Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, 2019 George Mason University

#### Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, 2019 Virginia Commonwealth University

#### Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Seasonal Variation Of Nutrient Loading In A Stoichiometric Producer-Consumer System, 2019 Texas Tech University

#### Seasonal Variation Of Nutrient Loading In A Stoichiometric Producer-Consumer System, Lale Asik, Jackson Kulik, Kevin R. Long, Angela Peace

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Understanding The Role Of Macrophages In Lung Inflammation Through Mathematical Modeling, 2019 Virginia Commonwealth University

#### Understanding The Role Of Macrophages In Lung Inflammation Through Mathematical Modeling, Sarah B. Minucci

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Parameter Identification For A Stochastic Seirs Epidemic Model: Case Study Influenza, 2019 Marshall University

#### Parameter Identification For A Stochastic Seirs Epidemic Model: Case Study Influenza, Olusegun M. Otunuga, Anna Mummert

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Quantifying The Contribution Of Environmental Pathways To The Transmission Of Clostridium Difficile, 2019 University of Tennessee, Knoxville

#### Quantifying The Contribution Of Environmental Pathways To The Transmission Of Clostridium Difficile, Lindsey R. Fox, Cara Sulyok, Judy Day, Cristina Lanzas, Suzanne Lenhart

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Pbpk Model Of Low-Concentration Vitamin D Supplementation In The Absence Of Sunlight, 2019 Southern New Hampshire University

#### A Pbpk Model Of Low-Concentration Vitamin D Supplementation In The Absence Of Sunlight, Megan Sawyer

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Optimal Spraying Strategies For Controlling Re-Infestation By Chagas Disease Vectors, 2019 Virginia Commonwealth University

#### Optimal Spraying Strategies For Controlling Re-Infestation By Chagas Disease Vectors, Bismark Oduro, Winfried Just, Mario Grijalva

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Study Of Pair Formation Disease Models With A Two Phase Infection, 2019 Howard University

#### A Study Of Pair Formation Disease Models With A Two Phase Infection, Berlinda Rosa Batista

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Β Cell Network Dysfunction In Pancreatic Islets By Silencing Hub Cells, 2019 University of Maryland - Baltimore County

#### Β Cell Network Dysfunction In Pancreatic Islets By Silencing Hub Cells, Janita Patwardhan, Bradford E. Peercy

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Pharmacokinetic Model Of Lead Absorption And Calcium Competitive Dynamics, 2019 State University of New York at New Paltz

#### A Pharmacokinetic Model Of Lead Absorption And Calcium Competitive Dynamics, Anca R. Radulescu

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

On The Complexity Of Computing Galois Groups Of Differential Equations, 2019 The Graduate Center, City University of New York

#### On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun

*All Dissertations, Theses, and Capstone Projects*

The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions (integrals, exponentials and algebraic functions) and understand the algebraic relations among the solutions.

Hrushovski first proposed an algorithm for computing the differential ...

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, 2019 University of Lynchburg

#### Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

*Undergraduate Theses and Capstone Projects*

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic ...

Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, 2019 Western Kentucky University

#### Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, Nigar Karimli

*Masters Theses & Specialist Projects*

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that ...

A Stage-Structured Oyster Population Model For Reef Restoration, 2019 William & Mary

#### A Stage-Structured Oyster Population Model For Reef Restoration, Rachel Wilson

*Undergraduate Honors Theses*

Oysters have experienced drastic declines in their population because of environmental factors and harvesting pressures, making them a focal species for restoration eﬀorts [1, 22]. Oyster shell has become a limited resource and alternative substrates are not as suitable for larval recruitment and shell accumulation [1, 2, 7]. For this reason, restoration eﬀorts are restricted, despite the attempts in the private and public sector. To increase the eﬀectiveness of restoration, the dynamics of oyster reef systems must be further analyzed and understood. This thesis proposes a stage-structured ordinary diﬀerential equation model to investigate the dynamics of deterministic and stochastic oyster ...

Condensed Forms For Linear Port-Hamiltonian Descriptor Systems, 2019 Technische Universität Berlin

#### Condensed Forms For Linear Port-Hamiltonian Descriptor Systems, Lena Scholz

*Electronic Journal of Linear Algebra*

Motivated by the structure which arises in the port-Hamiltonian formulation of constraint dynamical systems, structure preserving condensed forms for skew-adjoint differential-algebraic equations (DAEs) are derived. Moreover, structure preserving condensed forms under constant rank assumptions for linear port-Hamiltonian differential-algebraic equations are developed. These condensed forms allow for the further analysis of the properties of port-Hamiltonian DAEs and to study, e.g., existence and uniqueness of solutions or to determine the index. It can be shown that under certain conditions for regular port-Hamiltonian DAEs the strangeness index is bounded by $\mu\leq1$.

Modelling Non-Linear Functional Responses In Competitive Biological Systems., 2019 Western University

#### Modelling Non-Linear Functional Responses In Competitive Biological Systems., Nickolas Goncharenko

*Western Research Forum*

One of the most versatile and well understood models in mathematical biology is the Competitive Lotka Volterra (CLV) model, which describes the behaviour of any number of exclusively competitive species (that is each species competes directly with every other species). Despite it's success in describing many phenomenon in biology, chemistry and physics the CLV model cannot describe any non-linear environmental effects (including resource limitation and immune response of a host due to infection). The reason for this is the theory monotone dynamical systems, which was codeveloped with the CLV model, does not apply when this non-linear effect is introduced ...

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, 2019 Frostburg State University

#### Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

*CODEE Journal*

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem ...

Sir Models: Differential Equations That Support The Common Good, 2019 Dickinson College

#### Sir Models: Differential Equations That Support The Common Good, Lorelei Koss

*CODEE Journal*

This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns. We present models that have been used to study sustainable agriculture, drug and alcohol use, the spread of violent ideologies on the internet, criminal activity, and health issues such as bulimia and obesity.

Equilibrium Structures And Thermal Fluctuations In Interacting Monolayers, 2019 The University of Akron

#### Equilibrium Structures And Thermal Fluctuations In Interacting Monolayers, Emmanuel Rivera

*Williams Honors College, Honors Research Projects*

Coherency strains appear in interacting atomic monolayers due to differing bond lengths, which can arise from different materials or geometries. Examples include extended monolayers interacting with a substrate and the interacting walls of a multi-walled carbon nanotube. These strains can induce various equilibrium configurations, which we will analyze by means of a phenomenological model that incorporates forces from bond stretching and bending within each layer and the weak van der Waals interactions connecting the separate layers. We vary the strengths of each interaction to explore their effects on equilibrium structures, and the specific case of a two-walled carbon nanotube is ...