Author Information

Nickolas GoncharenkoFollow

Start Date

22-3-2019 9:15 AM

End Date

22-3-2019 9:20 AM

Department

Appilied Mathematics

Program

Appilied Mathematics

Year

2019

Supervisor Name

Xingfu Zou

Supervisor Email

xzou@uwo.ca

Abstract Text

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 the first time we propose a model extension, by incorporating a functional response, which solves this long standing problem. We name this new model a Functional Competitive Lotka Volterra (FCLV) model. We use a number of techniques most notably topology and monotone theory to perform a global analysis. The most important result obtained from the analysis is the existence of direct mapping between the solutions of CLV and FCLV models. This means that tools and results from CLV analysis directly applies to FCLV models. We use this result to analyse a model which describes within host competition between different organisms in the midgut of the mosquito. The implications of this model to malaria elimination in wild mosquito populations is discussed as well.

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Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

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Mar 22nd, 9:15 AM Mar 22nd, 9:20 AM

Modelling non-linear Functional Responses in Competitive Biological Systems.

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 the first time we propose a model extension, by incorporating a functional response, which solves this long standing problem. We name this new model a Functional Competitive Lotka Volterra (FCLV) model. We use a number of techniques most notably topology and monotone theory to perform a global analysis. The most important result obtained from the analysis is the existence of direct mapping between the solutions of CLV and FCLV models. This means that tools and results from CLV analysis directly applies to FCLV models. We use this result to analyse a model which describes within host competition between different organisms in the midgut of the mosquito. The implications of this model to malaria elimination in wild mosquito populations is discussed as well.