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Statistical Analysis Methods Applied To Early Outpatient Covid-19 Treatment Case Series Data, Eleftherios Gkioulekas, Peter A. Mccullough, Vladimir Zelenko

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

When confronted with a public health emergency, significant innovative treatment protocols can sometimes be discovered by medical doctors at the front lines based on repurposed medications. We propose a statistical framework for analyzing the case series of patients treated with such new protocols, that enables a comparison with our prior knowledge of expected outcomes, in the absence of treatment. The goal of the proposed methodology is not to provide a precise measurement of treatment efficacy, but to establish the existence of treatment efficacy, in order to facilitate the binary decision of whether the treatment protocol should be adopted on an …

Optimal Time-Dependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling The Spread Of Covid-19 Over Varied Contact Networks, Ryan L. Solorzano

Master's Theses

When attempting to mitigate the spread of an epidemic without the use of a vaccine, many measures may be made to dampen the spread of the disease such as physically distancing and wearing masks. The implementation of an effective test and quarantine strategy on a population has the potential to make a large impact on the spread of the disease as well. Testing and quarantining strategies become difficult when a portion of the population are asymptomatic spreaders of the disease. Additionally, a study has shown that randomly testing a portion of a population for asymptomatic individuals makes a small impact …

Using A Hybrid Agent-Based And Equation Based Model To Test School Closure Policies During A Measles Outbreak, Elizabeth Hunter, John D. Kelleher

Articles

Background

In order to be prepared for an infectious disease outbreak it is important to know what interventions will or will not have an impact on reducing the outbreak. While some interventions might have a greater effect in mitigating an outbreak, others might only have a minor effect but all interventions will have a cost in implementation. Estimating the effectiveness of an intervention can be done using computational modelling. In particular, comparing the results of model runs with an intervention in place to control runs where no interventions were used can help to determine what interventions will have the greatest …

A Hybrid Agent-Based And Equation Based Model For The Spread Of Infectious Diseases, Elizabeth Hunter, Brian Mac Namee, John D. Kelleher

Articles

Both agent-based models and equation-based models can be used to model the spread of an infectious disease. Equation-based models have been shown to capture the overall dynamics of a disease outbreak while agent-based models are able to capture heterogeneous characteristics of agents that drive the spread of an outbreak. However, agent-based models are computationally intensive. To capture the advantages of both the equation-based and agent-based models, we create a hybrid model where the disease component of the hybrid model switches between agent-based and equation-based. The switch is determined using the number of agents infected. We first test the model at …

On The Dynamics And Structure Of Multiple Strain Epidemic Models And Genotype Networks, Blake Joseph Mitchell Williams

Graduate College Dissertations and Theses

Mathematical disease modeling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modeling community to focus on the complexity of other factors such as contact structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics.

This body of work first explores the role of strain-transcending immunity in mathematical disease models, …

Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga

Olusegun Michael Otunuga

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to …

Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga

Mathematics Faculty Research

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to …

9th Annual Postdoctoral Science Symposium, University Of Texas Md Anderson Cancer Center Postdoctoral Association

Annual Postdoctoral Science Symposium Abstracts

The mission of the Annual Postdoctoral Science Symposium (APSS) is to provide a platform for talented postdoctoral fellows throughout the Texas Medical Center to present their work to a wider audience. The MD Anderson Postdoctoral Association convened its inaugural Annual Postdoctoral Science Symposium (APSS) on August 4, 2011.

The APSS provides a professional venue for postdoctoral scientists to develop, clarify, and refine their research as a result of formal reviews and critiques of faculty and other postdoctoral scientists. Additionally, attendees discuss current research on a broad range of subjects while promoting academic interactions and enrichment and developing new collaborations.

