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.
Study completed
Supervisor Consent
yes
Included in
Dynamic Systems Commons, Environmental Microbiology and Microbial Ecology Commons, Non-linear Dynamics Commons, Ordinary Differential Equations and Applied Dynamics Commons, Population Biology Commons
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.