Electronic Thesis and Dissertation Repository

Thesis Format



Master of Science


Applied Mathematics


Dr. Xingfu Zou


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.

Summary for Lay Audience

The burden of malaria on the human race, especially in developing countries demands the development of novel approaches to fight the spread of Plasmodium sp. parasites which cause malaria, and are transmitted by mosquitoes. One of the most promising is paratransgensis, a technique for eliminating a parasite from a disease vector populations (in this case mosquitoes) through the genetic engineering of a common colonizer of the host. We propose a simple model that can describe many different different examples of paratransgenesis, which we term a Functional Competitive Lotka-Volterra (FCLV) system. Our main focus is analyzing FCLV systems with contraction analysis, which we believe has been underused, but has great promise in the area of model analysis. We show that using contraction theory the analysis of an FCLV model can be reduced to a system of two dimensions less. This allows us to reach the conclusion that given a sufficiently strong genetically modified bacteria, once introduced into a mosquito it will always eliminate Plasmodium sp. within a mosquito.

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.