Rigorous Analysis Of An Edge-Based Network Disease Model, Sabrina Mai

Honors Undergraduate Theses

Edge-based network disease models, in comparison to classic compartmental epidemiological models, better capture social factors affecting disease spread such as contact duration and social heterogeneity. We reason that there should exist infinitely many equilibria rather than only an endemic equilibrium and a disease-free equilibrium for the edge-based network disease model commonly used in the literature, as there do not exist any changes in demographic in the model. We modify the commonly used network model by relaxing some assumed conditions and factor in a dependency on initial conditions. We find that this modification still accounts for realistic dynamics of disease spread …

Indicators For Early Assessment Of Palliative Care In Lung Cancer Patients: A Population Study Using Linked Health Data, Maria Kelly, Katie M. O'Brien, Michael Lucey, Kerri Clough-Gorr, Ailish Hannigan

Department of Mathematics Publications

Analysing linked, routinely collected data may be useful to identify characteristics of patients with suspected lung cancer who could benefit from early assessment for palliative care. The aim of this study was to compare characteristics of newly diagnosed lung cancer patients dying within 30 days of diagnosis (short term survivors) with those surviving more than 30 days. To identify indicators for early palliative care assessment we distinguished between characteristics available at diagnosis (age, gender, smoking status, marital status, comorbid disease, admission type, tumour stage and histology) from those available post diagnosis. A second aim was to examine the association between …

Analysis Of A Vector-Borne Diseases Model With A Two-Lag Delay Differential Equation, Y. Qaddura, Nsoki Mavinga

Mathematics & Statistics Faculty Works

We are concerned with the stability analysis of equilibrium solutions for a two-lag delay differential equation which models the spread of vector-borne diseases, where the lags are incubation periods in humans and vectors. We show that there are some values of transmission and recovery rates for which the disease dies out and others for which the disease spreads into an endemic. The proofs of the main stability results are based on the linearization method and the analysis of roots of transcendental equations. We then simulate numerical solutions using MATLAB. We observe that the solution could possess chaotic and sometimes unbounded …

Some Contributions To The Analysis Of Dual-Record System For Estimating Human Population Size., Kiranmoy Chatterjee Dr.

Doctoral Theses

Dual-record System (DRS) The problem of population size estimation is a very important administrative and statistical concern which includes a vast area of application in the fields of epidemiology, demography and official statistics. Federal agencies are generally interested to know the actual size (say, N ) of a specified population or any vital event that occurred in a specified area within a given time span. Census or civil registration system often fails to extract the true size of the population. The degree of inaccuracy depends on the actual size of the population, its diversity and of course, on the quality …

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …

A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson

Mathematics and Applied Mathematics Publications

We develop a host–vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species as well as host stage-structure (juvenile and adult stages), allowing for both species-specific and stage-specific biting rates of vectors on hosts. We use this ordinary differential equation model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates on species and/or life stages. Our analysis shows that increased exposure of juvenile hosts generally results in larger outbreaks of WNV infectious vectors when compared to differential host species exposure. We also find that …

Epidemiological, Clinical And Genetic Aspects Of Adult Onset Isolated Focal Dystonia In Ireland, L. Williams, E. Mcgovern, O. Kimmich, A. Molloy, I. Beiser, John Butler, F. Molloy, P. Logan, D.G. Healy, T. Lynch, R. Walsh, L. Cassidy, P. Moriarty, H. Moore, T. Mcswiney, C. Walsh, S. O'Riordan, M. Hutchinson

Articles

Background: Adult onset idiopathic isolated focal dystonia presents with a number of phenotypes. Reported prevalence rates vary considerably; well-characterized cohorts are important to our understanding of this disorder.

Aim: To perform a nationwide epidemiological study of adult onset idiopathic isolated focal dystonia in the Republic of Ireland.

Methods: Patients with adult onset idiopathic isolated focal dystonia were recruited from multiple sources. Diagnosis was based on assessment by a neurologist with an expertise in movement disorders. When consent was obtained, a number of clinical features including family history were assessed.

Results: On the prevalence date there were 592 individuals in Ireland …

Optimal Control Analysis Of Ebola Disease With Control Strategies Of Quarantine And Vaccination, Muhammad Dure Ahmad, Muhammad Usman, Adnan Khan, Mudassar Imran

Mathematics Faculty Publications

The 2014 Ebola epidemic is the largest in history, affecting multiple countries in West Africa. Some isolated cases were also observed in other regions of the world.

Inference On Time-To-Event Distribution From Retrospective Data With Imperfect Recall., Sedigheh Salehabadi Dr.

