No coexistence for free: neutral null models for multistrain pathogens

Recent approaches in computational modelling for controlling pathogen threats

In this review, we assess the status of computational modelling of pathogens. We focus on three disparate but interlinked research areas that produce models with very different spatial and temporal scope. First, we examine antimicrobial resistance (AMR). Many mechanisms of AMR are not well understood. As a result, it is hard to measure the current incidence of AMR, predict the future incidence, and design strategies to preserve existing antibiotic effectiveness. Next, we look at how to choose the finite number of bacterial strains that can be included in a vaccine. To do this, we need to understand what happens to vaccine and non-vaccine strains after vaccination programmes. Finally, we look at within-host modelling of antibody dynamics. The SARS-CoV-2 pandemic produced huge amounts of antibody data, prompting improvements in this area of modelling. We finish by discussing the challenges that persist in understanding these complex biological systems.

Modeling the transmission of antibiotic-resistant Enterobacterales in the community: A systematic review

BACKGROUND

Antibiotic-resistant Enterobacterales (ARE) are a public health threat worldwide. Dissemination of these opportunistic pathogens has been largely studied in hospitals. Despite high prevalence of asymptomatic colonization in the community in some regions of the world, less is known about ARE acquisition and spread in this setting. As explaining the community ARE dynamics has not been straightforward, mathematical models can be key to explore underlying phenomena and further evaluate the impact of interventions to curb ARE circulation outside of hospitals.

METHODS

We conducted a systematic review of mathematical modeling studies focusing on the transmission of AR-E in the community, excluding models only specific to hospitals. We extracted model features (population, setting), formalism (compartmental, individual-based), biological hypotheses (transmission, infection, antibiotic impact, resistant strain specificities) and main findings. We discussed additional mechanisms to be considered, open scientific questions, and most pressing data needs.

RESULTS

We identified 18 modeling studies focusing on the human transmission of ARE in the community (n=11) or in both community and hospital (n=7). Models aimed at (i) understanding mechanisms driving resistance dynamics; (ii) identifying and quantifying transmission routes; or (iii) evaluating public health interventions to reduce resistance. To overcome the difficulty of reproducing observed ARE dynamics in the community using the classical two-strains competition model, studies proposed to include mechanisms such as within-host strain competition or a strong host population structure. Studies inferring model parameters from longitudinal carriage data were mostly based on models considering the ARE strain only. They showed differences in ARE carriage duration depending on the acquisition mode: returning travelers have a significantly shorter carriage duration than discharged hospitalized patient or healthy individuals. Interestingly, predictions across models regarding the success of public health interventions to reduce ARE rates depended on pathogens, settings, and antibiotic resistance mechanisms. For E. coli, reducing person-to-person transmission in the community had a stronger effect than reducing antibiotic use in the community. For Klebsiella pneumoniae, reducing antibiotic use in hospitals was more efficient than reducing community use.

CONCLUSIONS

This study raises the limited number of modeling studies specifically addressing the transmission of ARE in the community. It highlights the need for model development and community-based data collection especially in low- and middle-income countries to better understand acquisition routes and their relative contribution to observed ARE levels. Such modeling will be critical to correctly design and evaluate public health interventions to control ARE transmission in the community and further reduce the associated infection burden.

A story of viral co-infection, co-transmission and co-feeding in ticks: how to compute an invasion reproduction number

With a single circulating vector-borne virus, the basic reproduction number incorporates contributions from tick-to-tick (co-feeding), tick-to-host and host-to-tick transmission routes. With two different circulating vector-borne viral strains, resident and invasive, and under the assumption that co-feeding is the only transmission route in a tick population, the invasion reproduction number depends on whether the model system of ordinary differential equations possesses the property of neutrality. We show that a simple model, with two populations of ticks infected with one strain, resident or invasive, and one population of co-infected ticks, does not have Alizon's neutrality property. We present model alternatives that are capable of representing the invasion potential of a novel strain by including populations of ticks dually infected with the same strain. The invasion reproduction number is analysed with the next-generation method and via numerical simulations.

Exploring factors shaping antibiotic resistance patterns in Streptococcus pneumoniae during the 2020 COVID-19 pandemic

Non-pharmaceutical interventions implemented to block SARS-CoV-2 transmission in early 2020 led to global reductions in the incidence of invasive pneumococcal disease (IPD). By contrast, most European countries reported an increase in antibiotic resistance among invasive Streptococcus pneumoniae isolates from 2019 to 2020, while an increasing number of studies reported stable pneumococcal carriage prevalence over the same period. To disentangle the impacts of the COVID-19 pandemic on pneumococcal epidemiology in the community setting, we propose a mathematical model formalizing simultaneous transmission of SARS-CoV-2 and antibiotic-sensitive and -resistant strains of S. pneumoniae. To test hypotheses underlying these trends five mechanisms were built into the model and examined: (1) a population-wide reduction of antibiotic prescriptions in the community, (2) lockdown effect on pneumococcal transmission, (3) a reduced risk of developing an IPD due to the absence of common respiratory viruses, (4) community azithromycin use in COVID-19 infected individuals, (5) and a longer carriage duration of antibiotic-resistant pneumococcal strains. Among 31 possible pandemic scenarios involving mechanisms individually or in combination, model simulations surprisingly identified only two scenarios that reproduced the reported trends in the general population. They included factors (1), (3), and (4). These scenarios replicated a nearly 50% reduction in annual IPD, and an increase in antibiotic resistance from 20% to 22%, all while maintaining a relatively stable pneumococcal carriage. Exploring further, higher SARS-CoV-2 R0 values and synergistic within-host virus-bacteria interaction mechanisms could have additionally contributed to the observed antibiotic resistance increase. Our work demonstrates the utility of the mathematical modeling approach in unraveling the complex effects of the COVID-19 pandemic responses on AMR dynamics.

Recombinant transmissible vaccines will be intrinsically contained despite the ability to superinfect

INTRODUCTION

Transmissible vaccines offer a novel approach to suppressing viruses in wildlife populations, with possible applications against viruses that infect humans as zoonoses - Lassa, Ebola, rabies. To ensure safety, current designs propose a recombinant vector platform in which the vector is isolated from the target wildlife population. Because using an endemic vector creates the potential for preexisting immunity to block vaccine transmission, these designs focus on vector viruses capable of superinfection, spreading throughout the host population following vaccination of few individuals.

AREAS COVERED

We present original theoretical arguments that, regardless of its R0 value, a recombinant vaccine using a superinfecting vector is not expected to expand its active infection coverage when released into a wildlife population that already carries the vector. However, if superinfection occurs at a high rate such that individuals are repeatedly infected throughout their lives, the immunity footprint in the population can be high despite a low incidence of active vaccine infections. Yet we provide reasons that the above expectation is optimistic.

EXPERT OPINION

High vaccine coverage will typically require repeated releases or release into a population lacking the vector, but careful attention to vector choice and vaccine engineering should also help improve transmissible vaccine utility.

