  Understanding the interplay of different traits in a co-infection system with
multiple strains has many applications in ecology and epidemiology. Because of
high dimensionality and complex feedbacks between traits manifested in
infection and co-infection, the study of such systems remains a challenge. In
the case where strains are similar (quasi-neutrality assumption), we can model
trait variation as perturbations in parameters, which simplifies analysis.
Here, we apply singular perturbation theory to many strain parameters
simultaneously, and advance analytically to obtain their explicit collective
dynamics. We consider and study such a quasi-neutral model of
susceptible-infected-susceptible (SIS) dynamics among N strains which vary in 5
fitness dimensions: transmissibility, clearance rate of single-and
co-infection, transmission probability from mixed coinfection, and
co-colonization vulnerability factors encompassing cooperation and competition.
This quasi-neutral system is analyzed with a singular perturbation method
through an appropriate slow-fast decomposition. The fast dynamics correspond to
the embedded neutral system, while the slow dynamics are governed by an
N-dimensional replicator equation, describing the time evolution of strain
frequencies. The coefficients of this replicator system are pairwise invasion
fitnesses between strains, which, in our model, are an explicit weighted sum of
pairwise asymmetries along all trait dimensions. Remarkably these weights
depend only on the parameters of the neutral system. Such model reduction
highlights the centrality of the neutral system for dynamics at the edge of
neutrality, and exposes critical features for maintenance of diversity.
