The population dynamics of bovine tuberculosis in possums : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University

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Massey University
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With the recent outcry concerning the spread of Bovine Tuberculosis throughout the New Zealand Possum population, there is an increasing need to study some of the diverse modelling approaches to this problem. This thesis centres on modelling the epidemics of this disease using two and three-dimensional dynamical systems, which describe the change in the possum population and change in the number of individuals that are diseased. Introductory material is covered in Chapter One, which reports on the first, through to some of the most recent research completed in the area of disease epidemics. A review of the previous model of possum tuberculosis is also introduced. Chapter Two looks at the effects on the dynamics of the model of changing the recovery curve parameter, which measures the degree of recovery of possums following a control operation. Detailed steady-state analysis is carried out on the system and local stability determined. In Chapter Three, a three-dimensional model is investigated that allows for a latent period following infection of disease. Instead of a possum being able to spread the disease immediately after becoming infected itself, there is a latent time until the disease becomes contagious. An in-depth description is given as to how this model originates, then steady-state analysis is explored, and finally local stability of the steady-states is examined. Restricting the contact rate of an individual possum with the rest of the population is the model studied in Chapter Four. Rather than a possum being able to come in contact with the whole population in a set time, as was the situation in the previous models, the number of contacts is fixed at some realistic value for the given time period. Steady-state analysis is carried out for this new model, along with the local stability analysis. Chapter Five looks at the various models and how they relate to the model in Chapter Two. as this model is the base for the subsequent ones. Computer generated plots are examined in order to display the numerical differences between the models. A brief comparison is given between these and some other models in the literature, and concludes by discussing some of the advantages and disadvantages of the various models. Finally, Chapter Six discusses the need for implementing spatially distributed models in the future, to allow for patchiness within the population.
Tuberculosis in cattle, Trichosurus vulpecula, Diseases