Closing the gap in the Janzen-Connell hypothesis: What determines pathogen diversity?

The high tree diversity in tropical forests has long been a puzzle to ecologists. In the 1970s, Janzen and Connell proposed that tree species (hosts) coexist due to the stabilizing actions of specialized enemies. This Janzen-Connell hypothesis was subsequently supported by theoretical studies. Yet, such studies have taken the presence of specialized pathogens for granted, overlooking that pathogen coexistence also requires an explanation. Moreover, stable ecological coexistence does not necessarily imply evolutionary stability. What are the conditions that allow Janzen-Connell effects to evolve? We link theory from community ecology, evolutionary biology and epidemiology to tackle this question, structuring our approach around five theoretical frameworks. Phenomenological Lotka-Volterra competition models provide the most basic framework, which can be restructured to include (single- or multi-)pathogen dynamics. This ecological foundation can be extended to include pathogen evolution. Hosts, of course, may also evolve, and we introduce a coevolutionary model, showing that host-pathogen coevolution can lead to highly diverse systems. Our work unpacks the assumptions underpinning Janzen-Connell and places theoretical bounds on pathogen and host ecology and evolution. The five theoretical frameworks taken together provide a stronger theoretical basis for Janzen-Connell, delivering a wider lens that can yield important insights into the maintenance of diversity in these increasingly threatened systems.

Pneumococcal population dynamics: Investigating vaccine-induced changes through multiscale modelling

The mechanisms behind vaccine-induced strain replacement in the pneumococcus remain poorly understood. There is emerging evidence that distinct pneumococcal lineages can co-colonise for significant time periods, and that novel recombinants can readily emerge during natural colonisation. Despite this, patterns of post-vaccine replacement are indicative of competition between specific lineages. Here, we develop a multiscale transmission model to investigate explicitly how within host dynamics shape observed ecological patterns, both pre- and post-vaccination. Our model framework explores competition between and within strains defined by distinct antigenic, metabolic and resistance profiles. We allow for strains to freely co-colonise and recombine within hosts, and consider how each of these types may contribute to a strain's overall fitness. Our results suggest that antigenic and resistance profiles are key drivers of post-vaccine success.

Quasi-neutral dynamics in a coinfection system with N strains and asymmetries along multiple traits

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 feedback between traits manifested in infection and co-infection, the study of such systems remains a challenge. In the case where strains are similar (quasi-neutrality assumption), we can model trait variation as perturbations in parameters, which simplifies analysis. Here, we apply singular perturbation theory to many strain parameters simultaneously and advance analytically to obtain their explicit collective dynamics. We consider and study such a quasi-neutral model of susceptible-infected-susceptible (SIS) dynamics among N strains, which vary in 5 fitness dimensions: transmissibility, clearance rate of single- and co-infection, transmission probability from mixed coinfection, and co-colonization vulnerability factors encompassing cooperation and competition. This quasi-neutral system is analyzed with a singular perturbation method through an appropriate slow-fast decomposition. The fast dynamics correspond to the embedded neutral system, while the slow dynamics are governed by an N-dimensional replicator equation, describing the time evolution of strain frequencies. The coefficients of this replicator system are pairwise invasion fitnesses between strains, which, in our model, are an explicit weighted sum of pairwise asymmetries along all trait dimensions. Remarkably these weights depend only on the parameters of the neutral system. Such model reduction highlights the centrality of the neutral system for dynamics at the edge of neutrality and exposes critical features for the maintenance of diversity.

Interplay between strain fitness and transmission frequency determines prevalence of antimicrobial resistance

The steep rise of infections caused by bacteria that are resistant to antimicrobial agents threatens global health. However, the association between antimicrobial use and the prevalence of resistance is not straightforward. Therefore, it is necessary to quantify the importance of additional factors that affect this relationship. We theoretically explore how the prevalence of resistance is affected by the combination of three factors: antimicrobial use, bacterial transmission, and fitness cost of resistance. We present a model that combines within-host, between-hosts and between-populations dynamics, built upon the competitive Lotka-Volterra equations. We developed the model in a manner that allows future experimental validation of the findings with single isolates in the laboratory. Each host may carry two strains (susceptible and resistant) that represent the host’s commensal microbiome and are not the target of the antimicrobial treatment. The model simulates a population of hosts who are treated periodically with antibiotics and transmit bacteria to each other. We show that bacterial transmission results in strain co-existence. Transmission disseminates resistant bacteria in the population, increasing the levels of resistance. Counterintuitively, when the cost of resistance is low, high transmission frequencies reduce resistance prevalence. Transmission between host populations leads to more similar resistance levels, increasing the susceptibility of the population with higher antimicrobial use. Overall, our results indicate that the interplay between bacterial transmission and strain fitness affects the prevalence of resistance in a non-linear way. We then place our results within the context of ecological theory, particularly on temporal niche partitioning and metapopulation rescue, and we formulate testable experimental predictions for future research.

The potential of genomics for infectious disease forecasting

Genomic technologies have led to tremendous gains in understanding how pathogens function, evolve and interact. Pathogen diversity is now measurable at high precision and resolution, in part because over the past decade, sequencing technologies have increased in speed and capacity, at decreased cost. Alongside this, the use of models that can forecast emergence and size of infectious disease outbreaks has risen, highlighted by the coronavirus disease 2019 pandemic but also due to modelling advances that allow for rapid estimates in emerging outbreaks to inform monitoring, coordination and resource deployment. However, genomics studies have remained largely retrospective. While they contain high-resolution views of pathogen diversification and evolution in the context of selection, they are often not aligned with designing interventions. This is a missed opportunity because pathogen diversification is at the core of the most pressing infectious public health challenges, and interventions need to take the mechanisms of virulence and understanding of pathogen diversification into account. In this Perspective, we assess these converging fields, discuss current challenges facing both surveillance specialists and modellers who want to harness genomic data, and propose next steps for integrating longitudinally sampled genomic data with statistical learning and interpretable modelling to make reliable predictions into the future.

Ecological and evolutionary dynamics of multi-strain RNA viruses

Potential interactions among co-circulating viral strains in host populations are often overlooked in the study of virus transmission. However, these interactions probably shape transmission dynamics by influencing host immune responses or altering the relative fitness among co-circulating strains. In this Review, we describe multi-strain dynamics from ecological and evolutionary perspectives, outline scales in which multi-strain dynamics occur and summarize important immunological, phylogenetic and mathematical modelling approaches used to quantify interactions among strains. We also discuss how host-pathogen interactions influence the co-circulation of pathogens. Finally, we highlight outstanding questions and knowledge gaps in the current theory and study of ecological and evolutionary dynamics of multi-strain viruses.

