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

Thumbnail Image
Open Access Location
Journal Title
Journal ISSN
Volume Title
Massey University
The Author
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.
Communicable diseases, Communicable diseases in animals, Leptospirosis in animals, New Zealand, Mathematical models