Mathematical models of transmission and control of infectious agents

Indeed, the ‘heavy lifting’ of healthcare is in the care of patients, the development and distribution of vaccines, drugs and devices, and the conception and implementation of sensible systems and policies. However, in recent decades, spectacular increases in the availability of computational capacity have paved the way for mathematical modelling to play an ever-increasing role in many aspects of public health, by supporting formal analyses at various scales of the processes involved. This chapter explores a particular kind of ‘modelling’—and it is not the common (bio)statistical kind. We focus on what we would call ‘dynamical’ modelling (as opposed to ‘statistical’ modelling). This essentially entails the reduction, to mathematics, of key facts and principles inherent in the ‘processes’ or ‘mechanisms’ in an epidemiological situation. We can then manipulate these mathematical constructs, in search of insights that, while ultimately implied in the model construction, are not superficially apparent from our primary data and our intuition.