The seminar meets on Thursdays at 2:30 pm.
Our email listserv is called "math-bio-seminar"-- subscribe here to stay up to date on meetings.
If you would like to speak at the seminar, please contact Richard Rebarber at firstname.lastname@example.org
Spring 2021 Schedule
Thursday, January 28, 2021
- James Pierce, University of Wisconsin - La Crosse
Title: Mathematical Models and Mergansers: Controlling Swimmer’s Itch Outbreaks
Abstract: Swimmer’s itch is an emerging disease caused by flatworm parasites that typically use water birds as definitive hosts. When parasite larvae accidentally penetrate human skin, they initiate localized inflammation that leads to intense itching and discomfort. Concerns about this issue have been growing recently due to an apparent increase in the global occurrence of swimmer’s itch and its subsequent impacts on recreational activities and revenues. Past work has identified the common merganser as a key definitive host for these worms in the Midwest of the United States; several snail species serve as intermediate hosts. Although past attempts at controlling swimmer’s itch have targeted snails, a handful of efforts have concentrated on treating water birds with the anti-parasitic drug, Praziquantel. Here we will provide an overview of swimmer’s itch in the Midwest region and will introduce a mathematical model aimed at its control. Specifically, we will talk about the possibility of controlling swimmer itch by administering Praziquantel at both transient and resident lakes. Initial findings suggest that treating birds at a transient lake during the spring migration significantly lowers the likelihood of swimmer’s itch cases at the resident lake and was a more efficient control strategy than treating waterfowl at the resident lake itself. These results could be used by both state agencies such as the Department of Natural Resources and/or lake managers as a tool for optimizing treatment plans to best manage future outbreaks of swimmer’s itch.
Thursday, February 18, 2021
- Aminur Rahman, University of Washington
Title: Physics-based models of cancer drug response in solid tumors: towards computer-aided treatment strategies
Abstract: Over the past few decades, cancer related deaths have fallen significantly as noted by the National Cancer Institute. However, assessing cancer treatments is still predominantly a trial and error process. This approach may result in delays to administer the correct treatment, the use of more invasive procedures than necessary, or an increase in toxicity due to superfluous treatments. Although these procedures may end up saving the patient, the treatment may also have an adverse effect on their quality of life. Reliable mechanistic models of drug response can potentially be used to aid oncologists and doctors in deciding on an optimal treatment strategy for the patient. We develop a modeling framework for tumor ablation, and present coupled transport - population models of varying complexity. First, we present a radially symmetric drug diffusion and binary cell death model, which produces a theoretical dose for optimal efficacy to toxicity ratios. Further, we investigate inhomogeneous - anisotropic drug diffusion, and develop an algorithm to locate the optimal injection points. Importantly, the mechanistic models outperform data-driven models in statistical tests. We conclude by discussing some current and future work towards developing computer-aided treatment strategies.
Thursday, February 25, 2021
- Glenn Ledder, UNL
Title: A Model for the COVID-19 Pandemic with Limited Vaccination
Abstract: Now that vaccines for COVID-19 are available and distribution has begun, a critical question arises: To what extent do protective measures need to be maintained as more people are vaccinated? Addressing this question requires careful attention to the way vaccination is incorpo- rated into the model. We augment our SEAIHRD (Susceptible, Exposed, Asymptomatic, (symp- tomatic) Infectious, Hospitalized, Recovered, Deceased) model by breaking up the susceptible class into a standard (S)usceptible class and a (P)re-vaccinated class, with proportions determined by a vaccine acceptance parameter. Susceptible and pre-vaccinated individuals move to the Exposed through infection in the standard way. In addition, a vaccination process moves individuals directly out of the pre-vaccinated class at a rate that follows a Michaelis-Menten mechanism; that is, the rate is linear when the pre-vaccinated class is small but quickly saturates due to limitations in the distribution speed. Most individuals who leave the pre-vaccinated class move into the recovered class, but a small fraction move back to the standard susceptible class, representing the probability of failing to mount a proper immune response. We use the model to investigate the impact of reduced compliance with protective measures.
