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Despite having this website for years, not one of my blog posts have been related to my thesis work. (I have written about some of my gene drive research, but that article is over on the SIAM News website). Most of my Ph.D. has been spent studying gene drives, or genetic elements that bias their own inheritance in target populations . By target populations, I mean any pest species specific to some region. But then what is a pest species? Worner and Gevrey  define a pest species as
Saturday thunderstorms are a good excuse to update this website! I wrote this toy model one Saturday afternoon long ago, so I will take this Saturday afternoon to tell you about it. This particular project I presented at the most recent Triangle Area Graduate Mathematics Conference (TAGMaC) at Duke. The title of my talk was the same as this blog post.
It is difficult to think that my second year as a graduate student is almost at an end here at NC State. This milestone seems swept up with the turbulence of the present time -- a sentiment I feel is shared by many. Whenever I do enjoy a brief respite, I like to wander back to this website and post a (sometimes) short update, which always just ends up being me talking about something I find interesting.
Our winter break is over; gone are the northern woods of Maine, back to Raleigh to finish the second year of my Ph.D. I’m trading the snow in the north for the thunderstorms of the south.
In the game agar.io, you navigate a circular blob in an environment populated by nutrients and other players. Consuming either of these increases the mass of your blob. The object of the game is to consume enough to become the largest blob. Although simple, those who have played it can attest to its addictive qualities. How do agents following such a simple ruleset provide for such an entertaining experience? Moreover, how does such stimulating behavior emerge from a system with so few rules? Ever since I first played this game, I've thought about programming my own version. However, the strategic aspect was more appealing than the gameplay. How often should you play passive rather than aggressive? Is foraging for particles of food across the landscape more efficient than hunting other players?
Take a look at the butterflies in Figure 1. Upon a quick glance, one may be tempted to classify them as the same species. However, this couldn't be farther from the truth! They are actually two different species of butterfly that can be found together in southern regions of Asia. But why do they look so similar? Is this pure chance, or something more?
Classes ended a few weeks ago and I'm soaking up as much sun as possible. In place of tedious coursework, I'm now free to focus on my research, both personal and otherwise! This is a welcome respite, as these past two semesters have been difficult both because of the workload and lack of any contiguous breaks during the semesters (the regular breaks were broken up and peppered throughout the semester as
wellness days). However, next semester is already looking much better, as classes are said to be in person and some level of normalcy will resume. Let's hope that this decision is the correct one!
The eastern gray squirrel (Sciurus carolinensis) is a common sight in the backyards of homes from as far north as Ontario all the way down to parts of Florida. The habitat of the gray squirrel stretches from the eastern coasts of North America to as far inland as Texas. In North America, the role played by the gray squirrel is an essential one, as they assist in the dispersal of hardwood trees. This is done via the burial of "mast," or what one typically thinks about a squirrel spending their time munching on -- acorns and other nuts. In other parts of the world, however, it is considered an invasive pest. This is because establishment of the gray squirrel in Europe has displaced native species, most notably the red squirrel (S. vulgaris). Species displacement is only one of a series of issues related to gray squirrel invasion and spread in Europe. Gray squirrels will remove the bark from trees to gnaw at the softer underlying tissue. This obviously damages trees, making them more susceptible to disease, and can make forest regeneration difficult. This concern is most prevalent in Europe, where broadleaved species such as oak and beech are most affected . The gray squirrel was first introduced to England in the nineteenth century, where it would eventually spread to all of Great Britain, and it was introduced to Italy in the mid-twentieth century.
I was reminded the other day of an interesting concept I read about sometime ago, called the critical community size of an epidemic. The idea, first introduced by Bartlett , is that a community must be of a certain size in order for an epidemic to persist indefinitely (that is, the size required for an epidemic to become endemic). Bartlett first discussed this idea in the context of measles, in which he theorized the critical community size of measles is between 250,000-300,000 people. Any measles epidemic in a community with a population less than this would eventually "fadeout," or disappear. This is because the number of susceptibles in the population decline until eventually reaching an amount insufficient to allow for continued spread of the pathogen!
Sometime last year I was reading Parasite Rex by Carl Zimmer when I came across the following passage:
Parasites may not only mark good ecological health; they may actually be vital for it. When ranchers overgraze their cattle and sheep on fragile grasslands, they can tip the ecology of the region over into a desert. As far as ecologists can tell, this move is pretty much irreversible, because the desert shrubs reorganize the soil in such a way that grasses can't penetrate back in... Ranchers usually dope up their livestock with medicine to kill as many intestinal worms as they can, but the parasites might be able to keep the livestock in a careful balance with the grass they depend on.
