Multi-Scale Superinfection Models in Evolutionary Epidemiology

The study of evolutionary epidemiology is vital to understand and control the spread of anti-microbial resistance, 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. 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 capturing the feedback loops between such scales is a formidable challenge.We will discuss the main technical challenges 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. We will distinguish between the cases when superinfection of the host facilitates the coexistence of two (or more) infections that interact synergistically by fuelling each other's spread (syndemic), and when these infections hinder each other. We show how in the former case multiple stable steady states are possible, while in the latter case the stable steady state is unique but possibly harder to compute. We discuss the consequent implications for public health control measures.