Modeling cellular co-infection and reassortment of bluetongue virus in Culicoides midges

When related segmented RNA viruses co-infect a single cell, viral reassortment can occur, potentially leading to new strains with pandemic potential. One virus capable of reassortment is bluetongue virus (BTV), which causes substantial health impacts in ruminants and is transmitted via Culicoides midges. Because midges can become co-infected by feeding on multiple different host species and remain infected for their entire life span, there is a high potential for reassortment to occur. Once a midge is co-infected, additional barriers must be crossed for a reassortant virus to emerge, such as cellular co-infection and dissemination of reassortant viruses to the salivary glands. We developed three mathematical models of within-midge BTV dynamics of increasing complexity, allowing us to explore the conditions leading to the emergence of reassortant viruses. In confronting the simplest model with published data, we estimate that the average life span of a bluetongue virion in the midge midgut is about 6 h, a key determinant of establishing a successful infection. Examination of the full model, which permits cellular co-infection and reassortment, shows that small differences in fitness of the two infecting strains can have a large impact on the frequency with which reassortant virions are observed. This is consistent with experimental co-infection studies with BTV strains with different relative fitnesses that did not produce reassortant progeny. Our models also highlight several gaps in existing data that would allow us to elucidate these dynamics in more detail, in particular the times it takes the virus to disseminate to different tissues, and measurements of viral load and reassortant frequency at different temperatures.

Quantifying mechanisms of coexistence in disease ecology

Pathogen coexistence depends on ecological processes operating at both within and between-host scales, making it difficult to quantify which processes may promote or prevent coexistence. Here, we propose that adapting modern coexistence theory-traditionally applied in plant communities-to pathogen systems provides an exciting approach for examining mechanisms of coexistence operating across different spatial scales. We first overview modern coexistence theory and its mechanistic decomposition; we subsequently adapt the framework to quantify how spatial variation in pathogen density, host resources and immunity, and their interaction may promote pathogen coexistence. We apply this derivation to an example two pathogen, multi-scale model comparing two scenarios with generalist and strain-specific immunity: one with demographic equivalency among pathogens and one with demographic trade-offs among pathogens. We then show how host-pathogen feedbacks generate spatial heterogeneity that promote pathogen coexistence and decompose those mechanisms to quantify how each spatial heterogeneity contributes to that coexistence. Specifically, coexistence of demographically equivalent pathogens occurs due to spatial variation in host resources, immune responses, and pathogen aggregation. With a competition-colonization trade-off, the superior colonizer requires spatial heterogeneity to coexist, whereas the superior competitor does not. Finally, we suggest ways forward for linking theory and empirical tests of coexistence in disease systems.

Uses of mathematical modeling to estimate the impact of mass drug administration of antibiotics on antimicrobial resistance within and between communities

BACKGROUND

Antibiotics are a key part of modern healthcare, but their use has downsides, including selecting for antibiotic resistance, both in the individuals treated with antibiotics and in the community at large. When evaluating the benefits and costs of mass administration of azithromycin to reduce childhood mortality, effects of antibiotic use on antibiotic resistance are important but difficult to measure, especially when evaluating resistance that "spills over" from antibiotic-treated individuals to other members of their community. The aim of this scoping review was to identify how the existing literature on antibiotic resistance modeling could be better leveraged to understand the effect of mass drug administration (MDA) on antibiotic resistance.

MAIN TEXT

Mathematical models of antibiotic use and resistance may be useful for estimating the expected effects of different MDA implementations on different populations, as well as aiding interpretation of existing data and guiding future experimental design. Here, strengths and limitations of models of antibiotic resistance are reviewed, and possible applications of those models in the context of mass drug administration with azithromycin are discussed.

CONCLUSIONS

Statistical models of antibiotic use and resistance may provide robust and relevant estimates of the possible effects of MDA on resistance. Mechanistic models of resistance, while able to more precisely estimate the effects of different implementations of MDA on resistance, may require more data from MDA trials to be accurately parameterized.

Modelling the effect of within-host dynamics on the diversity of a multi-strain pathogen

Multi-strain pathogens such as Group A Streptococcus, Streptococcus pneumoniae, and Staphylococcus aureus cause millions of infections each year with a substantial health burden. Control of multi-strain pathogens can be complicated by the high strain diversity often observed in endemic settings. It is not well understood how high strain diversity is maintained in populations, given that they compete with each other both directly (within an individual host) and indirectly (via host immunity). Previous modelling studies have investigated how indirect competition affects the prevalence and diversity of strains. However, these studies often make simplifying assumptions about the direct competition that occurs within hosts. Currently, little data is available to validate these assumptions, hence there is a need to clarify how sensitive model outputs are to these assumptions. In this study, we compare the dynamics of multi-strain pathogens under different assumptions about direct competition between strains using an agent-based model. We find that the assumptions made about direct competition can affect the epidemiological dynamics, particularly when there is no long-term immunity following infections and a low rate of importation of non-circulating strains. Our results suggest that while direct and indirect competition can each decrease strain diversity when they act in isolation, they may increase strain diversity when they act together. This finding highlights the importance of examining sensitivity to assumptions about strain competition. In particular, omitting consideration of direct competition can lead to inaccurate estimates of the likely effectiveness of control strategies as changes in strain diversity shift the level of direct strain competition.

Does plasmid-based beta-lactam resistance increase E. coli infections: Modelling addition and replacement mechanisms

Infections caused by antibiotic-resistant bacteria have become more prevalent during past decades. Yet, it is unknown whether such infections occur in addition to infections with antibiotic-susceptible bacteria, thereby increasing the incidence of infections, or whether they replace such infections, leaving the total incidence unaffected. Observational longitudinal studies cannot separate both mechanisms. Using plasmid-based beta-lactam resistant E. coli as example we applied mathematical modelling to investigate whether seven biological mechanisms would lead to replacement or addition of infections. We use a mathematical neutral null model of individuals colonized with susceptible and/or resistant E. coli, with two mechanisms implying a fitness cost, i.e., increased clearance and decreased growth of resistant strains, and five mechanisms benefitting resistance, i.e., 1) increased virulence, 2) increased transmission, 3) decreased clearance of resistant strains, 4) increased rate of horizontal plasmid transfer, and 5) increased clearance of susceptible E. coli due to antibiotics. Each mechanism is modelled separately to estimate addition to or replacement of antibiotic-susceptible infections. Fitness costs cause resistant strains to die out if other strain characteristics are maintained equal. Under the assumptions tested, increased virulence is the only mechanism that increases the total number of infections. Other benefits of resistance lead to replacement of susceptible infections without changing the total number of infections. As there is no biological evidence that plasmid-based beta-lactam resistance increases virulence, these findings suggest that the burden of disease is determined by attributable effects of resistance rather than by an increase in the number of infections.

