Abstract
The spread of antibiotic resistance, a major threat to human health, is poorly understood. Empirically, resistant strains gradually increase in prevalence as antibiotic consumption increases, but current mathematical models predict a sharp transition between full sensitivity and full resistance. In other words, we do not understand what drives persistent coexistence between resistant and sensitive strains of disease-causing bacteria in host populations. Without knowing what drives patterns of resistance, we cannot accurately predict the impact of potential strategies for managing resistance. Here, we show that within-host dynamics—bacterial growth, strain competition, and host immune responses—promote frequency-dependent selection for resistant strains, explaining patterns of resistance at the population level. By capturing these processes in a parsimonious mathematical framework, we resolve a long-standing conflict between theory and observation. Our models capture widespread coexistence for multiple bacteria-drug combinations across 30 European countries and explain associations between carriage prevalence and resistance prevalence among bacterial subtypes. A mechanistic understanding of resistance evolution is needed to accurately forecast the impact and effectiveness of resistance-management strategies.
Despite the global public health threat of antibiotic resistance1, 2, we currently lack a mechanistic understanding of how resistance spreads in human populations3. This gap in our knowledge is reflected in the inability of mathematical models to explain why resistance prevalence gradually increases as we move from countries with low antibiotic consumption to those with high antibiotic consumption3–8 (Fig. 1A). Although the mechanism driving this pattern seems intuitively obvious—greater antibiotic consumption selects for more resistance—the simplest models of disease transmission (Fig. 1B) are unable to capture the gradual rise that is observed. Instead, these models predict competitive exclusion9—that is, that above a particular level of antibiotic consumption, resistant strains fully outcompete sensitive strains, while below this treatment-rate threshold, they are unable to emerge at all (Fig. 1C).
This theoretical prediction stands in stark contrast to empirical patterns of widespread coexistence between sensitive and resistant strains, a trend that holds across multiple bacteria-drug combinations6–8. While previous work has suggested that multiple strain carriage within individuals may promote limited amounts of coexistence3, 10, existing models cannot reproduce coexistence along the 4- to 20-fold range of treatment rates over which it is observed. Moreover, the reason why multiple carriage may promote limited coexistence is unclear. Without identifying an explicit, general mechanism for widespread coexistence, we will be unable to predict the likely impact of public health interventions for managing resistance.
Here, we show that within-host dynamics explain observed patterns of resistance in commensal bacteria. Specifically, we develop a suite of models that explicitly integrate within-host bacterial growth, strain competition, and bacterial subtype-specific host immune responses that, when calibrated to data across 30 European countries, provides a parsimonious and general explanation for empirical patterns of resistance in three commensal bacterial species, and also explains patterns of resistance among competing subtypes in the commensal bacterium Streptococcus pneumoniae.
Results
Existing models fail to capture widespread coexistence
We begin by analysing a standard model of resistant disease transmission developed by Lipsitch and colleagues3, 10. A central feature of this model is that hosts can become dual carriers—that is, carriers of both sensitive and resistant strains simultaneously—through sequential colonisation events (Fig. 2A). This model makes two key assumptions: (1) that dual carriage is balanced, with each strain carried in equal measure; and (2) that if a dual carrier is re-colonised, the incoming strain “knocks out” one of the two resident strains at random. Together, these assumptions preserve the crucial requirement of structural neutrality at the population level10, meaning that selection does not produce coexistence “for free” by artificially promoting transmission of rare strains. In this “within-host balancing” model, the amount of coexistence is governed by the parameter k, the efficiency of co-colonisation relative to single colonisation. While setting k = 0 eliminates dual carriage and recovers competitive exclusion, allowing dual carriage (0 < k ≤ 1) promotes limited coexistence (Fig. 2B). We calibrated this model to European data on penicillin use and penicillin nonsusceptibility among S. pneumoniae (Methods). Due to the limited range of coexistence predicted by the balancing model, we found that it cannot readily capture observed patterns of resistance3, 5 (Fig. 2C), even when co-colonisation is more efficient than single colonisation (k > 1; text S2).
Although the balancing model preserves neutrality at the between-host level10, we argue that it violates the principle of structural neutrality at the within-host level. Specifically, a structurally-neutral model should not predict that balancing selection promotes stable coexistence between two strains if the strains are biologically identical10. The balancing model meets this requirement at the population level3, 10. However, at the within-host level, when an invading strain colonises a host already carrying a larger resident strain, the balancing model implicitly assumes that the invading strain multiplies within the host—at the expense of the resident strain—until both strains are present in equal frequency, even if the two strains are biologically identical. Moreover, if a dual carrier is recolonised, knockout immediately eliminates one of the host’s existing strains, an assumption which simplifies the mathematical model but which does not have a clear mechanistic explanation. In order to preserve neutral within-host dynamics, we developed a new model that relaxes these two non-neutral assumptions.
Within-host neutrality captures widespread coexistence
In our novel “within-host neutral” model, which exhibits structural neutrality at all levels, hosts are assumed to have a fixed carrying capacity beyond which bacterial growth cannot be supported. If a host is already colonised, a new strain can invade, but rather than reaching the same frequency as the resident strain, we assume that the new strain does not increase in frequency after co-colonisation, since the host is already at carrying capacity (Fig. 2D). Strikingly, integrating within-host neutrality greatly promotes coexistence (Fig. 2E), allowing us to readily capture patterns of S. pneumoniae resistance across European countries (Fig. 2F). We originally developed this model as an individual-based simulation which allows us to track arbitrary within-host strain frequencies for each host, but the model can be approximated using a four-state system of differential equations, which simplifies analysis and model calibration (Methods).
It is generally agreed that antibiotic resistance is associated with a fitness cost11, 12, because in the absence of such a cost, resistant strains would fully outcompete sensitive strains. We have thus far parameterised this cost by assuming that resistant strains are associated with reduced transmission. Alternatively, it is possible to assume that resistant strains suffer reduced within-host growth11, 12, such that a resistant strain will, in the absence of antibiotic treatment, be outcompeted within the host by any sensitive strains (Fig. 2G). We captured this process of within-host competition using a five-state differential equation model based on our within-host neutral model (Methods). This addition further expands the parameter space over which coexistence is maintained (Fig. 2H), improving the model fit to patterns of S. pneumoniae penicillin non-susceptibility (Fig. 2I).
To verify the generality of our results, we re-parameterised the three models for two additional facultatively-pathogenic commensal bacteria, Escherichia coli and Staphylococcus aureus (Methods), and recalibrated the models to pan-European patterns of resistance against the most widely used antibiotics for all three species, which yielded a further four bacteria-drug combinations6, 8. Here, too, the empirical data are better captured by the within-host neutral models than by the balancing model (Fig. 3). Using the Akaike Information Criterion to select the most parsimonious model, we found that the within-host competition model has the most support across all bacteria-drug combinations (Figs. 2, 3).
Within-host dynamics promotes coexistence via frequency-dependent selection
Analysis of our model reveals that frequency-dependent selection13 is the mechanism through which within-host dynamics promote coexistence. That is, the within-host processes we have identified result in fitness advantages for either resistant or sensitive strains when those strains are rare. If resistant cells colonise a host already carrying a sensitive strain, and that host subsequently takes antibiotics, the sensitive strain is cleared and the resistant cells can grow to occupy the host’s now-vacated niche; by contrast, if resistant cells colonise a host already carrying a resistant strain, antibiotic treatment has no such effect. Hence, resistant cells benefit from a fitness advantage when sensitive-strain carriers are common. Within-host competition has a complementary effect, providing sensitive cells with a fitness advantage when resistant-strain carriers are common, because sensitive cells colonising a resistant-strain carrier can grow over time to become the dominant strain in the host. Either or both of these mechanisms can promote stable coexistence by equalising the fitness of resistant and sensitive strains at intermediate carriage frequencies.
