Transmission Fitness in Co-colonization and the Persistence of Bacterial Pathogens

2020

Bull Math Biol

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Multi-type infection processes are ubiquitous in ecology, epidemiology and social systems, but remain hard to analyze and to understand on a fundamental level. Here, we study a multi-strain susceptible-infected-susceptible model with coinfection. A host already colonized by one strain can become more or less vulnerable to co-colonization by a second strain, as a result of facilitating or competitive interactions between the two. Fitness differences between N strains are mediated through $$N^2$$ N 2 altered susceptibilities to secondary infection that depend on colonizer-cocolonizer identities ($$K_{ij}$$ K ij ). By assuming strain similarity in such pairwise traits, we derive a model reduction for the endemic system using separation of timescales. This ‘quasi-neutrality’ in trait space sets a fast timescale where all strains interact neutrally, and a slow timescale where selective dynamics unfold. We find that these slow dynamics are governed by the replicator equation for N strains. Our framework allows to build the community dynamics bottom-up from only pairwise invasion fitnesses between members. We highlight that mean fitness of the multi-strain network, changes with their individual dynamics, acts equally upon each type, and is a key indicator of system resistance to invasion. By uncovering the link between N-strain epidemiological coexistence and the replicator equation, we show that the ecology of co-colonization relates to Fisher’s fundamental theorem and to Lotka-Volterra systems. Besides efficient computation and complexity reduction for any system size, these results open new perspectives into high-dimensional community ecology, detection of species interactions, and evolution of biodiversity.

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Predicting N-Strain Coexistence from Co-colonization Interactions: Epidemiology Meets Ecology and the Replicator Equation

2020

Bull Math Biol

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“…We explore another mode of strain interactions, namely altered susceptibilities to coinfection, whereby N strains compete in SIS endemic scenarios of no persistent immunity and no virulence. Coinfection models with up to two strains have described vulnerability to coinfection with a single parameter (Alizon et al, 2013;Davies et al, 2019;Gaivão et al, 2017;van Baalen & Sabelis, 1995), two coefficients (Lipsitch, 1997) or four coefficients (Gjini et al, 2016) depending on model structure and aims, but very few analytical investigations have been done for a larger number of interacting strains (Adler & Brunet, 1991), recognizing the difficulties of including within-and between-strain details for such coefficients (Mosquera & Adler, 1998). Moreover, analytic solutions for strain frequency dynamics in coinfection models remain rare, due to nonlinearities even for N = 2.…”

Section: Introductionmentioning

confidence: 99%

The ratio of single to co‐colonization is key to complexity in interacting systems with multiple strains

2021

Ecology and Evolution

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The high number and diversity of microbial strains circulating in host populations have motivated extensive research on the mechanisms that maintain biodiversity. However, much of this work focuses on strain‐specific and cross‐immunity interactions. Another less explored mode of pairwise interaction is via altered susceptibilities to co‐colonization in hosts already colonized by one strain. Diversity in such interaction coefficients enables strains to create dynamically their niches for growth and persistence, and “engineer” their common environment. How such a network of interactions with others mediates collective coexistence remains puzzling analytically and computationally difficult to simulate. Furthermore, the gradients modulating stability‐complexity regimes in such multi‐player endemic systems remain poorly understood. In a recent study (Madec & Gjini, Bulletin of Mathematical Biology , 82), we obtained an analytic representation for N ‐type coexistence in an SIS epidemiological model with co‐colonization. We mapped multi‐strain dynamics to a replicator equation using timescale separation. Here, we examine what drives coexistence regimes in such co‐colonization system. We find the ratio of single to co‐colonization, µ , critically determines the type of equilibrium and number of coexisting strains, and encodes a trade‐off between overall transmission intensity R 0 and mean interaction coefficient in strain space, k . Preserving a given coexistence regime, under fixed trait variation, requires balancing between higher mean competition in favorable environments, and higher cooperation in harsher environments, and is consistent with the stress gradient hypothesis. Multi‐strain coexistence tends to steady‐state attractors for small µ , whereas as µ increases, dynamics tend to more complex attractors. Following strain frequencies, evolutionary dynamics in the system also display contrasting patterns with µ , interpolating between multi‐stable and fluctuating selection for cooperation and mean invasion fitness, in the two extremes. This co‐colonization framework could be applied more generally, to study invariant principles in collective coexistence, and to quantify how critical shifts in community dynamics get potentiated by mean‐field and environmental gradients.

“…Yet, it remains unclear which other factors, besides persistent host immunity, make strains compete or cooperate with each other, and whether there are environmental factors that can shift their fitness balance epidemiologically.Here, we set out to study another mode of strain interactions, that has received, albeit less, modeling attention, namely interactions between strains via altered susceptibilities, not after, but during infection, in endemic scenarios of no immunity (SIS). Co-colonization vulnerability in SIS models with up to 2 strains, has been shown to be important in several studies (Alizon et al, 2013;Davies et al, 2019;Gaivão et al, 2017;Gjini et al, 2016;Lipsitch, 1997), but very few analytical investigations have been done for a larger number of interacting strains (Adler and Brunet, 1991). In a recent mathematical study, extending the cocolonization interaction space to N -strains, we have provided a new analytical front for understanding a complex SIS system of multiple strains interacting upon co-colonization (Madec and Gjini, 2019).…”

mentioning

confidence: 99%

The key to complexity in interacting systems with multiple strains

2020

Preprint

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Ecological community structure, persistence and stability are shaped by multiple forces, acting on multiple scales. These include patterns of resource use and limitation, spatial heterogeneities, drift and migration. Pathogen strains co-circulating in a host population are a special type of an ecological community. They compete for colonization of susceptible hosts, and sometimes interact via altered susceptibilities to co-colonization. Diversity in such pairwise interaction traits enables the multiple strains to create dynamically their niches for growth and persistence, and ‘engineer’ their common environment. How such a network of interactions with others mediates collective coexistence remains puzzling analytically and computationally difficult to simulate. Furthermore, the gradients modulating stability-complexity regimes in such multi-player systems remain poorly understood. In a recent study, we presented an analytic framework for N-type coexistence in an SIS epidemiological system with co-colonization interactions. The multi-strain complexity was reduced from O(N2) dimensions of population structure to only N equations for strain frequency evolution on a long timescale. Here, we examine the key drivers of coexistence regimes in such a system. We find the ratio of single to co-colonization μ critically determines the type of equilibrium for multi-strain dynamics. This key quantity in the model encodes a trade-off between overall transmission intensity R0 and mean interaction coefficient in strain space k. Preserving a given coexistence regime, under fixed trait variation, can only be achieved from a balance between higher competition in favourable environments, and higher cooperation in harsher environments, consistent with the stress gradient hypothesis in ecology. Multi-strain coexistence regimes are more stable when μ is small, whereas as μ increases, dynamics tends to increase in complexity. There is an intermediate ratio that maximizes the existence and stability of a unique coexistence equilibrium between strains. This framework provides a foundation for linking invariant principles in collective coexistence across biological systems, and for understanding critical shifts in community dynamics, driven by simple and random pairwise interactions but potentiated by mean-field and environmental gradients.