Time Scales in Disease Transmission Dynamics

Time scale arguments are implicitly present in many models in epidemiology in the sense that only the relevant time scales are considered. I start by discussing the most important time scales. The relative magnitude of most time scales remains the same for all epidemic diseases. However, the time scales of immunity decay and pathogen evolution differ dramatically among pathogens, and this has importance for the associated models. I will discuss three examples of how time scale considerations may lead to different models—analyzing different biological questions. For measles, the demographic time scale plays a central role for our understanding of repeated epidemics. In contrast, the SIR model cannot explain the epidemiology of influenza where the separation of demography and evolution is not possible. That implies that the epidemiology of influenza differs dramatically from that of measles. The outbreak of foot-and-mouth disease in the UK in 2001 provides an example of a disease spreading rapidly in a fully susceptible population. Here, the details of the local disease spread play a crucial role that is poorly captured by simple SIR models. In the ongoing Covid-19 pandemic, the time scale of the epidemic and that of virus evolution cannot be separated, and the course of the pandemic has been directly affected by virus evolution. The coincidence of these two time scales may in fact be a characteristic for pandemics.