Mathematical models of infectious diseases in ungulate populations
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In this thesis we develop a suite of mathematical models to understand the epidemiological dynamics of infectious diseases in ungulate hosts. Using ordinary differential equation frameworks, we explored the key routes of transmission that promote the persistence of the highly virulent African swine fever (ASF) infection in wild boar and tested control strategies that could limit ASF outbreaks and its persistence. These modelling techniques were extended to investigate the impact of an ASF outbreak on endemic tuberculosis in wild boar. The generality of the model framework meant the results could add new perspective on the coexistence of multiple pathogens. Motivated by the work on the persistence of ASF, we used a suite of stochastic continuous-time Markov chain models to show that latent and chronic infection could have a significant impact on the mean time to pathogen extinction. We also developed a model framework to assess how hosts, including ungulates, contribute to tick-borne infections. This expands on previously studied models such that the regulation of tick density is dependent on the density of the specific hosts on which different tick stages feed. Our results outlined the effect host density and composition could have on tick-borne prevalence and incidence levels. The work in this thesis has highlighted how mathematical models are important tools for understanding epidemiological dynamics in wildlife systems with our work having had an impact on the management of key, current, endemic and emerging diseases in ungulates.