Plasmid co-infection: linking biological mechanisms to ecological and evolutionary dynamics

As infectious agents of bacteria and vehicles of horizontal gene transfer, plasmids play a key role in bacterial ecology and evolution. Plasmid dynamics are shaped not only by plasmid-host interactions but also by ecological interactions between plasmid variants. These interactions are complex: plasmids can co-infect the same cell and the consequences for the co-resident plasmid can be either beneficial or detrimental. Many of the biological processes that govern plasmid co-infection-from systems that exclude infection by other plasmids to interactions in the regulation of plasmid copy number-are well characterized at a mechanistic level. Modelling plays a central role in translating such mechanistic insights into predictions about plasmid dynamics and the impact of these dynamics on bacterial evolution. Theoretical work in evolutionary epidemiology has shown that formulating models of co-infection is not trivial, as some modelling choices can introduce unintended ecological assumptions. Here, we review how the biological processes that govern co-infection can be represented in a mathematical model, discuss potential modelling pitfalls, and analyse this model to provide general insights into how co-infection impacts ecological and evolutionary outcomes. In particular, we demonstrate how beneficial and detrimental effects of co-infection give rise to frequency-dependent selection on plasmid variants. This article is part of the theme issue 'The secret lives of microbial mobile genetic elements'.

Challenges in modeling the emergence of novel pathogens

The emergence of infectious agents with pandemic potential present scientific challenges from detection to data interpretation to understanding determinants of risk and forecasts. Mathematical models could play an essential role in how we prepare for future emergent pathogens. Here, we describe core directions for expansion of the existing tools and knowledge base, including: using mathematical models to identify critical directions and paths for strengthening data collection to detect and respond to outbreaks of novel pathogens; expanding basic theory to identify infectious agents and contexts that present the greatest risks, over both the short and longer term; by strengthening estimation tools that make the most use of the likely range and uncertainties in existing data; and by ensuring modelling applications are carefully communicated and developed within diverse and equitable collaborations for increased public health benefit.

Modeling the effect of vaccination on selection for antibiotic resistance in Streptococcus pneumonia e

Vaccines against bacterial pathogens can protect recipients from becoming infected with potentially antibiotic-resistant pathogens. However, by altering the selective balance between antibiotic-sensitive and antibiotic-resistant bacterial strains, vaccines may also suppress-or spread-antibiotic resistance among unvaccinated individuals. Predicting the outcome of vaccination requires knowing what drives selection for drug-resistant bacterial pathogens and what maintains the circulation of both antibiotic-sensitive and antibiotic-resistant strains of bacteria. To address this question, we used mathematical modeling and data from 2007 on penicillin consumption and penicillin nonsusceptibility in Streptococcus pneumoniae (pneumococcus) invasive isolates from 27 European countries. We show that the frequency of penicillin resistance in S. pneumoniae can be explained by between-host diversity in antibiotic use, heritable diversity in pneumococcal carriage duration, or frequency-dependent selection brought about by within-host competition between antibiotic-resistant and antibiotic-sensitive S. pneumoniae strains. We used our calibrated models to predict the impact of non-serotype-specific pneumococcal vaccination upon the prevalence of S. pneumoniae carriage, incidence of disease, and frequency of S. pneumoniae antibiotic resistance. We found that the relative strength and directionality of competition between drug-resistant and drug-sensitive pneumococcal strains was the most important determinant of whether vaccination would promote, inhibit, or have little effect upon the evolution of antibiotic resistance. Last, we show that country-specific differences in pathogen transmission substantially altered the predicted impact of vaccination, highlighting that policies for managing antibiotic resistance with vaccines must be tailored to a specific pathogen and setting.

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.

Understanding the evolution of multiple drug resistance in structured populations

The evolution of multidrug resistance (MDR) is a pressing public health concern. Yet many aspects, such as the role played by population structure, remain poorly understood. Here, we argue that studying MDR evolution by focusing upon the dynamical equations for linkage disequilibrium (LD) can greatly simplify the calculations, generate more insight, and provide a unified framework for understanding the role of population structure. We demonstrate how a general epidemiological model of MDR evolution can be recast in terms of the LD equations. These equations reveal how the different forces generating and propagating LD operate in a dynamical setting at both the population and metapopulation levels. We then apply these insights to show how the LD perspective: (i) explains equilibrium patterns of MDR, (ii) provides a simple interpretative framework for transient evolutionary dynamics, and (iii) can be used to assess the consequences of different drug prescription strategies for MDR evolution.

Host Specialisation, Immune Cross-Reaction and the Composition of Communities of Co-circulating Borrelia Strains

We use mathematical modelling to examine how microbial strain communities are structured by the host specialisation traits and antigenic relationships of their members. The model is quite general and broadly applicable, but we focus on Borrelia burgdorferi, the Lyme disease bacterium, transmitted by ticks to mice and birds. In this system, host specialisation driven by the evasion of innate immunity has been linked to multiple niche polymorphism, while antigenic differentiation driven by the evasion of adaptive immunity has been linked to negative frequency dependence. Our model is composed of two host species, one vector, and multiple co-circulating pathogen strains that vary in their host specificity and their antigenic distances from one another. We explore the conditions required to maintain pathogen diversity. We show that the combination of host specificity and antigenic differentiation creates an intricate niche structure. Unequivocal rules that relate the stability of a strain community directly to the trait composition of its members are elusive. However, broad patterns are evident. When antigenic differentiation is weak, stable communities are typically composed entirely of generalists that can exploit either host species equally well. As antigenic differentiation increases, more diverse stable communities emerge, typically around trait compositions of generalists, generalists and very similar specialists, and specialists roughly balanced between the two host species.

Pneumococcal Competition Modulates Antibiotic Resistance in the Pre-Vaccination Era: A Modelling Study

The ongoing emergence of antibiotic resistant strains and high frequencies of antibiotic resistance of Streptococcus pneumoniae poses a major public health challenge. How and which ecological and evolutionary mechanisms maintain the coexistence of antibiotic resistant and susceptible strains remains largely an open question. We developed an individual-based, stochastic model expanding on a previous pneumococci modelling framework. We explore how between- and within-host mechanisms of competition can sustain observed levels of resistance to antibiotics in the pre-vaccination era. Our framework considers that within-host competition for co-colonization between resistant and susceptible strains can arise via pre-existing immunity (immunological competition) or intrinsic fitness differences due to resistance costs (ecological competition). We find that beyond stochasticity, population structure or movement, competition at the within-host level can explain observed resistance frequencies. We compare our simulation results to pneumococcal antibiotic resistance data in the European region using approximate Bayesian computation. Our results demonstrate that ecological competition for co-colonization can explain the variation in co-existence of resistant and susceptible pneumococci observed in the pre-vaccination era. Furthermore, we show that within-host pneumococcal competition can facilitate the maintenance of resistance in the pre-vaccination era. Accounting for these competition-related components of pneumococcal dynamics can improve our understanding of drivers for the emergence and maintenance of antibiotic resistance in pneumococci.

