Modelling infectious diseases in multiple species : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Applied Mathematics at Massey University, Albany, New Zealand
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Date
2019
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Massey University
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Abstract
Leptospirosis is an infectious disease caused by bacteria in the genus
Leptospira and is considered as the disease of interest in this thesis. It is
the highest occurring occupational disease in New Zealand and the country
has one of the highest (per capita) incidences of human leptospirosis in the
world. Transmission commonly occurs by contact with infectious animals, or
materials contaminated by them. The disease is the cause of great financial
losses to the country due to both the medical cost of treating infectious
individuals, as well as due to production losses in the farming industry.
As such, studying the dynamics of infection and possible control measures
for the disease in animals, which also minimises exposure to humans, is an
important area of research.
This thesis aims to develop New Zealand specific models demonstrating
the dynamics of leptospirosis infection within and between multiple host
species, specifically rats and sheep, thus contributing towards an understanding
of not only how ecological exchanges between different host populations
influence the spreading of the disease, but also how the incidence of leptospirosis
may be diminished. This is achieved with the use of compartmental SI type
models of increasing complexity, with simpler models used as building blocks
in constructing the more advanced systems.
The models presented involving only rats consider an age structure within
the population, with different behaviours and infection risks associated with
each age class. Models involving only sheep focus on the periodic forcing
implemented on the host population by the farmer, and also include an age
structure, albeit a somewhat simpler one than the one in the rat models.
The seasonal forcing on the livestock population results in a cyclical system
which is displayed using limit cycle diagrams. This behaviour is mirrored
in the model considering both host species in concert. Each model presents a
variety of results, including bifurcation diagrams and quasi-basic reproduction
numbers which display the behaviour of the system. The effect of varying
various parameter values on the system is explored, and how these may
change in relation to climate change is discussed. Parameter values used
in numerical results demonstrating analytical ones are New Zealand specific
and the model is used to predict conditions under which the infection will
persist in the population.
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Keywords
Communicable diseases, Communicable diseases in animals, Leptospirosis in animals, New Zealand, Mathematical models