Mentor: Dr. Nina H. Fefferman

Welcome to the webpage for my REU. My name is John Nelson Huffman. I was born in Hattiesburg, Mississippi. At the age of 2 my family moved to Tupelo, MS, and I grew up in that town. I am a rising senior at Hendrix College in Conway, Arkansas, majoring in Computer Science with a minor in Mathematics.

Biosurveillance involves determining when unusual patterns of disease arise in a population. In the past what constitutes an unusual disease pattern, e.g. epidemic or pre-epidemic conditions, has been defined statically by examining historical precedent. However, since many epidemics are the result of new diseases or diseases affecting novel populations, the historal data is often inadequate. When this is the case our ability to define, and therefore detect, these unusual patterns is diminished, putting the population at greater risk.

This summer I will be modeling self-organizing biosurveillance systems. Through my research I hope to develop and test new biologically inspired algorithms which will allow us to define unusual disease patterns dynamically rather than statically and lead to earlier, more accurate detections of epidemic or pre-epidemic conditions.

**Week 1:**

After arriving at Rutgers halfway through the week I participated in a day orientation where we met the staff at Dimacs and received some general explanations of the REU program, including the facilities available to us during our stay here. Later in the week, we attended seminars on finding cycles in graphs and how to give a good presentation.

**Week 2:**

During the second week I chose my project topic and prepared a presentation for my fellow REU students on what my research would entail. The powerpoint for this presentation can be found
here. As I work to develop new algorithms for biosurveillance, I will draw my inspiration from three potential biological systems: honey bee foraging, ant foraging, and bacteria quorum sensing. I will implement and test those algorithms by modeling a disease surveillance network as a dynamically connected graph.

**Week 3:**

During my third week I continued my exploration of the topic by reading papers on biosurveillance as well as literature about graphs in computer science, including their computer representation and modern developments of dynamic graph algorithms. I also began to construct my computational model using Java. I will first focus on the one dimensional analysis of disease incidence rates for single diseases. I will use national estimates of these rates and apply a Poisson distribution in order to generate test data sets for my model.

**Week 4:**

I continued to develop my computational model and research about my project. As I worked more on my model, it became apparent that before beginning to develop new algorithms for a dynamic network I would have to simplify my scope and first complete a computational model that emphasized distributed decision making. I also attended a talk on geometric regularity and the REU participants visited Telcordia Technologies to hear talks on their employees research.

**Week 5:**

After making some basic assumptions about my network and data set I was able to continue on the development of the model. While eventually I hope to implement a dynamically connected network, I will focus first on performing computations on a statically connected network. I was also made aware of SatScan (TM), a free piece of software designed to scan and analyze multidimensional data for anomalies.

**Week 6:**

My network model is finally starting to come along. Using an algorithm from Knuth, I was able to generate Poisson distributed numbers to simulate weekly disease incidences at each of the nodes in my network. Now that I am able to simulate endemic disease patterns, I will be trying to contruct anomalies, i.e. epidemics, in my disease data.

**Week 7:**

In order to simiulate epidemics, I utilized an SIR disease model. This model breaks a population into three groups, Susceptibles, Infecteds, and Recovereds, and provides differential equations for each of these populations that dictate how the members of the population transition between the groups. I first encoded this model into my program. Then, by beginning the infected curve at the point in time when I wanted an epidemic to begin, I was able to simiulate an epidemic by feeding the value of the curve, plus my orignial disease incidence rate, into my function to generate Poisson distributed numbers. This method provides a realisic data set because the Poisson distribution ensures some degree of stochasticity in the weekly incidence data, but allows those incidences to average out to a mean incidence rate characteristic of the disease being investigated. I then prepared a final presentation on my summer's research and delivered it to my fellow REU participants, my mentor, and other professors.

**Week 8:**

On Monday morning I left for the Czech Republic to take part in mathematical and theoretical computer science related seminars and workshops for two weeks at Charles University in Prague through an exchange program with DIMATIA. After various flight delays, cancelations, and rebooking, we eventually made it to Prague. During our first week there, we attended lectures on various topic in discete mathematics, most of which involved graph theory in some capacity, and worked on problems given to us by the professors there.

**Week 9:**

During our second week in Prague, DIMATIA's annual Mid-summer Combinatorial Workshop began. This workshop was attended by various members of the discrete mathematics community from numerous countries different home institutions. The workshop centered around presentations given on the current research of the various attendees. While the topics of the talks varied with the interests of the speakers, most of the talks centered around combinatorial and/or graph theortetical ideas. Our REU group would attend the workshop talks in the morning, then receive an REU specific lecture from one of the members of the Charles University faculty in the afternoons.

**Week 10:**

With the Mid-summer Combinatorial Workshop ending the previous Friday, our last week in Prague saw a return to our previous schedule of attending lectures given by Charles University faculty in the mornings, then working on problems during the afternoon. The program then ended on Wednesday.

Contact: huffmanjn@hendrix.edu