Factors favouring the evolution of multidrug resistance in bacteria

The evolution of multidrug antibiotic resistance in commensal bacteria is an important public health concern. Commensal bacteria such as Escherichia coli, Streptococcus pneumoniae or Staphylococcus aureus, are also opportunistic pathogens causing a large fraction of the community-acquired and hospital-acquired bacterial infections. Multidrug resistance (MDR) makes these infections harder to treat with antibiotics and may thus cause substantial additional morbidity and mortality. Here, we develop an evolutionary epidemiology model to identify the factors favouring the evolution of MDR in commensal bacteria. The model describes the evolution of antibiotic resistance in a commensal bacterial species evolving in a host population subjected to multiple antibiotic treatments. We combine statistical analysis of a large number of simulations and mathematical analysis to understand the model behaviour. We find that MDR evolves more readily when it is less costly than expected from the combinations of single resistances (positive epistasis). MDR frequently evolves when bacteria are in contact with multiple drugs prescribed in the host population, even if individual hosts are only treated with a single drug at a time. MDR is favoured when the host population is structured in different classes that vary in their rates of antibiotic treatment. However, under most circumstances, recombination between loci involved in resistance does not meaningfully affect the equilibrium frequency of MDR. Together, these results suggest that MDR is a frequent evolutionary outcome in commensal bacteria that encounter the variety of antibiotics prescribed in the host population. A better characterization of the variability in antibiotic use across the host population (e.g. across age classes or geographical location) would help predict which MDR genotypes will most readily evolve.

Population structure across scales facilitates coexistence and spatial heterogeneity of antibiotic-resistant infections

Antibiotic-resistant infections are a growing threat to human health, but basic features of the eco-evolutionary dynamics remain unexplained. Most prominently, there is no clear mechanism for the long-term coexistence of both drug-sensitive and resistant strains at intermediate levels, a ubiquitous pattern seen in surveillance data. Here we show that accounting for structured or spatially-heterogeneous host populations and variability in antibiotic consumption can lead to persistent coexistence over a wide range of treatment coverages, drug efficacies, costs of resistance, and mixing patterns. Moreover, this mechanism can explain other puzzling spatiotemporal features of drug-resistance epidemiology that have received less attention, such as large differences in the prevalence of resistance between geographical regions with similar antibiotic consumption or that neighbor one another. We find that the same amount of antibiotic use can lead to very different levels of resistance depending on how treatment is distributed in a transmission network. We also identify parameter regimes in which population structure alone cannot support coexistence, suggesting the need for other mechanisms to explain the epidemiology of antibiotic resistance. Our analysis identifies key features of host population structure that can be used to assess resistance risk and highlights the need to include spatial or demographic heterogeneity in models to guide resistance management.

Estimating the contribution of different age strata to vaccine serotype pneumococcal transmission in the pre vaccine era: a modelling study

BACKGROUND

Herd protection through interruption of transmission has contributed greatly to the impact of pneumococcal conjugate vaccines (PCVs) and may enable the use of cost-saving reduced dose schedules. To aid PCV age targeting to achieve herd protection, we estimated which population age groups contribute most to vaccine serotype (VT) pneumococcal transmission.

METHODS

We used transmission dynamic models to mirror pre-PCV epidemiology in England and Wales, Finland, Kilifi in Kenya and Nha Trang in Vietnam where data on carriage prevalence in infants, pre-school and school-aged children and adults as well as social contact patterns was available. We used Markov Chain Monte Carlo methods to fit the models and then extracted the per capita and population-based contribution of different age groups to VT transmission.

RESULTS

We estimated that in all settings, < 1-year-old infants cause very frequent secondary vaccine type pneumococcal infections per capita. However, 1-5-year-old children have the much higher contribution to the force of infection at 51% (28, 73), 40% (27, 59), 37% (28, 48) and 67% (41, 86) of the total infection pressure in E&W, Finland, Kilifi and Nha Trang, respectively. Unlike the other settings, school-aged children in Kilifi were the dominant source for VT infections with 42% (29, 54) of all infections caused. Similarly, we estimated that the main source of VT infections in infants are pre-school children and that in Kilifi 39% (28, 51) of VT infant infections stem from school-aged children whereas this was below 15% in the other settings.

CONCLUSION

Vaccine protection of pre-school children is key for PCV herd immunity. However, in high transmission settings, school-aged children may substantially contribute to transmission and likely have waned much of their PCV protection under currently recommended schedules.

Systematic comparison of coexistence in models of drug-sensitive and drug-resistant pathogen strains

A number of mathematical models have recently been proposed to explain empirical trends of pathogen diversity. In particular, long-term coexistence of both drug-sensitive and drug-resistant variants of a single pathogen is something of a mystery, given that simple models of pathogens competing for the same ecological niche predict competitive exclusion, and more complex models admitting coexistence require assumptions that may not be justified. Coinfection is among the candidate mechanisms to generate coexistence, as it occurs in many pathogens and provides the opportunity for strains to interact directly. Recently, coinfection and competitive release have been described as creating a form of negative frequency-dependent selection that promotes coexistence, and a range of models containing coinfection have been proposed as having generic stable coexistence of multiple strains. This abundance of new models presents the challenge of comparison and interpretation. To this end, we describe a dimensionless quantity that can be used to compare the amount of coexistence generated by different models. We focus on models that include coinfection, although this framework could be generalized to a larger class of structured models.

Impact of Antimicrobial Treatment for Acute Otitis Media on Carriage Dynamics of Penicillin-Susceptible and Penicillin-Nonsusceptible Streptococcus pneumoniae

Background

Despite concerns that antimicrobial treatment of prevalent infections may select for drug-resistant bacteria, the effects of antimicrobial treatment on colonization dynamics have not been well quantified.

Methods

We measured impacts of antimicrobial treatment on nasopharyngeal carriage of penicillin-susceptible Streptococcus pneumoniae (PSSP) and penicillin-nonsusceptible (PNSP) lineages at the end of treatment and 15, 30, and 60 days after treatment in a previously conducted randomized, double-blinded, placebo-controlled trial of amoxicillin-clavulanate for stringently defined acute otitis media.

Results

In intention-to-treat analyses, immediate treatment with amoxicillin-clavulanate reduced PSSP carriage prevalence by 88% (95% confidence interval [CI], 76%-96%) at the end of treatment and by 27% (-3%-49%) after 60 days but did not alter PNSP carriage prevalence. By the end of treatment, 7% of children who carried PSSP at enrollment remained colonized in the amoxicillin-clavulanate arm, compared with 61% of PSSP carriers who received placebo; impacts of amoxicillin-clavulanate persisted at least 60 days after treatment among children who carried PSSP at enrollment. Amoxicillin-clavulanate therapy reduced PSSP acquisition by >80% over 15 days. Among children who carried PNSP at enrollment, no impacts on carriage prevalence of S. pneumoniae, PSSP, or PNSP were evident at follow-up visits.

Conclusions

Although the absolute risk of carrying PNSP was unaffected by treatment, antimicrobial therapy conferred a selective impact on colonizing pneumococci by accelerating clearance and delaying acquisition of PSSP.

