanding and modeling physical systems often involves working with complex equations called Partial Differential Equations (PDEs). These equations are essential for describing the relationships between variables and their derivatives, allowing us to analyze a wide range of phenomena, from fluid dynamics to quantum mechanics. Traditionally, the discovery of PDEs relied on mathematical derivations and expert knowledge. However, the advent of data-driven approaches and machine learning (ML) techniques has transformed this process. By harnessing ML techniques and data analysis methods, data-driven approaches have revolutionized the task of uncovering complex equations that describe physical systems. The primary goal in …

Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid

Western Research Forum

General systems of differential equations don't have restrictions on the number or type of equations. For example, they can be over or under-determined, and also contain algebraic constraints (e.g. algebraic equations such as in Differential-Algebraic equations (DAE) and Partial differential algebraic equations (PDAE). Increasingly such general systems arise from mathematical modeling of engineering and science problems such as in multibody mechanics, electrical circuit design, optimal control, chemical kinetics and chemical control systems. In most applications, only real solutions are of interest, rather than complex-valued solutions. Much progress has been made in exact differential elimination methods, which enable characterization of all …

On Honey Bee Colony Dynamics And Disease Transmission, Matthew I. Betti

Electronic Thesis and Dissertation Repository

The work herein falls under the umbrella of mathematical modeling of disease transmission. The majority of this document focuses on the extent to which infection undermines the strength of a honey bee colony. These studies extend from simple mass-action ordinary differential equations models, to continuous age-structured partial differential equation models and finally a detailed agent-based model which accounts for vector transmission of infection between bees as well as a host of other influences and stressors on honey bee colony dynamics. These models offer a series of predictions relevant to the fate of honey bee colonies in the presence of disease …

Study Of Virus Dynamics By Mathematical Models, Xiulan Lai

Electronic Thesis and Dissertation Repository

This thesis studies virus dynamics within host by mathematical models, and topics discussed include viral release strategies, viral spreading mechanism, and interaction of virus with the immune system.

Firstly, we propose a delay differential equation model with distributed delay to investigate the evolutionary competition between budding and lytic viral release strategies. We find that when antibody is not established, the dynamics of competition depends on the respective basic reproduction numbers of the two viruses. If the basic reproductive ratio of budding virus is greater than that of lytic virus and one, budding virus can survive. When antibody is established for …

Modeling Leafhopper Populations And Their Role In Transmitting Plant Diseases., Ji Ruan

Electronic Thesis and Dissertation Repository

This M.Sc. thesis focuses on the interactions between crops and leafhoppers.

Firstly, a general delay differential equations system is proposed, based on the infection age structure, to investigate disease dynamics when disease latencies are considered. To further the understanding on the subject, a specific model is then introduced. The basic reproduction numbers $\cR_0$ and $\cR_1$ are identified and their threshold properties are discussed. When $\cR_0 < 1$, the insect-free equilibrium is globally asymptotically stable. When $\cR_0 > 1$ and $\cR_1 < 1$, the disease-free equilibrium exists and is locally asymptotically stable. When $\cR_1>1$, the disease will persist.

Secondly, we derive another general delay differential equations system to examine how different life stages of leafhoppers affect crops. The basic reproduction numbers $\cR_0$ is determined: when …