|Jordan Angel and Sam Peters||Game Theory Analysis of Vaccination Coverage with Epidemic Modeling|
|Chris Brewer and Jessica Holt Lunsford||Prevalence of Infection in Seasonally Forced Compartmental Models|
|Sharon Cameron||Prisoner's Dilemma Implementation on Watts-Strogatz Networks and Real Networks|
|Wandi Ding||Optimal Control Applied to Native-Invasive Species Competition via a PDE Model|
|Randall Hayes||Variation, Selection, Inheritance: A Public Outreach Podcast by the National Science Foundation’s BEACON Center for the Study of Evolution in Action|
|Nicole Holt||Quality of Life and BMI changes among Overweight Children of Southern Appalachia: A survey of PLAN (Parent-Led Activity and Nutrition for Healthy Living) Participants.|
|Tracy L. Holt||Racial Disparity in Albuminura and its Association with Hypertension Prevalence|
|Anuj Mubayi||Transmission Dynamics of Kala-azar in the Indian State of Bihar|
|Abhishek Pandey||Parameter Estimation and Model Selection for Dengue Transmission|
|Sam Peters||Game Theory and Evolutionary Dynamic|
|Sydney Philipps, Dan Rossi and Rachel Von Arb||Mathematical Models of Infectious Diseases:
Two-Strain Infections in Metapopulations
|Byron Roland and Caleb Shimberg||Analysis of Influenza-Like Illness Outbreaks at ETSU|
|Schehrazad Selmane||Optimal Isolation Control Strategy for a Tuberculosis Model|
|Caleb Shimberg||Parameter Selection for Ordinary Least Square Estimation of Contact Processes: Revisiting the Dissemination of Scientific Innovation|
|David Torres-Nunez||Dynamic Bayesian Models for Projecting Cancer Incidence in Puerto Rico.|
|Mandi Traud||Ant-idemics!: Modeling Disease Spread on Cumulative & Time-Ordered Ant Networks|
|Katia Vogt Geisse and Yiqiang Zheng||Potential repercussions of antiviral treatment for pandemic influenza using a seasonally forced SIR Model|
|Katia Vogt Geisse and Qing Han||The Impact of School Closures on Pandemic Influenza|
Acknowledgment: Many thanks to the Honors College of ETSU for the facilitation of the poster boards!
Chris Brewer and Jessica Holt Lunsford, Abstract:
Seasonal Infection modeling is used to describe the behavior of infection during various seasonal cycles within a fixed population. We use compartmental differential equations to achieve an understanding of the behavior of each aspect of infection and transmission that is assigned to each equation. We carry out with graphical data based upon calculated sensitivity equations that are compared over time for each of the parameters involved in the model.
Sharon Cameron, Abstract:
Wandi Ding, Abstract:
We consider an optimal control problem of a system of parabolic partial differential equations modeling the competition between an invasive and a native species. The motivating example is cottonwood-salt cedar competition, where the effect of disturbance in the system (such as flooding) is taken to be a control variable. Flooding being detrimental at low and high levels, and advantageous at medium levels led us to consider the quadratic growth function of the control. The objective is to maximize the native species and minimize the invasive species while minimizing the cost of implementing the control. A new existence result for an optimal control with these quadratic growth functions is given. Numerical examples are given to illustrate the results. Our findings will provide suggestions to the natural resource managers for controlling the invasive species.
Randall Hayes, Abstract:
Variation, Selection, Inheritance (VSI) is a 15-minute weekly podcast on evolution, broadly defined as any systems that display variation, heredity, and selection. These three abstract principles are embodied in different ways in biological, cultural, and technological systems because of the differing constraints under which those systems operate. For instance, biological information is generally not contagious at the level of the single organism (although there are many exceptions among microorganisms). Cultural practices such as languages, religions, and the use of mathematical models are contagious. These differences often obscure common evolutionary principles. This podcast explores the interplay between the common principles and the system-specific constraints.
A podcast is a recorded program in audio or video format. Rather than being broadcast on radio, it is delivered automatically to the listener’s computer or mobile device by free subscription through the Internet, through such services as Apple Computer’s iTunes or Google’s Feedfetcher. VSI’s content consists of interviews with scientists and teachers, evolution book reviews, evolutionary analyses of popular culture, and answering listener e-mails. Interviews focus on evolution, but also cover more personal “How I became a scientist” stories in order to increase the human dimension of science. There are currently ten episodes of VSI available, with more in production. Listeners can subscribe at the VSI website, http://variationselectioninheritance.podbean.com.
Nicole Holt, Abstract:
Childhood obesity has become an important public health concern, especially in rural areas. The prevalence of childhood obesity in Southern Appalachia is among the highest in the United States. Overweight children have increased risk of serious health problems along with psychosocial problems. Sixty seven overweight/obese children 5-11 years old and their parents were recruited from four primary care clinics in Southern Appalachia to participate in a primary care clinic based child obesity study. Part of this study was to measure the child’s BMI at baseline and at three month follow up, along with the parent report of the pediatric quality of life inventory.