The evolution of antibiotic resistance in a structured host population

The evolution of antibiotic resistance in opportunistic pathogens such as Streptococcus pneumoniae, Escherichia coli or Staphylococcus aureus is a major public health problem, as infection with resistant strains leads to prolonged hospital stay and increased risk of death. Here, we develop a new model of the evolution of antibiotic resistance in a commensal bacterial population adapting to a heterogeneous host population composed of untreated and treated hosts, and structured in different host classes with different antibiotic use. Examples of host classes include age groups and geographic locations. Explicitly modelling the antibiotic treatment reveals that the emergence of a resistant strain is favoured by more frequent but shorter antibiotic courses, and by higher transmission rates. In addition, in a structured host population, localized transmission in host classes promotes both local adaptation of the bacterial population and the global maintenance of coexistence between sensitive and resistant strains. When transmission rates are heterogeneous across host classes, resistant strains evolve more readily in core groups of transmission. These findings have implications for the better management of antibiotic resistance: reducing the rate at which individuals receive antibiotics is more effective to reduce resistance than reducing the duration of treatment. Reducing the rate of treatment in a targeted class of the host population allows greater reduction in resistance, but determining which class to target is difficult in practice.

The effects of individual nonheritable variation on fitness estimation and coexistence

Demographic theory and data have emphasized that nonheritable variation in individual frailty enables selection within cohorts, affecting the dynamics of a population while being invisible to its evolution. Here, we include the component of individual variation in longevity or viability which is nonheritable in simple bacterial growth models and explore its ecological and evolutionary impacts. First, we find that this variation produces consistent trends in longevity differences between bacterial genotypes when measured across stress gradients. Given that direct measurements of longevity are inevitably biased due to the presence of this variation and ongoing selection, we propose the use of the trend itself for obtaining more exact inferences of genotypic fitness. Second, we show how species or strain coexistence can be enabled by nonheritable variation in longevity or viability. These general conclusions are likely to extend beyond bacterial systems.

Host contact dynamics shapes richness and dominance of pathogen strains

The interaction among multiple microbial strains affects the spread of infectious diseases and the efficacy of interventions. Genomic tools have made it increasingly easy to observe pathogenic strains diversity, but the best interpretation of such diversity has remained difficult because of relationships with host and environmental factors. Here, we focus on host-to-host contact behavior and study how it changes populations of pathogens in a minimal model of multi-strain interaction. We simulated a population of identical strains competing by mutual exclusion and spreading on a dynamical network of hosts according to a stochastic susceptible-infectious-susceptible model. We computed ecological indicators of diversity and dominance in strain populations for a collection of networks illustrating various properties found in real-world examples. Heterogeneities in the number of contacts among hosts were found to reduce diversity and increase dominance by making the repartition of strains among infected hosts more uneven, while strong community structure among hosts increased strain diversity. We found that the introduction of strains associated with hosts entering and leaving the system led to the highest pathogenic richness at intermediate turnover levels. These results were finally illustrated using the spread of Staphylococcus aureus in a long-term health-care facility where close proximity interactions and strain carriage were collected simultaneously. We found that network structural and temporal properties could account for a large part of the variability observed in strain diversity. These results show how stochasticity and network structure affect the population ecology of pathogens and warn against interpreting observations as unambiguous evidence of epidemiological differences between strains.

Resistance diagnostics as a public health tool to combat antibiotic resistance: A model-based evaluation

Rapid point-of-care resistance diagnostics (POC-RD) are a key tool in the fight against antibiotic resistance. By tailoring drug choice to infection genotype, doctors can improve treatment efficacy while limiting costs of inappropriate antibiotic prescription. Here, we combine epidemiological theory and data to assess the potential of resistance diagnostics (RD) innovations in a public health context, as a means to limit or even reverse selection for antibiotic resistance. POC-RD can be used to impose a nonbiological fitness cost on resistant strains by enabling diagnostic-informed treatment and targeted interventions that reduce resistant strains' opportunities for transmission. We assess this diagnostic-imposed fitness cost in the context of a spectrum of bacterial population biologies and find that POC-RD have a greater potential against obligate pathogens than opportunistic pathogens already subject to selection under "bystander" antibiotic exposure during asymptomatic carriage (e.g., the pneumococcus). We close by generalizing the notion of RD-informed strategies to incorporate carriage surveillance information and illustrate that coupling transmission-control interventions to the discovery of resistant strains in carriage can potentially select against resistance in a broad range of opportunistic pathogens.

Emerging Challenges and Opportunities in Infectious Disease Epidemiology

Much of the intellectual tradition of modern epidemiology stems from efforts to understand and combat chronic diseases persisting through the 20th century epidemiologic transition of countries such as the United States and United Kingdom. After decades of relative obscurity, infectious disease epidemiology has undergone an intellectual rebirth in recent years amid increasing recognition of the threat posed by both new and familiar pathogens. Here, we review the emerging coalescence of infectious disease epidemiology around a core set of study designs and statistical methods bearing little resemblance to the chronic disease epidemiology toolkit. We offer our outlook on challenges and opportunities facing the field, including the integration of novel molecular and digital information sources into disease surveillance, the assimilation of such data into models of pathogen spread, and the increasing contribution of models to public health practice. We next consider emerging paradigms in causal inference for infectious diseases, ranging from approaches to evaluating vaccines and antimicrobial therapies to the task of ascribing clinical syndromes to etiologic microorganisms, an age-old problem transformed by our increasing ability to characterize human-associated microbiota. These areas represent an increasingly important component of epidemiology training programs for future generations of researchers and practitioners.

Herd immunity alters the conditions for performing dose schedule comparisons: an individual-based model of pneumococcal carriage

Background

There is great interest in the use of reduced dosing schedules for pneumococcal conjugate vaccines, a strategy premised on maintaining an acceptable level of protection against disease and carriage of the organism. We asked about the practicality of measuring differential effectiveness against carriage in a population with and without widespread use of the vaccine for infants.

Methods

We adapted an existing transmission-dynamic, individual-based stochastic model fitted to the prevaccine epidemiology of pneumococcal carriage in the United States, and compared the observed vaccine-type carriage prevalence in different arms of a simulated trial with one, two, or three infant doses plus a 12-month booster. Using these simulations, we calculated vaccine efficacy that would be estimated at different times post-enrollment in the trial and calculated required sample sizes to see a difference in carriage prevalence.

Results

In a pneumococcal conjugate vaccine (PCV)-naïve population, the difference in vaccine-type (VT) pneumococcal carriage prevalence between trial arms was less than 7% and varied with sampling time. In a population already receiving routine PCV administration, VT pneumococcal prevalence is nearly indistinguishable between trial arms. Relative efficacy of different dosing schedules was strongly dependent on the time between enrollment and sampling, with maximal prevalence differences reached 1–3 years post-enrollment. Moreover, vaccine efficacy estimates were typically slightly higher in trials in communities already receiving vaccination. Despite this, much larger sample sizes—by more than an order of magnitude—are required for a vaccine trial conducted in a population receiving routine PCV administration as compared to in a PCV-naïve population.

Conclusions

These findings highlight some underappreciated aspects of clinical trials of pneumococcal conjugate vaccines with efficacy endpoints, such as the context- and time-dependence of efficacy estimates. They support the wisdom of conducting comparative dose schedule trials of conjugate vaccine effects on carriage in vaccine-naïve populations.

