Physical Sciences and Mathematics Commons^™

Stochastic Delay Differential Equations With Applications In Ecology And Epidemics, Hebatallah Jamil Alsakaji

Dissertations

Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and predictions in various areas of life sciences, such as population dynamics, epidemiology, immunology, physiology, and neural networks. The memory or time-delays, in these models, are related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period, and so on. In ordinary differential equations (ODEs), the unknown state and its derivatives are evaluated at the same time instant. In DDEs, however, the …

Efficient Time-Stepping Approaches For The Dispersive Shallow Water Equations, Linwan Feng

Dissertations

This dissertation focuses on developing efficient and stable (high order) time-stepping strategies for the dispersive shallow water equations (DSWE) with variable bathymetry. The DSWE extends the regular shallow water equations to include dispersive effects. Dispersion is physically important and can maintain the shape of a wave that would otherwise form a shock in the shallow water system.

In some cases, the DSWE may be simplified when the bathymetry length scales are small (or large) in relation to other length scales in the shallow water system. These simplified DSWE models, which are related to the full DSWEs, are also considered in …

On The Stability Of Some Non-Stationary Nonlinear Systems, Rustamjon V. Mullajonov, Shakhodathon N. Abdugapparova, Jumagul V. Mirzaahmedova

Scientific Bulletin. Physical and Mathematical Research

The objective of the theory of stability of motion is to establish signs that make it possible to judge whether the motion in question is stable or unstable. Since in reality perturbing factors always inevitably exist, it becomes clear that the problem of stability of movement assumes very important theoretical and practical significance.

Mathematical modeling of processes and phenomena in animate and inanimate nature always involves a certain classification of them in accordance with their complexity. Many processes and phenomena are modeled by large-scale systems (CMS), which consist of separate subsystems, united by communication functions. In many cases, CMS is …

On The Qualitative Analysis Of Volterra Iddes With Infinite Delay, Osman Tunç, Erdal Korkmaz, Özkan Atan

Applications and Applied Mathematics: An International Journal (AAM)

This investigation deals with a nonlinear Volterra integro-differential equation with infinite retardation (IDDE).We will prove three new results on the stability, uniformly stability (US) and square integrability (SI) of solutions of that IDDE. The proofs of theorems rely on the use of an appropriate Lyapunov-Krasovskii functional (LKF). By the outcomes of this paper, we generalize and obtain some former results in mathematical literature under weaker conditions.

Avia 201 Project 1 Windtunnel Lab Form Ver 1.20 20200323, Nihad E. Daidzic

Aviation Department Publications

To introduce aviation/aeronautics/aerospace students to wind tunnel(s) and methods used in experimental identification of various aerodynamic (and stability) coefficients of airfoils (2D), wings (3D) and scale models.

Discrete Evolutionary Population Models: A New Approach, K. Mokni, Saber Elaydi, M. Ch-Chaoui, A. Eladdadi

Mathematics Faculty Research

In this paper, we apply a new approach to a special class of discrete time evolution models and establish a solid mathematical foundation to analyse them. We propose new single and multi-species evolutionary competition models using the evolutionary game theory that require a more advanced mathematical theory to handle effectively. A key feature of this new approach is to consider the discrete models as non-autonomous difference equations. Using the powerful tools and results developed in our recent work [E. D'Aniello and S. Elaydi, The structure of ω-limit sets of asymptotically non-autonomous discrete dynamical systems, Discr. Contin. Dyn. Series B. …

Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu

Mathematics Faculty Research

We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external fluctuations in the transmission, treatment and recovery rates. We assume external fluctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By defining R_T,n and ℛ_T,n as the basic deterministic and stochastic reproduction …