This thesis describes four years of research to quantify and characterise the system dynamics of bat-origin viral emergence events. Chapters 2–5 are comprised of four quantitative analyses: a compartmental model comparison of stochastic henipavirus serological dynamics in captive bats (Eidolon helvum in Ghana), a quantitative literature review of domesticated animals as bridging hosts of henipavirus and filovirus spillover, a statistical model of Ebola spillover observation probabilities, and a Bayesian model of syndromic differentiation of and surveillance for haemorrhagic fevers. By adapting, extending, and developing new analytical methods to infer the ecological and epidemiological dynamics of bat-origin viruses, I demonstrate through these chapters that 1) spillover of Ebola virus and other rare zoonotic pathogens is more common than typically accounted for, especialy when resulting in small outbreaks and singleton spillovers, 2) many gaps exist in knowledge of the emergence risks posed by henipaviruses and filoviruses, including fundamental aspects of viral dynamics in reservoir hosts and the roles of domesticated animals as potentially bridging or amplifying hosts, 3) common febrile illnesses and underdeveloped health infrastructure combine to create a primary barrier to detection of rare disease, and 4) many of the observation biases involved in spillover research and outbreak detection are mutually compounding and self-reinforcing. I synthesise these findings in Chapter 6, attempting to reconcile the many uncertainties in the quantitative study of zoonotic spillover and emergence with the urgent need for action to prevent and mitigate future epidemics. I conclude by emphasising the importance of core health infrastructure, as well as global redistribution of the means of good health and greater political engagement by scientists with the social forces that shape unequal distributions of disease.