Management of Invasive Species using Optimal Control Theory

In my dissertation I will discuss the use of optimal control theory to determine management strategies for an invasive species. I focus on a Diaprepes Root Weevil, which is an invasive species having a substantial negative impact on citrus tree growth in regions such as Florida and California. At the larva stage of the life cycle Diaprepes Root Weevils cause destruction of citrus trees at the root level resulting in loss of citrus crops. This detrimental effect for farmers motivates research into how to minimize the economic loss due to the Diaprepes Root Weevil. For my work, I use optimal control theory to determine levels of pesticide or biological control to apply to the Diaprepes Root Weevil to reduce the economic loss. Advisers: Richard Rebarber and Brigitte Tenhumber

A mathematical model of contact tracing during the 2014-2016 west African ebola outbreak

The 2014-2016 West African outbreak of Ebola Virus Disease (EVD) was the largest and most deadly to date. Contact tracing, following up those who may have been infected through contact with an infected individual to prevent secondary spread, plays a vital role in controlling such outbreaks. Our aim in this work was to mechanistically represent the contact tracing process to illustrate potential areas of improvement in managing contact tracing efforts. We also explored the role contact tracing played in eventually ending the outbreak. We present a system of ordinary differential equations to model contact tracing in Sierra Leonne during the outbreak. Using data on cumulative cases and deaths we estimate most of the parameters in our model. We include the novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Our work highlights the importance of incorporatingchanging behavior into one’s model as needed when indicated by the data and reported trends. Our results show that a larger contact tracing program would have reduced the death toll of the outbreak. Counting the total number of people being traced and including changes in behavior in our model led to better understanding of disease management

Prediction and Optimal Scheduling of Advertisements in Linear Television

Advertising is a crucial component of marketing and an important way for companies to raise awareness of goods and services in the marketplace. Advertising campaigns are designed to convey a marketing image or message to an audience of potential consumers and television commercials can be an effective way of transmitting these messages to a large audience. In order to meet the requirements for a typical advertising order, television content providers must provide advertisers with a predetermined number of impressions in the target demographic. However, because the number of impressions for a given program is not known a priori and because there are a limited number of time slots available for commercials, scheduling advertisements efficiently can be a challenging computational problem. In this case study, we compare a variety of methods for estimating future viewership patterns in a target demographic from past data. We also present a method for using those predictions to generate an optimal advertising schedule that satisfies campaign requirements while maximizing advertising revenue

Prediction and Optimal Scheduling of Advertisements in Linear Television

Advertising is a crucial component of marketing and an important way for companies to raise awareness of goods and services in the marketplace. Advertising campaigns are designed to convey a marketing image or message to an audience of potential consumers and television commercials can be an effective way of transmitting these messages to a large audience. In order to meet the requirements for a typical advertising order, television content providers must provide advertisers with a predetermined number of impressions in the target demographic. However, because the number of impressions for a given program is not known a priori and because there are a limited number of time slots available for commercials, scheduling advertisements efficiently can be a challenging computational problem. In this case study, we compare a variety of methods for estimating future viewership patterns in a target demographic from past data. We also present a method for using those predictions to generate an optimal advertising schedule that satisfies campaign requirements while maximizing advertising revenue

Searching for Superspreaders: Identifying Epidemic Patterns Associated with Superspreading Events in Stochastic Models

The importance of host transmissibility in disease emergence has been demonstrated in historical and recent pandemics that involve infectious individuals, known as superspreaders, who are capable of transmitting the infection to a large number of susceptible individuals. To investigate the impact of superspreaders on epidemic dynamics, we formulate deterministic and stochastic models that incorporate differences in superspreaders versus nonsuperspreaders. In particular, continuous-time Markov chain models are used to investigate epidemic features associated with the presence of superspreaders in a population. We parameterize the models for two case studies, Middle East respiratory syndrome (MERS) and Ebola. Through mathematical analysis and numerical simulations, we find that the probability of outbreaks increases and time to outbreaks decreases as the prevalence of superspreaders increases in the population. In particular, as disease outbreaks occur more rapidly and more frequently when initiated by superspreaders, our results emphasize the need for expeditious public health interventions