Electronic supplementary material

The online version of this article (10.1186/s12879-019-3833-6) contains supplementary material, which is available to authorized users.

Within-host dynamics shape antibiotic resistance in commensal bacteria

The spread of antibiotic resistance, a major threat to human health, is poorly understood. Simple population-level models of bacterial transmission predict that above a certain rate of antibiotic consumption in a population, resistant bacteria should completely eliminate non-resistant strains, while below this threshold they should be unable to persist at all. This prediction stands at odds with empirical evidence showing that resistant and non-resistant strains coexist stably over a wide range of antibiotic consumption rates. Not knowing what drives this long-term coexistence is a barrier to developing evidence-based strategies for managing the spread of resistance. Here, we argue that competition between resistant and sensitive pathogens within individual hosts gives resistant pathogens a relative fitness benefit when they are rare, promoting coexistence between strains at the population level. To test this hypothesis, we embed mechanistically explicit within-host dynamics in a structurally neutral pathogen transmission model. Doing so allows us to reproduce patterns of resistance observed in the opportunistic pathogens Escherichia coli and Streptococcus pneumoniae across European countries and to identify factors that may shape resistance evolution in bacteria by modulating the intensity and outcomes of within-host competition.

Evolutionary epidemiology models to predict the dynamics of antibiotic resistance

The evolution of resistance to antibiotics is a major public health problem and an example of rapid adaptation under natural selection by antibiotics. The dynamics of antibiotic resistance within and between hosts can be understood in the light of mathematical models that describe the epidemiology and evolution of the bacterial population. "Between-host" models describe the spread of resistance in the host community, and in more specific settings such as hospitalized hosts (treated by antibiotics at a high rate), or farm animals. These models make predictions on the best strategies to limit the spread of resistance, such as reducing transmission or adapting the prescription of several antibiotics. Models can be fitted to epidemiological data in the context of intensive care units or hospitals to predict the impact of interventions on resistance. It has proven harder to explain the dynamics of resistance in the community at large, in particular because models often do not reproduce the observed coexistence of drug-sensitive and drug-resistant strains. "Within-host" models describe the evolution of resistance within the treated host. They show that the risk of resistance emergence is maximal at an intermediate antibiotic dose, and some models successfully explain experimental data. New models that include the complex host population structure, the interaction between resistance-determining loci and other loci, or integrating the within- and between-host levels will allow better interpretation of epidemiological and genomic data from common pathogens and better prediction of the evolution of resistance.

Inferring Pathogen Type Interactions Using Cross-sectional Prevalence Data: Opportunities and Pitfalls for Predicting Type Replacement

BACKGROUND

Many multivalent vaccines target only a subset of all pathogenic types. If vaccine and nonvaccine types compete, vaccination may lead to type replacement. The plausibility of type replacement has been assessed using the odds ratio (OR) of co-infections in cross-sectional prevalence data, with OR > 1 being interpreted as low risk of type replacement. The usefulness of the OR as a predictor for type replacement is debated, as it lacks a theoretical justification, and there is no framework explaining under which assumptions the OR predicts type replacement.

METHODS

We investigate the values that the OR can take based on deterministic S usceptible- I infected- S usceptible and S usceptible- Infected- Recovered- S usceptible multitype transmission models. We consider different mechanisms of type interactions and explore parameter values ranging from synergistic to competitive interactions.

RESULTS

We find that OR > 1 might mask competition because of confounding due to unobserved common risk factors and cross-immunity, as indicated by earlier studies. We prove mathematically that unobserved common risk factors lead to an elevation of the OR, and present an intuitive explanation why cross-immunity increases the OR. We find that OR < 1 is predictive for type replacement in the absence of immunity. With immunity, OR < 1 remains predictive under biologically reasonable assumptions of unidirectional interactions during infection, and an absence of immunity-induced synergism.

CONCLUSIONS

Using the OR in cross-sectional data to predict type replacement is justified, but is only unambiguous under strict assumptions. An accurate prediction of type replacement requires pathogen-specific knowledge on common risk factors and cross-immunity.

Multiple infection of cells changes the dynamics of basic viral evolutionary processes

The infection of cells by multiple copies of a given virus can impact viral evolution in a variety of ways, yet some of the most basic evolutionary dynamics remain underexplored. Using computational models, we investigate how infection multiplicity affects the fixation probability of mutants, the rate of mutant generation, and the timing of mutant invasion. An important insight from these models is that for neutral and disadvantageous phenotypes, rare mutants initially enjoy a fitness advantage in the presence of multiple infection of cells. This arises because multiple infection allows the rare mutant to enter more target cells and to spread faster, while it does not accelerate the spread of the resident wild-type virus. The rare mutant population can increase by entry into both uninfected and wild-type-infected cells, while the established wild-type population can initially only grow through entry into uninfected cells. Following this initial advantageous phase, the dynamics are governed by drift or negative selection, respectively, and a higher multiplicity reduces the chances that mutants fix in the population. Hence, while increased infection multiplicity promotes the presence of neutral and disadvantageous mutants in the short-term, it makes it less likely in the longer term. We show how these theoretical insights can be useful for the interpretation of experimental data on virus evolution at low and high multiplicities. The dynamics explored here provide a basis for the investigation of more complex viral evolutionary processes, including recombination, reassortment, as well as complementary/inhibitory interactions.

Managing the emergence of pathogen resistance via spatially targeted antimicrobial use

From agriculture to public health to civil engineering, managing antimicrobial resistance presents a considerable challenge. The dynamics underlying resistance evolution reflect inherently spatial processes. Resistant pathogen strains increase in frequency when a strain that emerges in one locale can spread and replace pathogen subpopulations formerly sensitive to the antimicrobial agent. Moreover, the strength of selection for antimicrobial resistance is in part governed by the extent of antimicrobial use. Thus, altering how antimicrobials are used across a landscape can potentially shift the spatial context governing the dynamics of antimicrobial resistance and provide a potent management tool. Here, we model how the efficacy of adjusting antimicrobial use over space to manage antimicrobial resistance is mediated by competition among pathogen strains and the topology of pathogen metapopulations. For several pathogen migration scenarios, we derive critical thresholds for the spatial extent of antimicrobial use below which resistance cannot emerge, and relate these thresholds to (a) the ability to eradicate antimicrobial-sensitive pathogens locally and (b) the strength of the trade-off between resistance ability and competitive performance where antimicrobial use is absent. We find that in metapopulations where patches differ in connectedness, constraining antimicrobial use across space to mitigate resistance evolution only works if the migration of the resistant pathogen is modest; yet, this situation is reversed if the resistant strain has a high colonization rate, with variably connected metapopulations exhibiting less sensitivity to reducing antimicrobial use across space. Furthermore, when pathogens are alternately exposed to sites with and without the antimicrobial, bottlenecking resistant strains through sites without an antimicrobial is only likely to be effective under a strong competition-resistance trade-off. We therefore identify life-history constraints that are likely to suggest which pathogens can most effectively be controlled by a spatially targeted antimicrobial regime. We discuss implications of our results for managing and thinking about antimicrobial resistance evolution in spatially heterogeneous contexts.

