Jacob Norton's Homepage

Research Interests

In general, I am interested in investigating infectious disease dynamics, theoretical biology, and computational methods in the social sciences. More specifically, I am interested in disease and population "invasion" and the effects of rarity, either natural or otherwise, on the dynamics of zoonotic diseases and population dynamics. I am also interested in individual-based (or agent based) modeling of seemingly intractable problems both in the biological and social science realms and uncertainty quantification in all types of modeling. More recently, I have also been more interested in using techniques from network theory to tackle some spatial aspects and small population issues of the same biological and social science problem. Finally, I am interested in human associated species and their evolution and spatial distribution.

More elucidating comments coming in the future.

SAMSI graduate fellow: Program on Mathematical and Statistical Ecology

SMASI Tipping Points working group First, feel free to read a blog post by Karna Gowda (Northwestern University) about our work in the tipping points working group at the Statistical and Applied Mathematical Sciences Institute (SAMSI) with Christopher Strickland, (University of North Carolina at Chapel Hill and SAMSI), Lou Gross (University of Tennessee Knoxville), Phil Dixon (Iowa State University), and Michael Just (NC State).

We explored the boundaries of applicability of the cross convergent mapping (CCM) method proposed by Sugihara et al. (2012). In particular, we explored how process and observational noise affects the method, and whether a space-for-time substitution could make the method applicable to originally thought of as too short time-series of as few as 10 data points with many spatial replicates.

Past REU summer (2013) project as graduate advisor

REU Students at SMB 2012 Working with Dr. Alun Lloyd (Mathematics) I advised four undergraduate students as we modeled the spread of illicit drugs, especially methamphetamine, through both urban and rural populations using techniques used to model the spread of infectious diseases. In particular, we used compartmental models to capture the basic spread of drug use and optimal control theory to assess effectiveness of control strategies. We also developed a multi-patch (also known as metapopulation or network model) to investigate the dynamics of the illict drug market in the state which has an abundance of data on methamphetamine use, Oklahoma.

Past REU summer (2012) project as graduate advisor

REU Students at SMB 2012 Picture taken at the poster session at the annual Society for Mathematical Biology conference in Knoxville, TN, July 2012.

Working under the direction of Dr. Mette Olufsen and Dr. Adam Mahdi I helped advise four undergraduate students on work relating to cardiovascular regulation. In particular, we worked to first recreate a model of baroreceptor behavior developed by Dr. Mahdi, and then expand it to include heart rate dynamics. This work is currently ongoing with the Virtual Rat Project.

Other research interests

Antimicrobial Resistance in Agriculture: NSF-GRFP Honorable Mention

The emergence of antimicrobial resistance in human pathogens presents a worldwide threat to public health. Specifically, agricultural antimicrobial use is of concern because antimicrobial drugs are often pre-emptively given to healthy animals, including swine, and it has been estimated that this represents as much as 70% of US antimicrobial usage. I proposed modeling antimicrobial resistance and subsequent crossover to human populations from swine farms using both stochastic models and differential equation models. Although some preparatory work was completed, without NSF funding, my work on this project quickly waned.

Understanding the dynamics of HIV/AIDS

With Dr. Georgiy Bobashev and others, we studied HIV discordant couples in order to predict seroconversion (going from, in this case, HIV negative to HIV positive). Discordant couples are couples where one member has HIV and the other does not and, in our case, they continue to have unprotected sex. This was primarily a statistical endeavor.

Spatially explicit model of Barley Yellow Dwarf Virus

Flow diagram of two strain model Disease spread on ring lattice

My REG experience during the summer of 2011 focused on modeling spatially explicit infectious disease dynamics of a plant disease, Barley yellow dwarf virus, by simulation of a contact process on a ring lattice. I worked with Dr. Kevin Gross (Statistics and Biology) and Dr. Alun Lloyd (Mathematics). Results were shared at the Graduate School Research Symposium, March 20, 2012, McKimmon Center, NCSU.

Rare host effects on host-affiliate dynamics

Though I am not actively pursuing this research currently, it is still of long-term interest. In biology, a host is an organism that harbors an affiliate such as a symbiont, commensal, or parasite. The increasing rarity of hosts makes rare host effects on host-affiliate dynamics a topic of growing biological interest. This project is an initial step to better understand the overall effect of rarity in host species and its effect on coextinction, the loss of a species due to the loss of another species, by investigating host-affiliate dynamics in food webs. We will use incidence matrices, matrices that characterize the relationship between two classes of species (here hosts and affiliates), and differential-equation models to investigate the dynamics of food webs that consist of one host, one generalist affiliate, and one specialist affiliate. Specifically, we will look at how both generalist and specialist affiliate populations decrease as a consequence of incrementally more rare host species. Research will also focus on the competitive interactions between the generalist and specialist affiliates. Competition is interesting to investigate here because of the unevenly distributed negative impact competition might have on the population of affiliates even before hosts become extinct. Finally, simulations will be run to understand possible outcomes for existing host-affiliate communities to help give guidance to possible conservation applications. In sum, this research will address the increasingly critical question of coextinction of affiliates due to rare host species by gaining insight into simple host-affiliate food webs.

Bird Migration and Invasive Species Spread

Another form of "invasion", though temporally cyclical and not related to infectious disease, is avian migration and species spread. Unfortunately, my interest in modeling avian movement began from a project in Dr. Gilliam's Population Ecology class, and I have done nothing since.

Last Update: Wednesday, March 09, 2016
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