Pandemic viruses have historically caused tremendous damage to lives and livelihoods. The coronavirus, COVID-19, has proven to be a significant issue around the world. In this paper it is argued that systems of controlling similar types of disasters need to be improved through learning from past experience and from others, as well as through improved modelling for better decision making. In doing so, the focus will be on resilience modelling and learning from incidents. Therefore, in this paper, first the introduction deals with hybrid approaches in operational research highlighting the differences between hybrid modelling and hybrid models. Second, an introduction to mathematical modelling of epidemics is provided and how such modelling leads to certain types of public health modelling is demonstrated. Third, resilience modelling will be discussed as a complimentary type of modelling, where concepts related to robustness, redundancy, resourcefulness, and rapidity are introduced. Fourth, resilience modelling will be extended to new principles taking COVID-19 as an example for the analysis. Fifth, the analysis will then be used to compare degrees of resilience for different countries. Finally, other modelling approaches for managing – and learning from – pandemics, in terms of root cause analysis, bowtie modelling and safety barriers, are proposed.