The increase in emerging infectious diseases has led to the allocation of significant time and resources for the development of pandemic preparedness plans worldwide. Nevertheless, real-time management of emerging disease outbreaks is often marked by confusion and uncertainty as decision-makers are challenged to make impactful decisions with little time and incomplete information. Health authorities typically approach such threats by individual level interventions, such as vaccines and antivirals. This does not, however, detail how these targeted interventions and countermeasures should be used to optimally benefit total population health. Mathematical modelling of complex systems represents the bridging science that is needed. This chapter discusses the conceptual design and structure of mathematical models of communicable diseases, using transmission dynamics in the context of respiratory-borne pathogens within human populations. It demonstrates the necessity of assembling appropriate expertise related to mathematical modelling, epidemiology, public health, virology, and clinical management to ensure valuable quantitative decision-support tools to assist policymakers at the time of crisis.