Thursday, March 4, 2021
- John DeLong, UNL
Title: Modeling the tangled bank: eco-evolutionary dynamics in multi-species, multi-trait, and non-equilibrium systems
Thursday, March 11, 2021
- Kurt E. Anderson, University of California Riverside
Title: Trophic Dynamics on Spatial Networks
Abstract: Connectivity among communities influences processes such as population persistence, genetic structure, and species diversity. While most research has focused on the magnitude of connectivity among communities, a growing body of work has demonstrated the importance of the patterns of connectivity. I will examine the stability properties of spatial food webs considering patterns in dispersal variation and spatial connectivity, asking how these connectivity patterns alter food web structure and dynamics. I will examine both analyses of local stability in a generalized food web modeling framework as well as simulations of full nonequilibrium dynamics.
Thursday, March 18, 2021
- Drew Tyre, UNL
Title: West Nile Virus prediction & decision making
Thursday, March 25, 2021
- Yu Jin, UNL
Title: The dynamics of a two host-two virus system in a chemostat environment
Abstract: The coevolution or coexistence of multiple viruses with multiple hosts has been an important issue in viral ecology. In this work, we study the mathematical properties of the solutions of a chemostat (ODE) model for two host species and two virus species. By virtue of the global dynamics of its submodels and the theories of uniform persistence, we derive sufficient conditions for the coexistence of two hosts with two viruses and coexistence of two hosts with one virus, as well as occurrence of Hopf bifurcation. In this talk, I will present some proof details for the global dynamics of the model.
Thursday, April 15, 2021
- Yawen Guan, UNL
Title: Statistical Calibration of an Arctic Sea Ice Model
Abstract: Arctic sea ice plays an important role in the global climate. Sea ice models governed by physical equations have been used to simulate the state of the ice including characteristics such as ice thickness, concentration, and motion. More recent models also attempt to capture features such as fractures or leads in the ice. These simulated features can be partially misaligned or misshapen when compared to observational data, whether due to numerical approximation or incomplete physics. In order to make realistic forecasts and improve understanding of the underlying processes, it is necessary to calibrate the numerical model to field data. Traditional calibration methods based on generalized least-square metrics are flawed for linear features such as sea ice cracks. We develop a statistical emulation and calibration framework that accounts for feature misalignment and misshapenness, which involves optimally aligning model output with observed features using cutting edge image registration techniques.
Thursday, April 29, 2021
- Clay Cressler, UNL
Title: Multistability, immunity, and infection chronicity
Abstract: A striking feature of controlled infection experiments is the variability in infection outcome amongst individuals. Even when exposing genetically identical hosts to identical doses of genetically identical parasites, some hosts will clear the infection quickly and some will become chronically infected. Here, I investigate how positive feedback loops occurring within the immune response can generate multistability amongst equilibria representing qualitatively distinct infection outcomes. I show that small differences in the initial immune state (which are rarely, if ever, measured by experimentalists) can lead to opposing infection outcomes. I also show that variation in infection dose can alter infection outcome in ways that mirror experimental studies. Finally, I discuss how immunological feedbacks open up the possibility for parasite manipulation of immunity, manipulation that definitely occurs in nature.
Here are the talks we had before:
Fall 2020 Schedule
Thursday, September 3, 2020
- Richard Rebarber, UNL
Title: Harvesting Peregrine Falcon Populations: guaranteeing population growth under uncertainty
Abstract: Structure population models are increasingly used in decision making but typically have many parameters that are unknown or highly uncertain. We develop a method to combine a population projection matrix model with a matrix of arbitrary perturbations to identify the region of the parameter space that is consistent with the goal of maintaining population growth. We illustrate the advantages of the method using the recent decision of the US Fish and Wildlife Service to allow minimal harvesting of peregrine falcons after their removal from the Endangered Species List.
