Emerging infectious diseases have long been recognized as a continuous, inevitable, unpredictable threat to the global public health. Hence, understanding the underlying dynamics why they spread and what causes epidemics gives key ideas of intervention strategies. In this talk, we will present the development of three mathematical models for the spread of emerging infectious diseases: 2009 A/H1N1 pandemic and 2015 Middle East respiratory syndrome (MERS) outbreak in the Republic of Korea, and the Ebola virus disease (EVD) outbreak in West Africa. Using the laboratory-confirmed case data in the first two emerging infectious diseases, the spreading dynamics of transmission is investigated. Results suggest that heterogeneity plays a key role in the spread of two emerging infectious diseases in the Republic of Korea. Our findings show that interventions in the early stage of the outbreak could reduce the epidemic size up to 19% for the 2009 pandemic influenza, and up to 80% for the 2015 MERS outbreak. In Ebola outbreak in West Africa, we present the estimation of the number of maximum sickbeds using the controlled EVD model under the frame of optimal control theory.