Quasi-neutral dynamics in a co-infection system with N strains

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 the strains are similar (quasi-neutrality assumption), we can model trait variation as perturbations in parameters, which simplifies analysis. Applying perturbation to many parameters at the same time is mathematically not easy. In this study, we advance in this direction. We consider and study such a quasi-neutral model of susceptible-infected-susceptible (SIS) type with N strains and variation in transmission, clearance, and co-colonization traits. The slow-fast dynamics and the Tikhonov's theorem are essential approaches that we use to analyze the system, under the perspective of the replicator equation, where the variables are frequencies of N strains. Coefficients of this replicator system, that inherently are pairwise invasion fitnesses of strains, characterize not only pairwise outcomes but also determine collective behavior. We illustrate the model framework by investigating particularly dynamics with two strains (N=2), and explicitly analyzing different fitness dimensions and their interplay for maintenance and stabilization of diversity.