I've finally taken the time to move my website over from Wordpress to a more fitting domain! For those who weren't aware, since the beginning of my undergraduate career (about 5 years ago, as I'm writing this) I posted to a website I made using Wordpress. At the time, I thought doing so would help motivate me to undertake more interesting projects and develop my communication skills as an aspiring biomathematician. What ended up happening was that I focused less on the blog side of things and emphasized the rate at which I churned out posts about my personal projects. Because of the amount of time it took to do this, and what little time I had between all of my responsibilities, the quality of the posts were... lackluster.
Some time ago as part of a course on agent-based modeling, we were tasked with developing and analyzing our own model as a final project. At the time of the class, there was a large outbreak of measles in Samoa, so I had wanted the project to somehow relate to measles. In the case of Samoa, the primary reason for the explosive growth of the outbreak was ascribed to the abysmally low levels of measles vaccination at the time. Coincidentally, the Samoan outbreak occurred alongside a strong resurgence of the disease in the United States, at one point potentially threatening its elimination status . These outbreaks, as well as outbreaks in the past, shared a common element of occurring in communities of unvaccinated individuals, most notably Orthodox Jewish communities. The issue of communities of unvaccinated individuals and their roles in promoting the spread of disease seemed an interesting approach to the wider problem of herd immunity, and so I eventually resolved on this as my project.
Suppose you’re an epidemiologist who recently came into possession of a time-machine. Following an outbreak of a mysterious disease in a small community of individuals, your job is to go back in time to do everything you can in order to curb the spread of the disease. The only information of the system you have is the (i) contact network of the community and (ii) the index case of the mysterious new disease. Your only allowed intervention is the quarantine of a single individual in the population. Of course, you could try to convince the people in the community that you are a time traveling epidemiologist, but they would very quickly dismiss you as a crackpot. Furthermore, you are not allowed to remove the index case, as clever as that may seem.
As part of a broader study of gene drives in controlling vector-borne diseases, I am specifically looking at how density-dependent dynamics in populations affect gene drive performance and subsequent disease control efforts.
A collaborative project with the goal of mathematically modeling the opioid epidemic at the state level and using the results to inform directions of control.
This paper is about the number 1. The number 2 is left for future work.
This paper is about the number 2. The number 3 is left for future work.
This paper is about the number 3. The number 4 is left for future work.
For this project, with the help of Prof. David Hiebeler at the University of Maine, we studied the behavior of a theoretical population of organisms with landscape-dependent fecundity and mortality (exactly which one was varied for different experiments). The poster I prepared for this conference is shown below.
I presented the research I did at the Mathematical and Theoretical Biology Institute at multiple venues, including at the institute itself, the 2018 annual SACNAS conference in San Antonio, TX, and at the 2018 NIMBIoS Undergraduate Research Conference in Knoxville, Tennessee.
I presented some of my personal research of a predator-prey system with parasitic infection at e-BEER in 2020. The poster I made is attached below. Originally the project started out as a fun side project in NetLogo, with the goal of illustrating existence between a predator (represented by sheep), prey (the grass of a pasture), and a parasite ( H. contortus). Eventually it grew to encompass a class project, and I was so interested in the results that I shared them at e-BEER.
I gave a talk virtually at TAGMaC 2020 about the research I did as an undergraduate mathematically modeling the opioid epidemic in Maine. Since then, the project has become more ambitious in studying a general model of the opioid epidemic (for any state) using Maine as a case study. This research was funded in large part by the Margaret Chase Smith Policy Center at the University of Maine.
I gave talks on my gene drive research (how genetic load is modulated by density-dependence) at SMB 2021, SIAM DS21, and as a poster presentation at the GGI 4th annual retreat (see below). A paper summarizing these results will be submitted in the coming months.
I gave a talk at MathFest as part of a contributed paper session on using modeling in differential equations courses. In this talk, I highlighted my own experience using these methods in my mentorship activities, as well as emphasizing the use of computational tools (e.g. NetLogo) to demonstrate important concepts.
Undergraduate course, University 1, Department, 2014
This is a description of a teaching experience. You can use markdown like any other post.
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.