How Prey Defense Patterns Predator-Prey Distributions

In ecology, predator and prey species share a common interest in survival. However, this common interest places these species at odds with each other. Predators need to consume prey for their survival. Prey, on the other hand, do not survive if they are consumed. To meet their needs, predators engage in foraging or prey-taxis behaviors whereby they seek areas of high prey density. For prey there are numerous defense strategies to engage including aposematic mechanisms to advertise they are not worth the predator’s while, attacking the predator through chemical or community defense mechanisms, and alarm calls to seek assistance from predators at` higher trophic levels of the food chain; to name a few. In this talk, we will focus on competition between prey-taxis and chemical defense; placing a particular emphasis on conditions leading to spatial segregation between predator and prey, or as it is known in mathematics, pattern formation. We will also discuss other prey defense mechanisms such as the burglar alarm hypothesis and the potential impact of prey defense mechanisms on prey species in resource competition

Co-Adventurers in Discovery: Collaborative Research Between Undergraduate Students and Faculty

There are many opportunities available beyond the classroom for undergraduate students to engage in cutting-edge scholarship. Some of the opportunities include study abroad, internships, and independent study. We strongly suggest that students experience such programs. Independent study courses can serve not only to sharpen the student’s engagement skills with the open-ended questions of current research, but also to enhance his or her own relationship with faculty. In this article we share the experiences of a biology student and a mathematics faculty member coming together as co-adventurers learning from each other about the mechanisms and mathematics involved in cardiac arrhythmia through collaborative mathematical modeling research. Biology and mathematics have a long history of an explosive synergy that enriches and extends both fields (Cohen, 2004) (Reed, 2004), and this synergy led us to the fruitful journey reported here. As there is no end in sight for opportunities to engage in such multi-disciplinary student-faculty collaborative research, we encourage everyone to take advantage of such opportunities

Co-Adventurers in Discovery: Collaborative Research Between Undergraduate Students and Faculty

There are many opportunities available beyond the classroom for undergraduate students to engage in cutting-edge scholarship. Some of the opportunities include study abroad, internships, and independent study. We strongly suggest that students experience such programs. Independent study courses can serve not only to sharpen the student’s engagement skills with the open-ended questions of current research, but also to enhance his or her own relationship with faculty. In this article we share the experiences of a biology student and a mathematics faculty member coming together as co-adventurers learning from each other about the mechanisms and mathematics involved in cardiac arrhythmia through collaborative mathematical modeling research. Biology and mathematics have a long history of an explosive synergy that enriches and extends both fields (Cohen, 2004) (Reed, 2004), and this synergy led us to the fruitful journey reported here. As there is no end in sight for opportunities to engage in such multi-disciplinary student-faculty collaborative research, we encourage everyone to take advantage of such opportunities

Spectral Properties of a Sequence of Matrices Connected to Each Other via Schur Complement and Arising in a Compartmental Model

We consider a sequence of real matrices An which is characterized by the rule that An−1 is the Schur complement in An of the (1,1) entry of An, namely −en, where en is a positive real number. This sequence is closely related to linear compartmental ordinary differential equations. We study the spectrum of An. In particular,we show that An has a unique positive eigenvalue λn and {λn} is a decreasing convergent sequence. We also study the stability of An for small n using the Routh-Hurwitz criterion

Modeling and simulation of Caenorhabditis elegans chemotaxis in response to a dynamic engineered bacteria

Parasitic helminthes remain important causative agents of human, plant and animal diseases. Helminthes seek out food sources and navigate toward potential hosts using olfaction of simple chemical cues in a process called chemoattraction. While several studies have examined how nematodes, including Caenorhabditis elegans, behave in response to a chemoattractant, how the characteristics of the chemoattractant affect worm behavior has yet to explored. In this manuscript, we develop a mathematical model to examine how characteristics of common chemoattractants affect movement and behavior in the model nematode C. elegans. Specifically, we model a scenario where a toxic, engineered bacteria designed to express a chemoattractant influences the behavior of a population of worms. Through the model we observe that, under static conditions, the diffusion rate of the chemoattractant is critical in influencing choice of C. elegans. Here, the higher diffusion rate, the more the worms are attracted to the chemoattractant. We then show that if the worms learn that the chemoattractant is associated with toxicity, choice index is counterintuitively more strongly reduced with increasing diffusion rate. Finally, our model predicts a tradeoff between pulse period and attractant strength when the chemoattractant is dynamically pulsed in the environment. Our results reveal unique tradeoffs that govern chemoattraction in worms and may have implications in designing novel strategies for preventing or treating infections with parasitic worms

Modeling of Humoral Immune Response to Repeated Influenza A Virus Infections

Seasonal infections by Influenza A virus (IAV) causes hundreds of thousands of deaths worldwide each year, with most individuals being infected multiple times throughout their lifetimes. The relative impact of the components of the host immune system in controlling the severity and duration of repeated challenges from an IAV infection remains unclear. In particular, the differential contribution of the humoral immune response in primary and secondary challenges from IAV are relatively little explored. We develop a parsimonious mathematical model of the humoral immune response to IAV infection with biologically meaningful and identifiable parameters. We show the relative sensitivity of the viral load and antibody response to dynamics of B cell proliferation and antibody production. We relate immunoglobin class switching to a CD4+ T-cell driven process for the formation of humoral memory. Results of this study help to illuminate the relative contribution of CD4+ T-cells, B-cells, and antibody in the control of IAV infection and formation of humoral memory