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Ordinary Differential Equations and Applied Dynamics Commons™
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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
On The Spatial Modelling Of Biological Invasions, Tedi Ramaj
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 …
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Spora: A Journal of Biomathematics
Viral hepatitis negatively affects the health of millions, with the worst health outcomes associated with the hepatitis D virus (HDV). Fortunately, HDV is rare and requires prior infection with the hepatitis B virus (HBV) before it can establish infection and transmit. Here, we develop a mathematical model of HBV and HDV transmission in Sub-Saharan Africa to investigate the effects of hepatitis B vaccination on both HBV and HDV. Our findings illustrate a hepatitis B vaccination rate above 0.006 year-1 reduces hepatitis D by over 90%, and a vaccination rate above 0.0221 year-1 reduces hepatitis B by over 90%, …
Dynamical Modeling In Cell Biology With Ordinary Differential Equations, Renee Marie Dale
Dynamical Modeling In Cell Biology With Ordinary Differential Equations, Renee Marie Dale
LSU Doctoral Dissertations
Dynamical systems have been of interest to biologists and mathematicians alike. Many processes in biology lend themselves to dynamical study. Movement, change, and response to stimuli are dynamical characteristics that define what is 'alive'. A scientific relationship between these two fields is therefore natural. In this thesis, I describe how my PhD research variously related to biological, mathematical, and computational problems in cell biology. In chapter 1 I introduce some of the current problems in the field. In chapter 2, my mathematical model of firefly luciferase in vivo shows the importance of dynamical models to understand systems. Data originally collected …
Parts Of The Whole: Why I Teach This Subject This Way, Dorothy Wallace
Parts Of The Whole: Why I Teach This Subject This Way, Dorothy Wallace
Numeracy
The importance of mathematics to biology is illustrated by search data from Google Scholar. I argue that a pedagogical approach based on student research projects is likely to improve retention and foster critical thinking about mathematical modeling, as well as reinforce quantitative reasoning and the appreciation of calculus as a tool. The usual features of a course (e.g., the instructor, assessment, text, etc.) are shown to have very different purposes in a research-based course.
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Electronic Theses and Dissertations
Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …