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

Modelling the Epidemiological Impact of Different Adult Pneumococcal Vaccination Strategies in the United Kingdom

INTRODUCTION

Pneumococcal conjugate vaccines (PCVs) were first introduced in the paediatric United Kingdom (UK) immunisation programme in 2006 which led to significant declines in invasive pneumococcal disease (IPD) caused by targeted serotypes. Although paediatric PCVs provide some indirect protection to adults, a significant IPD burden remains in older adults. Here, we compared three adult (65+ years-old) and risk group (2-64-year-old) vaccination scenarios, namely a continuation of the status quo with PPSV23 vaccination, using the recently licensed-in-adults PCV20, or using the new adult-focused 21-valent PCV, V116.

METHODS

A population-level compartmental dynamic transmission model (DTM) was adapted to the UK setting. The model described Streptococcus pneumoniae carriage transmission dynamics and disease progression in the presence of age- and serotype-specific pneumococcal vaccines. We calibrated the DTM to age- and serotype-specific IPD data in the UK and used the model to make projections under the different adult vaccination scenarios while keeping PCV13 immunisation in children.

RESULTS

The calibrated model yielded reasonable parameter values and model fits that closely matched observed IPD dynamics. Among 65+ year-olds, 10-year model projections predicted that the routine use of V116 would reduce IPD incidence by 15.5%, while PCV20 would reduce IPD incidence by 8.9% and the continued use of PPSV23 would increase incidence by 3.83%. There was a notable decrease in IPD incidence in the serotypes unique to V116. In the serotypes included in PCV20 but not V116, the model did not predict a resurgence of IPD.

CONCLUSIONS

Projections revealed that in adults, V116 led to significantly greater reductions in IPD in the 65+ year-old population compared with PCV20 or PPSV23.

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

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.

Mathematical assessment of the impact of cohort vaccination on pneumococcal carriage and serotype replacement

Although pneumococcal vaccines are quite effective in reducing disease burden, factors such as imperfect vaccine efficacy and serotype replacement present an important challenge against realizing direct and herd protection benefits of the vaccines. In this study, a novel mathematical model is designed and used to describe the dynamics of two Streptococcus pneumoniae (SP) serotypes, in response to the introduction of a cohort vaccination program which targets one of the two serotypes. The model is fitted to a pediatric SP carriage prevalence data from Atlanta, GA. The model, which is rigorously analysed to investigate the existence and asymptotic stability properties of the associated equilibria (in addition to exploring conditions for competitive exclusion), is simulated to assess the impact of vaccination under different levels of serotype-specific competition and illustrate the phenomenon of serotype replacement. The calibrated model is used to forecast the carriage prevalence in the pediatric cohort over 30 years.

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

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^2$$\end{document}N2 altered susceptibilities to secondary infection that depend on colonizer-cocolonizer identities (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{ij}$$\end{document}Kij). 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.