Life Sciences Commons^™

Homogenization Techniques For Population Dynamics In Strongly Heterogeneous Landscapes, Brian P. Yurk, Christina A. Cobbold

Faculty Publications

An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction–diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic …

Modeling Aggregation Of Proliferating Microglia In Response To Amyloid-Beta In Dementia, Adrienne C. Kinney, Ellen R. Swanson

Spora: A Journal of Biomathematics

Amyloid-beta plaques are prominent biological markers in dementia brains. In response to plaque formation, the brain's immune cells, microglia, become reactive. Microglia are measurable cells that surround amyloid-beta plaques, indicating their location. A system of partial differential equations describes the concentration of microglia in dementia brains by incorporating chemotactic signaling. However, this system fails to incorporate increasing numbers of reactive microglia cells in response to amyloid-beta aggregation. A system of ordinary differential equations describing the number of significant cells and proteins in the brain suggests the amount of reactive microglia increases significantly during the progression of dementia. We couple these …

Development Of Epithelial Tissues: How Are Cleavage Planes Chosen?, Ying Xin

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Medicine: Modeling Disease And Treatment, Lisette Depillis

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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 …

Uncovering Functional Relationships In Leukemia, Reginald Mcgee

Biology and Medicine Through Mathematics Conference

No abstract provided.

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.

Evolution Of Influenza H3n2: A Random Walk In High Dimensions, James R. Moore

Biology and Medicine Through Mathematics Conference

No abstract provided.

Dynamics Of Fluorescent Imaging In Glob-Driven Breakup, Lan Zhong, Christiaan Ketelaar, Richard J. Braun, Carolyn G. Begley, Peter Ewen King-Smith

Biology and Medicine Through Mathematics Conference

No abstract provided.

Role Of The Cost Of Plasticity In Determining The Features Of Fast Vision In Humans., Maria M. Del Viva Phd, Renato Budinich M. Sc, Laura Palmieri M. Sc, Vladimir S Georgiev Phd, Giovanni Punzi Phd

MODVIS Workshop

No abstract provided.

The Effects Of Disturbance And Species Specific Interactions On Diversity In An Agent Based Forest Simulation, Matthew E. Mills

Theses and Dissertations

In ecology literature, there is much data which suggests that conspecific negative density dependence (CNDD) and abiotic disturbances increase biodiversity in forests. This thesis elucidates the notion that not only do these two forces increase diversity, but they may also interact with one another in order to achieve higher levels of biodiversity. Abiotic disturbances, like fires and hurricanes, can indirectly impact conspecific effects because when these forces remove individuals from the landscape, the role of the conspecific effects will change. The interaction of these two factors in biodiversity are explored in an agent based forest simulation through a resource surface. …

Disease Models With Immigration, Reem Almarashi

Theses and Dissertations (Comprehensive)

In this thesis we focus first on studying the susceptible, exposed, and infected ($SEI$) disease model without immigration. We determine the basic reproduction number $\mathcal{R}_0$, which can be interpreted as the expected number of new cases that can be produced by a single infection in a completely susceptible population. Further, by using the Jacobian matrix, we determine the local stability of the disease model. Then we have the result that when $\mathcal{R}_0<1$ the DFE point is locally asymptotically stable(L.A.S). In contrast, when $\mathcal{R}_0>1$ we find that the endemic equilibrium is L.A.S. After that, we analyze the $SEI$ model with immigration of infected individuals.

Furthermore, we investigate the direction that the …

Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri

Theses and Dissertations

miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …