Background: Effective response to emerging infectious disease (EID) threats relies on health care systems that can detect and contain localised outbreaks before they reach a national or international scale. The Asia-Pacific region contains low and middle income countries in which the risk of EID outbreaks is elevated and whose health care systems may require international support to effectively detect and respond to such events. The absence of comprehensive data on populations, health care systems and disease characteristics in this region makes risk assessment and decisions about the provision of such support challenging. Methodology/principal findings: We describe a mathematical modelling framework that can inform this process by integrating available data sources, systematically explore the effects of uncertainty, and provide estimates of outbreak risk under a range of intervention scenarios. We illustrate the use of this framework in the context of a potential importation of Ebola Virus Disease into the Asia-Pacific region. Results suggest that, across a wide range of plausible scenarios, preemptive interventions supporting the timely detection of early cases provide substantially greater reductions in the probability of large outbreaks than interventions that support health care system capacity after an outbreak has commenced. Conclusions/significance: Our study demonstrates how, in the presence of substantial uncertainty about health care system infrastructure and other relevant aspects of disease control, mathematical models can be used to assess the constraints that limited resources place upon the ability of local health care systems to detect and respond to EID outbreaks in a timely and effective fashion. Our framework can help evaluate the relative impact of these constraints to identify resourcing priorities for health care system support, in order to inform principled and quantifiable decision making.