Epidemics in Competition: Partial Cross-Immunity

The competition between two pathogen strains during the course of an epidemic represents a fundamental step in the early evolution of emerging diseases as well as in the antigenic drift process of influenza. The outcome of the competition, however, depends not only on the epidemic properties of the two strains but also on the timing and size of the introduction, characteristics that are poorly captured by deterministic mean-field epidemic models. We describe those aspects of the competition that can be determined from the mean-field models giving the range of possible final sizes of susceptible hosts and cumulated attack rates that could be observed after an epidemic with two cross-reacting strains. In the limit where the size of the initial infection goes to zero, the possible outcomes lie on a (one dimensional) curve in the outcome space.

Within-host competition can delay evolution of drug resistance in malaria

In the malaria parasite P. falciparum, drug resistance generally evolves first in low-transmission settings, such as Southeast Asia and South America. Resistance takes noticeably longer to appear in the high-transmission settings of sub-Saharan Africa, although it may spread rapidly thereafter. Here, we test the hypothesis that competitive suppression of drug-resistant parasites by drug-sensitive parasites may inhibit evolution of resistance in high-transmission settings, where mixed-strain infections are common. We employ a cross-scale model, which simulates within-host (infection) dynamics and between-host (transmission) dynamics of sensitive and resistant parasites for a population of humans and mosquitoes. Using this model, we examine the effects of transmission intensity, selection pressure, fitness costs of resistance, and cross-reactivity between strains on the establishment and spread of resistant parasites. We find that resistant parasites, introduced into the population at a low frequency, are more likely to go extinct in high-transmission settings, where drug-sensitive competitors and high levels of acquired immunity reduce the absolute fitness of the resistant parasites. Under strong selection from antimalarial drug use, however, resistance spreads faster in high-transmission settings than low-transmission ones. These contrasting results highlight the distinction between establishment and spread of resistance and suggest that the former but not the latter may be inhibited in high-transmission settings. Our results suggest that within-host competition is a key factor shaping the evolution of drug resistance in P. falciparum.

The malaria parasite Plasmodium falciparum has evolved resistance to most antimalarial drugs, greatly complicating treatment and control of the disease. Curiously, although sub-Saharan Africa accounts for the majority of the global burden of malaria, the evolution of drug resistance in Africa has been markedly delayed compared to Asia and the Americas. One reason might be that, in a population in which the prevalence of infection is high, a newly emerged drug-resistant strain faces a high risk of extinction due to competition from drug-sensitive parasites that already “occupy” most of the host population. Using a mathematical model, we confirm that drug-resistant parasites face a much greater risk of extinction in a “high-transmission” setting like sub-Saharan Africa than in a “low-transmission” setting like Southeast Asia. However, we also find that when drug-resistant parasites manage to avoid extinction, their subsequent spread may be more rapid in high-transmission settings than in low-transmission settings, especially when selection is strong. These results offer a novel explanation for global patterns of drug resistance evolution in malaria and suggest a new dimension to consider in resistance prevention and containment efforts: namely, the intrinsic favorability of low- and high-transmission settings for establishment and spread of drug resistance.

Progression from latent infection to active disease in dynamic tuberculosis transmission models: a systematic review of the validity of modelling assumptions

Mathematical modelling is commonly used to evaluate infectious disease control policy and is influential in shaping policy and budgets. Mathematical models necessarily make assumptions about disease natural history and, if these assumptions are not valid, the results of these studies can be biased. We did a systematic review of published tuberculosis transmission models to assess the validity of assumptions about progression to active disease after initial infection (PROSPERO ID CRD42016030009). We searched PubMed, Web of Science, Embase, Biosis, and Cochrane Library, and included studies from the earliest available date (Jan 1, 1962) to Aug 31, 2017. We identified 312 studies that met inclusion criteria. Predicted tuberculosis incidence varied widely across studies for each risk factor investigated. For population groups with no individual risk factors, annual incidence varied by several orders of magnitude, and 20-year cumulative incidence ranged from close to 0% to 100%. A substantial proportion of modelled results were inconsistent with empirical evidence: for 10-year cumulative incidence, 40% of modelled results were more than double or less than half the empirical estimates. These results demonstrate substantial disagreement between modelling studies on a central feature of tuberculosis natural history. Greater attention to reproducing known features of epidemiology would strengthen future tuberculosis modelling studies, and readers of modelling studies are recommended to assess how well those studies demonstrate their validity.

Host population structure and treatment frequency maintain balancing selection on drug resistance

It is a truism that antimicrobial drugs select for resistance, but explaining pathogen- and population-specific variation in patterns of resistance remains an open problem. Like other common commensals, Streptococcus pneumoniae has demonstrated persistent coexistence of drug-sensitive and drug-resistant strains. Theoretically, this outcome is unlikely. We modelled the dynamics of competing strains of S. pneumoniae to investigate the impact of transmission dynamics and treatment-induced selective pressures on the probability of stable coexistence. We find that the outcome of competition is extremely sensitive to structure in the host population, although coexistence can arise from age-assortative transmission models with age-varying rates of antibiotic use. Moreover, we find that the selective pressure from antibiotics arises not so much from the rate of antibiotic use per se but from the frequency of treatment: frequent antibiotic therapy disproportionately impacts the fitness of sensitive strains. This same phenomenon explains why serotypes with longer durations of carriage tend to be more resistant. These dynamics may apply to other potentially pathogenic, microbial commensals and highlight how population structure, which is often omitted from models, can have a large impact.

Evaluating the promise of recombinant transmissible vaccines

Transmissible vaccines have the potential to revolutionize infectious disease control by reducing the vaccination effort required to protect a population against a disease. Recent efforts to develop transmissible vaccines focus on recombinant transmissible vaccine designs (RTVs) because they pose reduced risk if intra-host evolution causes the vaccine to revert to its vector form. However, the shared antigenicity of the vaccine and vector may confer vaccine-immunity to hosts infected with the vector, thwarting the ability of the vaccine to spread through the population. We build a mathematical model to test whether a RTV can facilitate disease management in instances where reversion is likely to introduce the vector into the population or when the vector organism is already established in the host population, and the vector and vaccine share perfect cross-immunity. Our results show that a RTV can autonomously eradicate a pathogen, or protect a population from pathogen invasion, when cross-immunity between vaccine and vector is absent. If cross-immunity between vaccine and vector exists, however, our results show that a RTV can substantially reduce the vaccination effort necessary to control or eradicate a pathogen only when continuously augmented with direct manual vaccination. These results demonstrate that estimating the extent of cross-immunity between vector and vaccine is a critical step in RTV design, and that herpesvirus vectors showing facile reinfection and weak cross-immunity are promising.