Applied Mathematics Commons^™

Pain As A Predictor Of Depression Treatment Outcomes In Women With Childhood Sexual Abuse, Ellen L. Poleshuck, Nancy L. Talbot, Haiyan Su, Xin Tu, Linda Chaudron, Stephanie Gamble, Donna E. Giles

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Objectives: Childhood sexual abuse (CSA) increases risk for both depression and pain in women. Pain is associated with worse depression treatment response. The contribution of pain to depression treatment outcomes in women with histories of CSA is unknown. This study examined whether clinically significant pain would be associated with worse depression and functioning outcomes among women with CSA histories treated with interpersonal psychotherapy. Method: Participants were 66 women with major depression and CSA who presented to a community mental health center. An interpersonal psychotherapy protocol planned for 14 weekly sessions followed by 2 biweekly sessions. Patients were classified as experiencing …

Migration And Mixing Between Populations In Disease Models, David Burger

Theses, Dissertations and Culminating Projects

The goal of this thesis is to model the spread of disease between populations and find ways to prevent its continued epidemic. This thesis studies disease spread as a function of migration in epidemiological models. The models are constructed using the compartmental approach, and we compare discrete and continuous time approximations. In the discrete model, we will look at ways that induced migration can cause an epidemic case to turn into a dieout case. It will be shown that migration can only effect the size of an outbreak, but cannot create or destroy one. For the continuous cases, we will …

Patch Models And Applications On The Spread Of Avian Influenza, Kimberly Rude

Theses, Dissertations and Culminating Projects

The avian influenza virus (AIV) is an infectious disease that predominantly affects birds. Economic losses due to large-scale deaths of domestic poultry as a result of past outbreaks have been devastating. Additionally, there is major concern about the spread of the virus to humans. The virus has spread to humans in the past, but has not yet been known to spread beyond one human. Since influenza viruses are known to mutate easily, there is serious concern that the virus could mutate into a strain that can be transmitted easily to and among humans.

There has been much speculation that migratory …

When To Spray: A Time-Scale Calculus Approach To Controlling The Impact Of West Nile Virus, Diana Thomas, Marion Weedermann, Lora Billings, Joan Hoffacker, Robert Washington-Allen

Department of Mathematics Faculty Scholarship and Creative Works

West Nile Virus (WNV) made its initial appearance in the New York City (NYC) metropolitan area in 1999 and was implicated in cases of human encephalitis and the extensive mortality in crows (Corvus sp.) and other avian species. Mosquitoes were found to be the primary vectors and NYC’s current policy on control strategies involved an eradication program that depends on the synchronicity of the summer mosquito population’s increases with the occurrence of cases in humans. The purpose of this paper is to investigate whether this is the most effective control strategy because past mathematical models assumed discrete behavior that …

Confidence Intervals For A Common Mean With Missing Data With Applications In An Aids Study, Hua Liang, Haiyan Su, Guohua Zou

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In practical data analysis, nonresponse phenomenon frequently occurs. In this paper, we propose an empirical likelihood based confidence interval for a common mean by combining the imputed data, assuming that data are missing completely at random. Simulation studies show that such confidence intervals perform well, even when the missing proportion is high. Our method is applied to an analysis of a real data set from an AIDS clinic trial study.

Topological Dynamics Of Two-Piece Eventually Expanding Maps, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this work we show that two-piece eventually expanding maps have the same topological dynamics as two-piece expanding maps. A two-piece eventually expanding map possesses an invariant set that is either a topological attractor or can be perturbed to become one.

Existence Of Multiple-Stable Equilibria For A Multi-Drug-Resistant Model Of Mycobacterium Tuberculosis, Abba B. Gumel, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

The resurgence of multi-drug-resistant tuberculosis in some parts of Europe and North America calls for a mathematical study to assess the impact of the emergence and spread of such strain on the global effort to effectively control the burden of tuberculosis. This paper presents a deterministic compartmental model for the transmission dynamics of two strains of tuberculosis, a drug-sensitive (wild) one and a multi-drug-resistant strain. The model allows for the assessment of the treatment of people infected with the wild strain. The qualitative analysis of the model reveals the following. The model has a disease-free equilibrium, which is locally asymptotically …

Delay-Induced Instabilities In Self-Propelling Swarms, Eric Forgoston, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann [Phys. Rev. E 71, 051904 (2005)] has shown that a large enough noise intensity will cause a translating swarm of individuals to transition to a rotating swarm with a stationary center of mass. We show that with the addition of a time delay, the model possesses a transition that depends on the size of the coupling amplitude. This transition is independent of the initial swarm state (traveling or rotating) and is characterized by …

Mathematical Analysis Of The Transmission Dynamics Of Hiv/Tb Coinfection In The Presence Of Treatment, Oluwaseun Sharomi, Chandra N. Podder, Abba B. Gumel, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

This paper addresses the synergistic interaction between HIV and mycobacterium tuberculosis using a deterministic model, which incorporates many of the essential biological and epidemiological features of the two diseases. In the absence of TB infection, the model (IIIV-only model) is shown to have a globally asymptotically stable, disease-free equilibrium whenever the associated reproduction number is less than unity and has a unique endemic equilibrium whenever this number exceeds unity. On the other hand, the model with TB alone (TB-only model) undergoes the phenomenon of backward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated …

Application Of Chimera Grid To Modelling Cell Motion And Aggregation In A Narrow Tube, Bong Jae Chung, P. C. Johnson, A. S. Popel

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A computational scheme using the Chimera grid method is presented for simulation of three-dimensional motion and aggregation of two red blood cells (RBCs) in a narrow tube. The cells are modelled as rigid ellipsoidal particles; the computational scheme is applicable to deformable fluid-filled particles. Attractive energy between two RBCs is modelled by a depletion interaction theory and used for simulating aggregation of two cells. Through the simulation, we show that the Chimera grid method is applicable to the simulation of three-dimensional motion and aggregation of multiple RBCs in a microvessel and microvascular network.

Numerical And Asymptotical Study Of Three-Dimensional Wave Packets In A Compressible Boundary Layer, Eric Forgoston, Michael Viergutz, Anatoli Tumin

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initialvalue problem. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as Mode S and Mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectra are analyzed numerically for a hypersonic flow. A comprehensive study of the spectrum is performed, including Reynolds number, Mach number and temperature …

Dynamics Of A Two Serotype Disease With Antibody Dependent Enhancement, Amy Fiorillo

Theses, Dissertations and Culminating Projects

The dengue virus is a serious infectious disease that can be found in many regions of Southeast Asia. There exist four serotypes of the virus. Recovery from one serotype produces a natural immunity from that serotype. However, it also creates complexes with a second infection and will increase viral production. This process is know as antibody dependent enhancement (ADE). As a result, it is very difficult to vaccinate against the disease. An optimal vaccination would have to cover all four serotypes at once. To understand the dynamics of the disease, we will study a mathematical model for two coexisting serotypes …

Raves, Clubs And Ecstasy: The Impact Of Peer Pressure, Baojun Song, Melissa Castillo-Garsow, Karen R. Ríos-Soto, Marcin Mejran, Leilani Henso, Carlos Castillo-Chavez

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Ecstasy has gained popularity among young adults who frequent raves and nightclubs. The Drug Enforcement Administration reported a 500 percent increase in the use of ecstasy between 1993 and 1998. The number of ecstasy users kept growing until 2002, years after a national public education initiative against ecstasy use was launched. In this study, a system of differential equations is used to model the peer-driven dynamics of ecstasy use. It is found that backward bifurcations describe situations when sufficient peer pressure can cause an epidemic of ecstasy use. Furthermore, factors that have the greatest influence on ecstasy use as predicted …

Distributed Blowing And Suction For The Purpose Of Streak Control In A Boundary Layer Subjected To A Favorable Pressure Gradient, Eric Forgoston, Anatoli Tumin, David E. Ashpis

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

An analysis of the optimal control by blowing and suction in order to generate streamwise velocity streaks is presented. The problem is examined using an iterative process that employs the Parabolized Stability Equations for an incompressible fluid along with its adjoint equations. In particular, distributions of blowing and suction are computed for both the normal and tangential velocity perturbations for various choices of parameters.

Three-Dimensional Wave Packet In A Hypersonic Boundary Layer, Eric Forgoston, Anatoli Tumin

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A three-dimensional wave packet generated by a local disturbance in a hypersonic boundary layer flow is studied with the aid of the previously solved initial-value problem. The solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of discrete and continuous modes. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using previous analysis of the discrete and continuous spectrum, we numerically compute the inverse Fourier transform. The two-dimensional inverse Fourier transform is found for Mode …

Chaotic Desynchronization Of Multistrain Diseases, Ira Schwartz, Leah Shaw, Derek Cummings, Lora Billings, Marie Mccrary, Donald Burke

Department of Mathematics Faculty Scholarship and Creative Works

Multistrain diseases are diseases that consist of several strains, or serotypes. The serotypes may interact by antibody-dependent enhancement rADE, in which infection with a single serotype is asymptomatic, but infection with a second serotype leads to serious illness accompanied by greater infectivity. It has been observed from serotype data of dengue hemorrhagic fever that outbreaks of the four serotypes occur asynchronously. Both autonomous and seasonally driven outbreaks were studied in a model containing ADE. For sufficiently small ADE, the number of infectives of each serotype synchronizes, with outbreaks occurring in phase. When the ADE increases past a threshold, the system …

Disease Outbreaks In Coupled Populations : An Application To Measles Spread In Cameroon, Kirsten Maggie Viz

Theses, Dissertations and Culminating Projects

Many childhood diseases can be modeled mathematically using a system of differential equations that group the overall population into compartments. Much research has been done to understand and control the spread of these diseases within a single population and between coupled populations with constant parameters. In this thesis, we are concerned with how a disease is spread through and between coupled populations using models with time-varying parameters and asymmetric coupling.

Measles outbreaks in the West African country of Cameroon present a good example of disease spread with seasonality. By dividing Cameroon into two subpopulations and using parameters that reflect recent …

Controlling Wound Healing Through Debridement, M. A. Jones, Baojun Song, D. M. Thomas

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

The formation of slough (dead tissue) on a wound is widely accepted as an inhibitor to natural wound healing. In this article, a system of differential equations that models slough/wound interaction is developed. We prove a threshold theorem that provides conditions on the amount of slough to guarantee wound healing. As a state-dependent time scale, debridement (the periodic removal of slough) is used as a control. We show that closure of the wound can be reached in infinite time by debriding.