Physical Sciences and Mathematics Commons^™

Models Linking Epidemiology With Immunology And Ecology, Eric Shu Numfor

Doctoral Dissertations

Optimal control can be used to design intervention strategies for the control of infectious diseases and predator-prey systems. In this dissertation, we studied models encapsulating two relatively new areas of mathematical biology, which combine epidemiology with immunology and ecology.

We formulated immuno-epidemiological models of coupled within-host model of ordinary differential equations and between-host model of ordinary differential equations and partial differential equations, using the Human Immunodeficiency Virus (HIV) for illustration, and set a framework for optimal control of immuno-epidemiological models. By constructing an iterative sequence from a representation formula for a solution to the linked model and using the fixed-point …

A Spatial Analysis Of Streambank Heterogeneity And Its Contribution To Bank Stability, Paul Vanterpool Simmons

Masters Theses

Streambank erosion is a function of fluvial detachment and geotechnical failure mechanisms working in combination to cause bank retreat. It is generally agreed that bank stability is dependent on both types of erosion; however, few studies have attempted to correlate the driving and resisting forces between the two. It has been proposed that: (1) streambanks possess a spatial structure and dependence of non-erodible resistant structures such as root masses and rocks; (2) streambanks naturally “armor” themselves from fluvial erosion with a combination of hard points and resistive soil; and (3) the stability of the streambank can be predicted by the …