Ordinary Differential Equations and Applied Dynamics Commons^™

Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being Through Hybrid Mathematical Modeling, Maggie Renee Sullens

Doctoral Dissertations

Mathematical modeling can achieve otherwise inaccessible insights into bio-logical questions. We use ODE (ordinary differential equations) and Game Theory models to demonstrate the breadth and power of these models by studying three very different biological questions, involving socio-behavioral and socio-economic systems, conservation biology, policy and decision making, and organismal homeostasis.

We adapt techniques from Susceptible-Infected-Recovered (SIR) epidemiological models to examine the mental well-being of a community facing the collapse of the industry on which it’s economically dependent. We consider the case study of a fishing community facing the extinction of its primary harvest species. Using an ODE framework with a …

On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

Electronic Thesis and Dissertation Repository

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …

Coevolution Of Hosts And Pathogens In The Presence Of Multiple Types Of Hosts, Evan J. Mitchell

Electronic Thesis and Dissertation Repository

How will hosts and pathogens coevolve in response to multiple types of hosts? I study this question from three different perspectives. First, I model a scenario in which hosts are categorized as female or male. Hosts invest resources in maintaining their immune system at a cost to their reproductive success, while pathogens face a trade-off between transmission and duration of infection. Importantly, female hosts are also able to vertically transmit an infection to their newborn offspring. The main result is that as the rate of vertical transmission increases, female hosts will have a greater incentive to pay the cost to …

Population And Evolution Dynamics In Predator-Prey Systems With Anti-Predation Responses, Yang Wang

Electronic Thesis and Dissertation Repository

This thesis studies the impact of anti-predation strategy on the population dynamics of predator-prey interactions. This work includes three research projects.

In the first project, we study a system of delay differential equations by considering both benefit and cost of anti-predation response, as well as a time delay in the transfer of biomass from the prey to the predator after predation. We reveal some insights on how the anti-predation response level and the biomass transfer delay jointly affect the population dynamics; we also show how the nonlinearity in the predation term mediated by the fear effect affects the long term …

Mathematical Modelling Of Prophage Dynamics, Tyler Pattenden

Electronic Thesis and Dissertation Repository

We use mathematical models to study prophages, viral genetic sequences carried by bacterial genomes. In this work, we first examine the role that plasmid prophage play in the survival of de novo beneficial mutations for the associated temperate bacteriophage. Through the use of a life-history model, we determine that mutations first occurring in a plasmid prophage are far more likely to survive drift than those first occurring in a free phage. We then analyse the equilibria and stability of a system of ordinary differential equations that describe temperate phage-host dynamics. We elucidate conditions on dimensionless parameters to determine a parameter …

Phage-Bacteria Interaction And Prophage Sequences In Bacterial Genomes, Amjad Khan

Electronic Thesis and Dissertation Repository

In this investigation, we examined the interaction of phages and bacteria in bacterial biofilm colonies, the evolution of prophages (viral genetic material inserted into the bacterial genome) and their genetic repertoire. To study the synergistic effects of lytic phages and antibiotics on bacterial biofilm colonies, we have developed a mathematical model of ordinary differential equations (ODEs). We have also presented a mathematical model consisting of a partial differential equation (PDEs), to study evolutionary forces acting on prophages. We fitted the PDE model to three publicly available databases and were able to show that induction is the prominent fate of intact …

Modelling Walleye Population And Its Cannibalism Effect, Quan Zhou

Electronic Thesis and Dissertation Repository

Walleye is a very common recreational fish in Canada with a strong cannibalism tendency, such that walleyes with larger sizes will consume their smaller counterparts when food sources are limited or a surplus of adults is present. Cannibalism may be a factor promoting population oscillation. As fish reach a certain age or biological stage (i.e. biological maturity), the number of fish achieving that stage is known as fish recruitment. The objective of this thesis is to model the walleye population with its recruitment and cannibalism effect. A matrix population model has been introduced to characterize the walleye population into three …

On Honey Bee Colony Dynamics And Disease Transmission, Matthew I. Betti

Electronic Thesis and Dissertation Repository

The work herein falls under the umbrella of mathematical modeling of disease transmission. The majority of this document focuses on the extent to which infection undermines the strength of a honey bee colony. These studies extend from simple mass-action ordinary differential equations models, to continuous age-structured partial differential equation models and finally a detailed agent-based model which accounts for vector transmission of infection between bees as well as a host of other influences and stressors on honey bee colony dynamics. These models offer a series of predictions relevant to the fate of honey bee colonies in the presence of disease …

Modeling Purple Sea Urchin And California Sheephead Populations In Southern California Kelp Forests, Olivia Rachel Williams

Senior Projects Spring 2017

In this project I am modelling the predator-prey relationship between California sheephead and purple sea urchin populations, respectively, in kelp forests off the coast of southern California. The Lotka-Volterra equations explain predator-prey relationships in their most basic form. These equations incorporate a set of biological assumptions that can be unrepresentative of many ecological systems. I will consider alternate models that incorporate variations of the Lotka-Volterra model which may better represent the biology of the purple sea urchins and California sheephead. Using biological characteristics of both species in kelp forests, I will set possible and likely parameters and solve for unknown …

Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer

Senior Independent Study Theses

No abstract provided.

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva

Electronic Theses and Dissertations

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

Optimal Theory Applied In Integrodifference Equation Models And In A Cholera Differential Equation Model, Peng Zhong

Doctoral Dissertations

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged also affects the harvesting behavior.

Cholera remains a public health threat in many parts of the world and improved …

Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan

HMC Senior Theses

We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model in higher dimensions are also presented.

Optimal Control Of Species Augmentation Conservation Strategies, Erin Nicole Bodine

Doctoral Dissertations

Species augmentation is a method of reducing species loss via augmenting declining or threatened populations with individuals from captive-bred or stable, wild populations. In this dissertation, species augmentation is analyzed in an optimal control setting to determine the optimal augmentation strategies given various constraints and settings. In each setting, we consider the effects on both the target/endangered population and a reserve population from which the individuals translocated in the augmentation are harvested. Four different optimal control formulations are explored. The first two optimal control formulations model the underlying population dynamics with a system of ordinary differential equations. Each of these …