Rock, Kat S. (2014) How much do we care about biting insects? : modelling the dynamics of vector-borne diseases. PhD thesis, University of Warwick.

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Abstract

Mathematical models of disease can aid understanding of, and provide a framework for, the study of disease spread and control. Vector-borne diseases are not only amongst the most significant diseases but also require tailored mathematics to model the specific biological interactions important in their spread. A key model in vector-borne epidemiology is the Ross-Macdonald ODE model. Simplification of this model using the quasi-equilibrium assumption (QEA) allowed stability and bifurcation analysis to be performed. The QEA was then used to examine the effect of avian malaria upon the Hawaiian honeycreeper, including ecological factors such as predation and climate change.

In contrast, amendments to the Ross-Macdonald model can incorporate higher levels of biological detail, specifically age and bite structure in the vector population. This was facilitated via a PDE model which led to the better understanding of biological mechanisms upon disease transmission and control. Disease-free analytic solutions of the PDE were derived, however the complexity introduced by disease necessitated the use of numerical analysis in order to solve the system. This novel PDE model enabled the study of human African trypanosomiasis. Effects of starvation and teneral susceptibility of tsetse were introduced in a way which is not possible using ODE models. This provides a new framework capable of investigating the impact of these on the control of disease.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QL Zoology
Library of Congress Subject Headings (LCSH):	Communicable diseases -- Transmission -- Mathematical models, Avian malaria -- Mathematical models, Hawaiian honeycreepers -- Mathematical models
Official Date:	March 2014
Dates:	Date Event March 2014 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Keeling, Matthew James ; Wood, D. A. (David A.)
Description:	This is an abridged version for electronic use; please see the official URL for details on how to access the full version
Extent:	x, 211 leaves : illustrations, charts
Language:	eng

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