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Invited Paper Session Abstracts - Current Research in Math Biology

Saturday, August 1, 1:00 p.m. - 3:50 p.m., Philadelphia Marriott Downtown, Grand Ballroom D

Mathematical biology investigates biological phenomena using mathematical techniques. This encourages collaborations between mathematicians and biologists, requiring mathematicians to learn relevant biology before applying mathematical techniques to the problem. Research in this area illustrates how biology and mathematics can work together to advance both fields.

In this session, we showcase current research in mathematical biology, with an undergraduate audience in mind. With a wide variety of biological applications and mathematical techniques that can be applied to investigate biological research questions, our session will demonstrate the breadth of this research area for undergraduates and other interested researchers.

Rebecca A. Everett, Haverford College
Nicholas A. Battista, The College of New Jersey

Integrating Disease and Ecosystem Ecology using Mathematical Models

1:00 p.m. - 1:20 p.m.
Rebecca Everett, Haverford College


An overlooked effect of ecosystem eutrophication is the potential to alter disease via changes in pathogen reproduction and transmission in primary producers that may feed back to alter net primary productivity and element recycling. Models in disease ecology rarely track organisms past death, yet death from infection can alter elemental recycling and nutrient supply to living hosts. We present a differential equation model that integrates key elements of disease and ecosystem ecology to track susceptible and infected hosts as well as nutrients. Using this model, we demonstrate that nutrient supply and recycling can interact with disease to alter predictions for both ecosystem and disease outcomes.


Social Organization and its Effects on Disease Spread

1:30 p.m. - 1:50 p.m.
Shelby Wilson, University of Maryland


Individuals living in social groups are susceptible to disease spread through their social networks. The networks structure, including group stability, clustering, and an individuals behavior and affiliation choice all have some impact on the effect of disease spread. Moreover, under certain scenarios, a social group may change its own structure to suppress the transmission of infectious disease. Evidence that social organization may protect populations from pathogens in certain circumstances prompts the question as to how social organization affects pathogenic spread on dynamic networks. We will introduce discrete-time dynamic social network model and discuss the effects of both pathogenic and parasitic epidemics. In each case, we highlight the bi-directional effects of social structure and infection dynamics.


Non-Exponentially Distributed Infection and Treatment Stages in a VectorBorne Disease Model

2:00 p.m. - 2:20 p.m.
Miranda Teboh Ewungkem, Lehigh University


In most epidemiological models, the common practice is to assume exponentially distributed residence times in disease stages. This assumption, which simplifies the model formulation and analysis, do not in some instances, allow for the accurate descriptions of the interactions between pathogen loads and time to reach a certain load size, and also the interaction between pathogen load size and drug levels within a human host. Here, we illustrate that through a vector-borne disease model in which arbitrarily distributed sojourn times for disease stages are considered.


Exploring the Predictive Abilities of a Mathematical Oncology Model

2:30 p.m. - 2:50 p.m.
Jana Gevertz, The College of New Jersey


Mathematical models of biological systems are often validated by fitting the model to the average of an often small experimental dataset. Here we ask the question of whether mathematical predictions for the average are actually applicable in samples that deviate from the average. We will explore this in the context of a mouse model of melanoma treated with two forms of immunotherapy: immune-modulating oncolytic viruses and dendritic cell injections. The talk will demonstrate how a mathematically optimal protocol for treating the average mouse can lack robustness, meaning the best for the average protocol can fail to be optimal (and in fact, can be far from optimal) in mice that differ from the average. We also show how mathematics can be used to identify an optimal treatment protocol that is robust to perturbations from the average. Time permitting, we will also explore how robustness influences the personalization of treatment protocols for individual mice.


Using Mutual Information to Select Optimal Data Collection Times for Tumor Model Calibration

3:00 p.m. - 3:20 p.m.
Allison Lewis, Lafayette College


With new advancements in technology, it is now possible to collect data for a variety of different metrics describing tumor growth including tumor volume, composition, and degree of vascularity, among others. However, taking measurements can be costly and invasive, limiting clinicians to a sparse collection schedule. As such, the determination of optimal times and metrics for which to collect data in order to best inform proper treatment protocols could be of great assistance to clinicians. We employ a Bayesian information-theoretic calibration protocol for experimental design in order to identify the optimal times at which to collect data for informing the patientspecific treatment parameters. Within this procedure, data collection times are chosen sequentially to maximize the reduction in parameter uncertainty with each added measurement, ensuring that a budget of n measurements results in maximum information gain about the parameter values.


A Comprehensive Approach Toward Reproductive Phenotype Discovery

3:30 p.m. - 3:50 p.m.
Erica Graham, Bryn Mawr College


A normally functioning menstrual cycle requires significant crosstalk between hormones originating in ovarian and brain tissues. Reproductive hormone dysregulation may cause abnormal function and sometimes infertility. The inherent complexity in this endocrine system is a challenge to identifying mechanisms of cycle disruption, particularly given the large number of unknown parameters in existing mathematical models. We develop a new endocrine model to limit model complexity and use simulated distributions of unknown parameters for model analysis. By employing Monte Carlo and statistical methods, we identify a collection of mechanisms that differentiate normal and abnormal phenotypes. We also discover an intermediate phenotype–displaying relatively normal hormone levels and cycle dynamics–that is grouped statistically with the irregular phenotype. Results provide insight into how clinical symptoms associated with ovulatory disruption may not be detected through hormone measurements alone.