Thursday, September 10, 2020
- Huijing Du, UNL
Title: Modeling the Interconnected Cavernous Structure of Bacterial Fruiting Bodies
Abstract: The formation of spore-filled fruiting bodies by myxobacteria is a fascinating case of multicellular self-organization by bacteria. Sporulation within the nascent fruiting body requires signaling between moving cells in order that the rod-shaped self-propelled cells differentiate into spores at the appropriate time. A new technique using Infrared Optical Coherence Tomography (OCT) revealed previously unknown details of the internal structure of M. xanthus fruiting bodies consisting of interconnected pockets of relatively high and low spore density regions. Modeling and computer simulations were used to test a hypothesized mechanism that could produce high-density pockets of spores. The mechanism consists of self-propelled cells aligning with each other and signaling by end-to-end contact to coordinate the process of differentiation resulting in a pattern of clusters observed in the experiment. The computational simulations can provide new insight into the mechanisms that can give rise to the pattern formation seen in other biological systems such as dictyostelids, social amoeba known to form multicellular aggregates observed as slugs under starvation conditions.
Thursday, September 24, 2020
- Abbey Long, UNL
Title: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
Abstract: In the past year, disease transmission models have entered the mainstream with the COVID-19 pandemic. In this talk, we will discuss the construction and components of a general disease transmission model, along with in important parameter, R_0. R_0 is the basic reproductive rate, and is the number of people the typical infective will infect. If R_0 > 1, the disease will continue to spread, but if R_0 < 1, the disease will die out. We will then apply these concepts to two specific models, called the treatment model and staged progression model.
Thursday, October 8, 2020
- Molly Creagar, UNL
Title: Density-dependent vital rates and their population dynamic consequences
Abstract: We present research from the paper “Density-dependent vital rates and their population dynamic consequences”, by Neubert and Caswell. Stage-structured population models incorporate of vital rates, such as rates of survival, reproduction, and development. In this talk, we discuss a stage-structured population model with density dependence in the vital rates, resulting in a nonlinear system of two equations. After constructing both a linear and a nonlinear version of the model, we perform a bifurcation and stability analysis, identify the resulting equilibria, and discuss conclusions that stem from the analysis.
Thursday, October 15, 2020
- Souparno Ghosh, Statistics, UNL
Title: Integral Projection Models: Statistical specifications and multivariate extensions
Abstract: Population dynamics with regard to evolution of traits has typically been studied using matrix projection models (MPMs). The Integral Projection Model (IPM) is the continuous analog of MPMs. Fitting these models has so far been done only with individual-level transition data which are used to estimate the demographic functions. These models enable forward propagation to learn about population statistics, e.g., analysis associated with the long term population growth rate. Demographic models are simply fitted to individuals and plugged in to the population scale model. The transition equations specified at the scale of the IPM play no part in the estimation of the parameters. However, standard specification of these models does not reflect incomplete knowledge of the process. Furthermore, model adequacy is not properly ascertained and, perhaps most importantly, when individual level data are not available, these models are rendered ineffective. To remedy these problems we propose a model at population level and estimate the parameters at the same level. We generalize the model to handle misalignment of individuals and incorporate uncertainty in the specification of IPM. Subsequently, we describe a coherent model to incorporate covariates that vary across both space and time.
Thursday, October 22, 2020
- Eva Strawbridge, James Madison University
Title: Helices in Fluids and Applications to Modelling Bacterial Carpets
Abstract: There are many biologically relevant situations which involve long slender bodies (e.g. worms, flagella, bacterial bodies, etc.) where it is important to understand the dynamic interactions of the body and the low Reynolds number fluid in which it moves. In this presentation, I will be discussing applications of the method of regularized stokeslets to periodically moving bodies in fluids. These models have applications to the study of locomotion as well as fluid mixing.
Thursday, October 29, 2020
- Collin Victor, UNL
Title: Continuous Data Assimilation with Mobile Observers
Abstract: When simulating dynamical systems, such as the weather, one major issue that arises is the lack of complete knowledge of the initial state. Data assimilation is a class of schemes, that helps to resolve this issue, by incorporating incoming data into the equations, driving the simulation to the correct solution. Recently, a promising new data assimilation algorithm (the AOT algorithm) has been proposed by Azouani, Olson, and Titi, which uses a feedback control term to incorporate observations at the PDE level. This talk will be an introduction to data assimilation and the AOT algorithm, a brief look at some recent results, and a computational study of a modification to the AOT algorithm. Specifically, we look at using the AOT algorithm in the context of measurement devices which move in time, such as satellites or drones. We find that, in the context of the Allen Cahn equations, by moving the sampling points dynamically, we can greatly reduce the number of sampling points required, while achieving better accuracy. Additionally, we show preliminary results indicating similar improvements for the 2D Incompressible Navier-Stokes equations.
Thursday, November 12, 2020
- Yu Jin, UNL
Title: The dynamics of a zooplankton-fish system in aquatic habitats
Abstract: Diel vertical migration is a common movement pattern of zooplankton in marine and freshwater habitats. In this paper, we use a temporally periodic reaction-diffusion-advection system to describe the dynamics of zooplankton and fish in aquatic habitats. Zooplankton live in both the surface water and the deep water, while fish only live in the surface water. Zooplankton undertake diel vertical migration to avoid predation by fish during the day and to consume sufficient food in the surface water during the night. We establish the persistence theory for both species as well as the existence of a time-periodic positive solution to investigate how zooplankton manage to maintain a balance with their predators via vertical migration. Numerical simulations discover the effects of migration strategy, advection rates, domain boundary conditions, as well as spatially varying growth rates, on persistence of the system.
Thursday, January 30, 2020
- Lyndsie Wszola, UNL School of Biological Sciences
Title: Evolving regulations for a changing world
Abstract: It has become increasingly clear that harvest from fish and wildlife populations can induce ecological and evolutionary changes in population stage and size structure, especially in fisheries. Harvest-induced evolution tends to reduce fish age and size at maturity regardless of regulation because intensive fish harvest favors early reproduction even without intentional size selection. We built a stage-structured eco-evolutionary model of harvest-induced changes in size and stage structure to assess how size-specific harvest regulations affect population stability, extinction risk, and recovery potential under ecologically and evolutionarily-induced changes in population stage structure. Our approach incorporates emerging evolutionary theory with the wealth of available fisheries data to provide a framework for evaluating regulations in the context of a changing world.
Thursday, February 13, 2020
- Matt Reichenbach, UNL
Title: Asymptotic Convergence to a Stable Stage Distribution
Abstract: One of the consequences of the Perron-Frobenius theorem is that powers of a positive irreducible matrix (normalized by its spectral radius) converge to a projection onto the eigenspace of the leading eigenvector. In particular, this fact guarantees that population models with a Leslie matrix approach a stable stage distribution. In this talk, I will first go over the generalization of this result to integral projection models with a compact operator, and also my recent result that the result is true in the case of a non-compact operator..
Thursday, February 27, 2020
- Amanda Laubmeier, UNL
Thursday, March 19, 2020
- Aminur Rahman, Texas Tech Department of Statistics, UNL
Title: Physics-based models and simulations of cancer drug response in solid tumors
Abstract: Over the past few decades, cancer related deaths have fallen significantly as noted by the National Cancer Institute. However, assessing cancer treatments is still predominantly a trial and error process. This approach may result in delays to administer the correct treatment, the use of more invasive procedures than necessary, or an increase in toxicity due to superfluous treatments. Although these procedures may end up saving the patient, the treatment may also have an adverse effect on their quality of life. Reliable mechanistic models of drug response can potentially be used to aid oncologists and doctors in deciding on an optimal treatment strategy for the patient. We develop a modeling framework for tumor ablation, and present coupled transport - population models of varying complexity. First, we present a radially symmetric drug diffusion and binary cell death model, which produces a theoretical dose for optimal efficacy to toxicity ratios. Further, we investigate inhomogeneous - anisotropic drug diffusion, and develop an algorithm to locate the optimal injection points. Importantly, we show that this modeling framework has the potential to be employed in computer-aided treatment strategies.
