Mathematical models of the impact of rabbit calicivirus disease (RCD) on the European rabbit, Oryctolagus cuniculus, in Australia
This thesis relates to the work of building a mathematical model of the impact of Rabbit Calicivirus Disease (RCD) on the European Rabbit, Oryctolagus cuniculus, in Australia. After introducing the general biology of rabbits and the immunology of RCD, we build a time-dependent single site model. We construct a single-site population dynamic model with age structure, seasonal birth rate, density dependent regulation of the population size and climatic variability for various regions of Australia. After investigating suitable parameter ranges, we incorporate the disease dynamics through an indirect transmission model based on two different hypotheses which we call the Strong Juvenile hypothesis and the Weak Juvenile hypothesis. These differ in their assumption about Juvenile immunity to the disease. The ecological impact of both hypotheses is tested for both the single site and multiple site (spatial) models. The disease impact is investigated by varying the disease virulence, i.e. a parameter measuring the "strength" of the virus. Subsequently, a multiple site (spatial) model for the Riverina region is built by using the single-site model as building block. Data from Lake Urana is used to parameterize a seasonal emigration rate from each site. Density dependent immigration is added together with a hazard coefficient which rabbits face when leaving one site and trying to become established in another. Acceptance in a new site is regulated by the population density at the entry site. Several spatial configurations of sites are tested and the spatial dynamics of the disease is investigated. Finally, we construct a model to investigate the long term evolution of the disease virus. We postulate the existence of several strains of the disease and trade-offs between disease characteristics. We allow for mutation of the virus and run the model for two contrasting geographical regions of Australia. We compare the results for the different regions and the different hypotheses regarding Juvenile immunity (the Strong Juvenile hypothesis and the Weak Juvenile hypothesis). It is shown, unexpectedly, that intermediate levels of disease virulence are not selected.