Doctoral Theses

Time-to-event data arises from measurements of time till the occurrence of an event of interest. Such data are common in the fields of biology, epidemiology, pub- lic health, medical research, economics and industry. The event of interest can be the death of a human being (Klein and Moeschberger, 2003), failure of a machine (Zhiguo et al., 2007), onset of menarche in adolescent and young adult females (Bergsten-Brucefors, 1976; Chumlea et al., 2003; Mirzaei, Sengupta and Das, 2015), onset (or relapse) of a disease (Klein and Moeschberger, 2003), dental develop- ment (Demirjian, Goldstien and Tanner, 1973; Eveleth and Tanner, 1990), breast …

Modeling Mortality Rates For Leukemia Between Men And Women In The United States, Blessed Quansah

UNLV Theses, Dissertations, Professional Papers, and Capstones

Leukemia related deaths increased dramatically over the last forty years. Leukemia is a malignant disease or cancer of the bone marrow and blood. It is characterized by the uncontrolled accumulation of blood cells. Leukemia is divided into two categories: myelogenous or lymphocytic, each of which can be acute or chronic. The terms, myelogenous or lymphocytic denote the cell type involved.

In this thesis, the proposed modeling techniques are applied to leukemia deaths data from the Surveillance Epidemiology and End Results (SEER). In particular, annual deaths data from 1969 to 2007 are used in the data analysis, which includes three major …

Modeling Transmission Dynamics Of Tuberculosis Including Various Latent Periods, Tracy Atkins

Electronic Theses and Dissertations

The systems of equations created by Blower et al. (1995) and Jia et al. (2007) designed to model the dynamics of Tuberculosis are solved using the computer software SIMULINK. The results are first employed to examine the intrinsic transmission dynamics of the disease through two models developed by Blower et al. (1995). The "simple transmission model" was used primarily to give insight to the behavior of the susceptible, latent, and infectious groups of individuals. Then, we consider a more detailed transmission model which includes several additional factors. This model captures the dynamics of not only the susceptible, latent and infectious …

The Effect Of The Hiv/Aids Epidemic On Africa's Truck Drivers, Christopher Kribs, Melanie Lee, Christine Roman, Shari Wiley, Carlos M. Hernandez-Suarez

Mathematics Faculty Publications

The AIDS epidemic is having a growing impact on the transport sector of the economy of sub-Saharan Africa, where long-distance truck drivers are at an increased risk of infection due to their frequent contacts with com- mercial sex workers. The spread of AIDS in the transport industry is especially signi¯cant to the economy, as truck drivers are largely responsible for trans- porting crops and supplies needed for daily subsistence. In this paper we analyze these e®ects via two models, one employing a switch and the other a Verhulst saturation function, to describe the rate at which new drivers are recruited …

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Yi Li

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Mathematics and Statistics Faculty Publications

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …

Genetic Epidemilogical Analysis Of Complex Disorders., Swapan Nath Dr.

Doctoral Theses

The present study can be broadly classified in the area of genetic epidemiology, which is conventionally defined as a science that deals with the aetiology, distribution, and control of disease in groups of relatives and with inherited causes of disease in populations (Morton 1982, 1993). One of the major goals of genetic epidemiology is the study of the nature and extent of clustering of a disease in families and in defined ethnic groups. The study of a disorder within the genetic epidemiological framework is performed by testing :(1) whether the disorder clusters in families?(2) whether observed familiarity is caused by …

Biometrical Genetics Of Insecticide Resistance:A Quantal Response Character., N Singh Dr.

Doctoral Theses

Geneses of the Froblems1.1.1 Resistence -A poblem in the fields of publio hosl th, agriculture, and endmel husbandry Discovery of the synthetic insecticides of residual toxcicity and their availability for civilian use after the World Mar I had presented a bright proapeot of freedom from insect bome diseases, Lindted fleld trials of chlorinated hydrocarbon insecticides in the sphere of ublic heal th had resulted in decline of the veotor/post pepulations by 'erdsia! and oonsaquentay the incidonce of vector borne diseases recorded drameatic falls. Inspired by such good results different combries and World Heoalth Organi zntion (WED) embarked upon the adventuro …