During emerging disease outbreaks, public health, emergency management officials and decision-makers increasingly rely on epidemiological models to forecast outbreak progression and determine the best response to health crisis needs. Outbreak response strategies derived from such modelling may include pharmaceutical distribution, immunisation campaigns, social distancing, prophylactic pharmaceuticals, medical care, bed surge, security and other requirements. Infectious disease modelling estimates are unavoidably subject to multiple interpretations, and full understanding of a model's limitations may be lost when provided from the disease modeller to public health practitioner to government policymaker. We review epidemiological models created for diseases which are of greatest concern for public health protection. Such diseases, whether transmitted from person-to-person (Ebola, influenza, smallpox), via direct exposure (anthrax), or food and waterborne exposure (cholera, typhoid) may cause severe illness and death in a large population. We examine disease-specific models to determine best practices characterising infectious disease outbreaks and facilitating emergency response and implementation of public health policy and disease control measures.