Tracy L. Holt, Abstract:
Anuj Mubayi, Abstract:
“Kala‐azar” (or Indian Visceral Leishmaniasis) is a vector‐borne infectious disease affecting poorest communities around the world. Bihar, a state in India, has one of the highest prevalence and mortality reported levels of Kala‐azar. Yet, the magnitude of the problem is difficult to assess because private health providers, who are not required to report them to the state health institution, handle most cases. We compute estimates of Kala‐ azar's reproduction numbers, an indirect measure of disease prevalence, and levels of underreporting for the 21 most affected districts of Bihar. The average reproduction number (number of secondary cases generated per infective) estimates for Bihar range from 1.3 (2003) to 2.1 (2005). The mean values of reproduction number for some districts are lower than one, however, high movements of individuals between districts are maintaining the infection. Model estimates show that the proportion of underreported cases declined from an average of about 88% in 2003 to about 73% in 2005. However, 8 districts in 2003 and 5 districts in 2005 had more than 90% levels of underreporting. The analysis on underreporting adjusted incidence rates shows that reported data misidentify four of the eight (2003) and three of the nine (2005) districts classified as high‐risk. In fact, seven (2003) and five (2005) of the most affected Kala‐azar districts had been classified as low‐risk when only reported incidence data were used.
Abhishek Pandey, Abstract:
The study of dengue dynamics at the population scale have significantly contributed to the understanding of dengue transmission. Most studies have used point estimates of parameter values derived from clinical and laboratory experiments: in particular, data on population-level parameters such as transmission or susceptibility are extremely limited due to inability to feasibly conduct experiments of infection in people and instead must be estimated from indirect population-level data. We suggest a Bayesian approach which uses Monte Carlo Markov Chain (MCMC) simulation to find estimates for the unknown parameters of a generic dengue mathematical model we formulated based on previous dengue models. Prior knowledge is combined with data on hospital visits to perform the statistical inference on the unknown parameters. Our model allows for the inclusion of different hypotheses about dengue epidemiology and we explore the consistency of clinical data with the epidemiological hypothesis by determining goodness of fit of the model to the data for each combination of hypothesis. We use Akaike Information Criterion and Bayes Information Criterion on the results from the Bayesian MCMC on our dengue model and select a model that most parsimoniously agrees with the data.
Sydney Philipps, Dan Rossi and Rachel Von Arb, Abstract:
Viruses and bacteria responsible for infectious diseases often mutate and are carried between geographical regions. We consider a mathematical model which begins to account for these factors. We assume two disjoint populations that only occasionally comingle, and two strains of a disease present in these populations. Of interest are the equations describing the dynamics of this system, the conditions under which epidemics will occur, and the long term behavior of the system under various initial conditions. We find general conditions under which a state of disease-free equilibrium is stable; we examine the sensitivity of our system to changes in modeling parameters; and we find evidence that two disease strains of unequal strength may coexist in a two population system.
Sam Peters, Abstract:
Basic game theory and genetic concepts are introduced and then synthesized in order to understand biological interactions in nature. Concepts such as fitness landscape and genetic sequence space are also examined and synthesized into the game theoretical framework. These models are extrapolated and viewed in whole for the effect they have on the species development including the continuance of diversity as well as the development of quasispecies.
Byron Roland and Caleb Shimberg, Abstract:
During the course of seven months, data was collected from the student health clinic located on East Tennessee State University campus. The clinic reported cases of influenza-like illnesses from certain patients by each nurse in the facility. A model of this influenza-like illness was created using a basic single outbreak SIR model. The differential equations defining the SIR model were solved numerically using a built-in MATLAB function called ode45 (based off an explicit Runge-Kutta(4,5) integration method). In this system of equations a fourth was created to report the incidence rate of the influenza like illness. This incidence rate is what we are going to fit to our data in order to determine transmission rates, reproductive rates, and recovery rates. In this there are two models, one with constant parameters and another with a time-dependent transmission rate. In the second model, we used another MATLAB function called Pchip (Piecewise Cubic Hermite Interpolating Polynomial) to interpolate the values of transmission rate over the time of the data. This interpolation allows us to vary the number of interpolating values of transmission and to explore subintervals for major shifts.
Schehrazad Selmane, Abstract:
Isolation, quarantine, disinfection, inoculation, and education have been the five important preventive control measures used to control an epidemic. Isolation, which is aimed at restricting the spread to susceptibles by restricting the movements of infectious cases, tops the list. In order to minimize the transmission of the disease and to break the transmission chain of the Mycobacterium tuberculosis, we consider an optimal control strategy associated with isolation of infectious individuals who spread the disease. The existence of an optimal control for an objective functional that takes into account both the number of infectious individuals and the cost of isolation strategy, the characterization of the optimal control, and the uniqueness of the optimality system are proved. The optimality system is solved numerically using the Forward-Backward Sweep method. The numerical results showed that isolation strategy will reduce the number of latently infected individuals.
