Martin Lopez-Garcia (Leeds) – Mathematical within-host models of viral and bacterial infections

At Leeds, we have been developing within-host models of infection for a number of years. Deterministic models of viral dynamics have been widely used in the past to understand average behaviours, and to quantify the efficacy of treatments. On the other hand, stochastic models allow one to incorporate discrete events (such as cellular burst, where an infected cell dies releasing N virions into the extracellular environment), to look at extinction events (e.g. probably of infection establishment vs short-time recovery of the host, for a given initial dose), and to account for variability in summary statistics such as the reproduction number (i.e., the number of cells infected by a typical infected cell during an infection). These heterogeneities can be important for example when looking at extinction events and/or the impact of small viral doses. Stochastic models also allow one to obtain summary statistics related to the infection dynamics across different scales (intra-cellular, within-host and population levels), and to link these scales via multi-scale modelling approaches. In this talk, I will discuss recent work that we have carried out in this area.