Disentangling how multiple traits drive 2 strain frequencies in SIS dynamics with coinfection. (7th April 2022) - Le, Thi Minh Thao; Madec, Sten; Gjini, Erida
Highlights: We present an analytical solution for strain frequency dynamics in a Susceptible-Infected-Susceptible system with coinfection, allowing for 5 fitness dimensions where 2 interacting strains may vary. Assuming strain similarity, via timescale separation, we expose neutral and non-neutral dynamics between two strains, with a replicator equation at its core, driven by mean-field values and relative trait variation. We illustrate the role of multiple traits in modulating the net outcome between two strains, focusing on the strains' mutual invasion fitnesses, their signs and magnitudes. We show that coinfection prevalence generates non-monotonic transitions in epidemiologic system outcome for the same relative variation between two strains. Our work contributes to a deeper fundamental understanding of coinfection as both a potential promoter and inhibitor of coexistence. Abstract: A general theory for competitive dynamics among many strains at the epidemiological level is required to understand polymorphisms in virulence, transmissibility, antibiotic resistance and other biological traits of infectious agents. Mathematical coinfection models have addressed specific systems, focusing on the criteria leading to stable coexistence or competitive exclusion, however, due to their complexity and nonlinearity, analytical solutions in coinfection models remain rare. Here we study a 2-strain Susceptible-Infected-Susceptible ( SIS ) compartmental model with co-infection/co-colonization, incorporating five strain fitness dimensions under the same framework: variation in transmissibility, duration of carriage, pairwise susceptibilities to coinfection, coinfection duration, and transmission priority effects from mixed coinfection. Taking advantage of a singular perturbation approach, under the assumption of strain similarity, we expose how strain dynamics on a slow timescale are explicitly governed by a replicator equation which encapsulates all traits and their interplay. This allows to predict explicitly not only the final epidemiological outcome of a given 2-player competition, but moreover, their entire frequency dynamics as a direct function of their relative variation and of strain-transcending global parameters. Based on mutual invasion fitnesses, we analyze and report rigorous results on transition phenomena in the 2-strain system, strongly mediated via endemic coinfection prevalence. We show that coinfection is not always a promoter of coexistence; instead, its effect to favour or prevent polymorphism is non-monotonic and depends on the type and level of phenotypic differentiation between strains. This framework offers a deeper analytical understanding of 2-strain competitive games in coinfection, with theoretical and practical applications in epidemiology, ecology and evolution.