Caleb Shimberg, Abstract:
There has recently been great interest in modeling the spread of ideas. It has been found that epidemiological models can be applied to the spread of ideas through a population, modeling them in much the same way as the spread of disease. Applying a subset selection algorithm based on the sensitivity matrix, we will calculate the reliability of optimal reduced parameter vectors for which estimation is to be sought. It should be noted that this algorithm requires prior knowledge of a nominal data set of values for all parameters and constant variances, in observations. We will also further analyze the sensitivity matrices for the reduced parameter vectors in order to compare the magnitude of change in the number of people in a population who adopt an idea due to relatively equal changes in each of the parameters. In this way we will assess the influence, over time, of several different factors on the dissemination of a scientific idea.
David Torres-Nunez, Abstract:
Projections of cancer incidence and mortality provide a valuable indication of the current and future situation of the cancer in Puerto Rico. These are invaluable inputs for planning and decision making, and assist in the efficient allocation of resources to meet the future needs for the prevention, detection, and treatment of cancer. We estimate the present and predict the future (2014) of incidence for the top cancer tumor types in Puerto Rico (PR), by gender, age group and primary cancer site, to design public policy. Incidence data from Puerto Rico Central Cancer Registry were obtained for the years 1985 to 2004. The dynamic autoregressive models used in modern epidemiology are function of age-period-cohort (APC). Robust priors were fitted using Bayesian methods. We use model selection using the Deviance Information Criteria (DIC) to compare APC model with Age-period (AP), Age-cohort (AC) and Period-cohort (PC) models. The model produces point estimations as well as probability intervals for 2009 and 2014 by gender and five (5) year age bands. We analyzed the fifteen (15) most important tumors types, including colon, lung and bronchus, breast in situ and malignant, and prostate among others. We introduce a novel robust and stable prior the autoregressive variance, the scaled beta prior of the second kind (Beta2 prior). We found that this leads to a stable convergence of the model at the Markov Chain Monte Carlo (MCMC) implementation. We also produce statistical tools to check the goodness of fit of the selected models.
Mandi Traud, Abstract:
Communication and interaction are conduits for disease spread and are frequent in large populations of social organisms. The total interactions over time of a group of individuals look very different from the interactions of that same group at a specific point in time, and it is these differences in relation to disease spread that this study focuses on. This preliminary study looks at small colonies of two different species of ants in multi-nest structures (each colony in their own structure) and the differences in disease progression through these structures. We compare how specific colonies of Formica subsericea and Camponotus chromaiodes travel between nests both taking into account the changing connections over time (time-ordered) and the total connections over the observation period (Cumulative) and how those differences affect disease spread for a particular set of transmission and recovery paramters.
Katia Vogt Geisse and Yiqiang Zheng, Abstract:
When there are limited resources, control
measures of an incipient influenza pandemic must be carefully
considered. Because there are several months needed before mass
producing vaccines to a new identified pandemic strain, antiviral
drugs are often considered the first line of defense in a pandemic
situation.Here we use an SIR disease model with seasonality (i.e.,
periodic transmission rate) to assess the efficacy of control
strategies via antiviral drug treatment during an outbreak of
pandemic influenza. We show that antiviral treatment can have a
detrimental impact on the final size of the pandemic in some
situations, which are independent of drug-resistance effects.
Antiviral treatment also has the potential to increase the size of
the major peak of the pandemic, and to cause it to occur earlier
than it would have if treatment were not used.Our studies suggest
that when a disease exhibits periodic patterns in transmission,
decisions of public health policy will be particularly important as
to how control measures such as drug treatment should be
Katia Vogt Geisse and Qing Han, Abstract:
When a new pandemic influenza strain has been identified, mass-production of vaccines can take several months, and antiviral drugs are expensive and usually in short supply. Social distancing measures, such as school closures, thus seem an attractive means to mitigate disease spread. However, different timing of school closures (i.e., start time and duration) can have different affects on the final size, peak time and peak size of the pandemic, and thus can sometimes produce surprising and undesirable results during a pandemic. Here we analyze hypothetical pandemics in various scenarios using a SIR model with age-dependent transmission rates to assess the efficacy of widespread school closures on mitigating pandemic influenza. We find that closure start date is closely related to the delay of the peak of the pandemic while closure duration is closely related to the reduction of the final size. Our studies also suggest that in different scenarios (i.e., with and without vaccinations and with different basic reproduction numbers), decisions of how school closures should be implemented have to be carefully considered.