Thursday, September 5
- Amanda Laubmeier, UNL
Title: Towards understanding factors influencing the benefit of diversity in predator communities for prey suppression
Thursday, September 12
- Glenn Ledder, UNL
Title: A discrete/continuous time consumer-resource model and it’s implications
Abstract: Most population models use either discrete time or continuous time. But what do we do in the case of a resource that grows continuously paired with a consumer that has a synchronized life history with annual birth pulses? Answer: We use a mixed time model consisting of differential equations on fixed time intervals and jump conditions. For analysis, it is better to think of it as a discrete model in which the continuous component is used to identify the discrete map. In this talk, I will show the simplest reasonable model for this scenario, and we will see that its dynamics can be even a little more complicated than a standard discrete model.
Thursday, September 19
- Richard Rebarber, UNL
Title: A discrete/continuous time Resource Competition Model and it’s implications
Abstract: Many ecological settings feature consumers that reproduce in annual birth pulses and feed on a resource that grows continuously, so that an appropriate model consists of a time-limited continuous model embedded in a discrete model. Last week Glenn Ledder discussed such a model with a single consumer species. This week I consider a similar model with two consumer species, with competition only in resource collection. For most parameter regimes corresponding to the stable and overcompensation cases for one consumer, the two consumers cannot coexist. In these cases, we show that the successful consumer is the one whose consumer-resource equilibrium point is at a lower level of the resource. We then consider a hypothetical situation where the two consumers have different timing of their birth pulses, and consider what happens when a stressor (say, a toxin) is introduced with it’s own release pulses; we show that under some circumstances, the stressor can change which consumer is successful. This is joint work with Amanda Laubmeir, Glenn Ledder, Terrence Pendleton and Jonathan Weisbrod.
Thursday, September 26
- Yu Jin, UNL
Title: We present a novel model that considers the longitudinal variation as introduced by the sinuosity of a meandering river where a main channel is laterally extended to point bars in bends. These regions offer different habitat conditions for aquatic populations and therefore may enhance population persistence. Our model is a nonstandard reaction– advection–diffusion model where the domain of definition consists of the real line (representing the main channel) with periodically added intervals (representing the point bars). We give an existence and uniqueness proof for solutions of the equations. We then study population persistence as the (in-) stability of the trivial solution and population spread as the minimal wave speed of traveling periodic waves. We conduct a sensitivity analysis to highlight the importance of each parameter on the model outcome. We find that sinuosity can enhance species persistence.
Thursday, October 3
- Matt Reichenbach, UNL
Thursday, November 7
- Amanda Laubmeier, UNL
Title: Integrating mathematical models and data to understand ecological processes
Abstract: Mathematical models for ecological populations can lead to an improved understanding of the factors driving population change. However, ecological data is equally informative in determining current and future population behaviors. The presentation will begin with a brief summary of my approach to studying ecological populations, which involves a balance of mathematical modelling, empirical data, and biological input. I will discuss model development for a particular project concerning interactions between an agricultural pest and its natural insect predators. Highlights of the project include designing experiments to test the model and using simulations to determine the qualities of an optimal predator community for pest suppression. As time allows, I will also discuss ongoing work in different ecological applications, including a theoretical project concerning competition between native and invasive trout species and a data-driven project concerning long-term monitoring of a perennial wildflower.
Thursday, November 21
- Drew Tyre, School of Natural Resources, UNL
Thursday, December 3
- Peter Wagner, Dept. of Earth and Atmospheric Sciences & School of Biological Sciences, UNL