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