Ordinary Differential Equations and Applied Dynamics Commons^™

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 …

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. For …

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 …