Contraction Analysis of Functional Competitive Lotka-Volterra Systems: Understanding Competition Between Modified Bacteria and Plasmodium within Mosquitoes.

We propose and analyze an extension to the classic Competitive Lotka-Volterra (CLV) model. The goal is to model competition between species, with a response from the environment. This response is a function of the population of all species and can represent numerous physical phenomena including resource limitation and immune response of a host due to infection. We name this new system a Functional Competitive Lotka-Volterra (FCLV) model. We mainly use the construction of contraction metrics, to determine global properties of the model. We use this result to analyze the competition between Plasmodium sp. and genetically engineered bacteria within the midgut of a mosquito. We find that the effect of the immune response of the mosquito on invaders has a significant effect on whether Plasmodium or the genetically engineered bacteria dominates, but that under certain conditions the bacterium can eliminate the Plasmodium from the mosquito.

Name thesis:degree_name

M Sc

Discipline thesis:degree_discipline

Applied Mathematics

Grantor dc:publisher

The University of Western Ontario

Year dc:date.issued

2020

Author dc:creator

• Goncharenko, Nickolas

Advisor dc:contributor.advisor

• Xingfu Zou

• Dynamical Systems
• Competitive Lotka Volterra System
• Microbiota Modelling
• Contraction Analysis
• Within Host Dynamics

Language dc:language.iso

en_ca

Handle dc:identifier.uri

https://hdl.handle.net/20.500.14721/30052

OAI identifier oai:identifier

oai:uwo.scholaris.ca:20.500.14721/30052