Multi-scale time-since-infection models in evolutionary epidemiology
The study of evolutionary epidemiology is vital to understand the complexity of pathogens’ dynamics and their impact on public health, but is inherently challenging because pathogen evolution is driven by forces acting at multiple scales: for example, HIV needs to escape the immune system within a host, but also needs to maintain the ability to be transmitted efficiently between hosts. I will argue that time-since-infection models are much more flexible than ODEs if we want to allow for realistic enough aspects of both within- and between-host scales, but that capturing the feedback loops between such scales is a formidable challenge.
Using HIV as an example, I will discuss current models and their limitations, with particular attention to the implications of the fundamental structural assumptions on models’ behaviour. Furthermore, I will discuss the main technical challenges I see in developing a general theory for time-since-infection models that allow for superinfection (e.g. multi-strain systems with partial cross-immunity), starting from the problem of characterising the system’s steady states.