Disentangling how multiple traits drive 2 strain frequencies in SIS dynamics with coinfection

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 SIS compartmental model with co-infection/co-colonization, incorporating multiple 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 us 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 coinfection prevalence. This framework offers a deeper analytical understanding of 2-strain competitive games in coinfection, with applications to virulence, interventions, antibiotic resistance, and social evolution theory.

Towards a mathematical understanding of colonization resistance in multispecies microbial communities

“…In more diverse communities (more species N > 2, and/or more traits varying), effects of context-altering perturbations are undoubtedly more complex, as we have shown in some cases (19; 20; 39). Among N species varying randomly only in co-colonization interaction phenotypes (susceptibilities K ij ), a key modulator of coexistence regimes is the ratio of single-to co-colonization in the system, µ (19), decreasing with R 0 and k .…”

“…Considering phenotypic similarity in micro-scale interaction trait space between species ( K i j = k + εα i j , with ε small), we have shown for N = 2 and for general N ≥2 in (18), that there are two timescales in such a system: a fast one where the species obey neutral dynamics, during which global colonization and co-colonization variables stabilize, and a slow timescale, where non-neutral dynamics happen, driven explicitly by species variation in the co-colonization interaction matrix K (or more traits as shown in (20; 39)). Applying the similarity assumption in N dimensions (18) (where k can reflect the mean of K ij , and ε their standard deviation), corresponds to a kind of Taylor approximation for the dynamics, which gets decomposed into a sum of different order terms.…”

“…microbial consortia in soil, cheese rinds, natural biofilms). With model extensions under way (20; 39), to increase scope and generality, for example more trait dimensions for species differences, including growth and clearance biases besides interaction coefficients, possibly relevant to more biological scenarios (63), we show the backbone of the replicator equation formalism, in terms of mutual invasion fitnesses, stays the same. This constitutes a big advantage as theoretical study of replicator dynamics has a long history and solid mathematical foundations (21).…”

“…The more general model for variation in other trait dimensions between similar species can be found in (20) where we formally derive that a similar replicator equation in terms of invasion fitnesses regulates the dynamics, but the mutual invasion fitness expression depends now on all traits. Besides the co-colonization interaction matrix K = ( K ij ), describing micro-scale susceptibilities to co-colonization (varied here) the 4 new trait axes we have included and studied in (20; 39) are: i) species-specific transmission/proliferation rates β i , ii) species-specific clearance rates in single colonization γ i , iii) pair-specific clearance rates in co-colonization ( γ ij ), and iv) species onward propagation biases from mixed co-colonization, depending on their order of arrival, . In this more complex scenario, the definition of ‘global context’ changes, as it may comprise also mean-field parameters in other traits, besides R 0 , k (relevant for the K ij -only model used here).…”

“…In this more complex scenario, the definition of ‘global context’ changes, as it may comprise also mean-field parameters in other traits, besides R 0 , k (relevant for the K ij -only model used here). The two-species system, namely the N = 2 dynamics in the case of 5-dimensional trait variation, is studied in (39), where the effect of the single to co-colonization ratio µ is shown to be very important, but this time influencing in a non-linear fashion. The dynamic colonization resistance of the N -species community emerges in this model again as a mean invasion fitness over all pairs in the system , dynamically shaped by their changing frequencies.…”