The purpose of this talk is to explore how heterogeneity in the connectivity of an epidemiological network impacts the interaction between strains in a co-infection SIS framework.

In the first part, we will present an epidemiological model of co-infection with multiple strains under the assumption of homogeneous connectivity among hosts. We will show that, under the assumption of neutrality, this model satisfies a neutral null property, an ecologically important concept. Mathematically, this neutrality means that the $\omega$-limit set of any trajectory is a central manifold that can be parameterized by the proportion $(z_i)$ of each strain $i$.

This neutrality can be relaxed using a slow-fast argument, leading to an equation for $(z_i)$ that describes the slow dynamics on the central manifold. This equation is the well-known replicator equation, whose parameters are explicitly linked to macro-level ecological parameters. This connection allows us to understand pathogen ecology through the epidemiological dynamics at the host scale.

In the second part, we will explain how this approach can be extended when considering a heterogeneous network of host connectivity. After precisely describing this new model, we will show that the final replicator equation retains traces of this heterogeneity, providing a direct way to model how the complexity of host interactions affects the dynamics of a pathogen and its multiple variants.