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

Quasi-neutral Dynamics in a Coinfection System with N Strains and Asymmetries along Multiple Traits