Identifying the mechanism of frequency-dependent selection helps to explain why previous model predictions for resistance prevalence are sensitive to a narrow range of antibiotic treatment rates3, 5, 10, and hence have been unable to support coexistence over the wide range of treatment rates measured empirically. Specifically, the “balancing” and “knockout” assumptions of the within-host balancing model create a bias against coexistence in two ways. First, balanced carriage of co-colonising strains decreases rare strains’ frequency-dependent fitness benefit because it reduces the scope for rare strains to grow within dual carriers. Second, knockout reduces the prevalence of dual carriage by depleting strain diversity among hosts. Both effects reduce the strength of frequency-dependent selection for resistance, biasing models against coexistence.
Patterns of coexistence among bacterial serotypes
Many bacterial species exhibit extensive diversity in the expression of capsular proteins exposed to host immune systems, which subdivides species into several distinct “serotypes” that, like resistant versus sensitive strains, are known to stably coexist in host populations14, 15. Host immune memory can promote coexistence between serotypes, because more common serotypes are more likely to provoke a host immune response owing to previous exposure, creating frequency-dependent selection for serotype diversity14, 15. However, similar considerations to those detailed above reveal that serotype diversity can also be promoted through a related mechanism that does not require host immune memory. In our within-host neutral model, coexistence is promoted by resistant strains multiplying to take the place of co-colonising sensitive strains that are cleared by antibiotic treatment. A similar mechanism might promote stable coexistence between commensal bacteria serotypes, so long as—when co-colonising a host— serotypes can be independently cleared by a host immune response, with any strains of the same serotype being cleared simultaneously. This would result in a fitness advantage for a strain co-colonising a host carrying a different serotype, promoting serotype diversity even in the absence of immune memory.
To test this hypothesis, we extended our individual-based model to track coexistence between five serotypes differing in their clearance rate, their transmission rate or their within-host growth rate. We found that independent clearance of serotypes from co-colonised hosts can promote stable coexistence between serotypes, even when serotypes exhibit intrinsic fitness differences (Fig. 4A). Unlike in previous models which have not explicitly tracked within-host dynamics14, 15, we find that acquired immunity is not needed to maintain limited amounts of serotype diversity. Moreover, we found that resistance prevalence varied across coexisting serotypes, with the direction of the trend in resistance prevalence among serotypes depending on whether the cost of resistance was parameterised as a transmission-rate cost or a growth-rate cost. When resistance is associated with a transmission-rate cost, resistance is more strongly selected in fitter serotypes, whether serotypes differ in fitness due to differences in duration of carriage4, transmissibility, or within-host growth (Fig. 4B. This reflects an empirical association between serotype fitness and resistance prevalence observed in S. pneumoniae4. By contrast, when resistance is associated with a within-host growth-rate cost (Fig. 4C), resistance is more strongly selected in less-fit serotypes (Fig. 4D). Thus, our model would predict that the association between resistance prevalence and serotype fitness may depend on the balance between these two putative costs of resistance.
Resistance prevalence among pneumococcal serotypes
Finally, we used this proof of principle to evaluate carriage distribution and resistance prevalence in a model with 30 co-circulating S. pneumoniae serotypes parameterised with observed differences in duration of carriage. We found that independent clearance of serotypes alone was insufficient to support the high diversity of pneumococcal serotype carriage observed in human populations, with only five serotypes maintained (text S4). However, introducing serotype-specific immunity14 to our within-host neutral framework was sufficient to capture much of the observed pneumococcal diversity and patterns of resistance among pneumococcal serotypes (Fig. 5).
Discussion
We have proposed a novel, parsimonious and pathogen-independent mathematical framework that, unlike previous models, captures empirical patterns of antibiotic resistance across countries differing in treatment rates and among serotypes. We argue that frequency-dependent selection drives these patterns of resistance and that coexistence of sensitive and resistant strains is promoted by integrating structural neutrality at the within-host level. Frequency-dependent selection has long been known to promote stable coexistence among animal, plant, and bacterial competitors16–19, and we show here that it could also have a pivotal role in maintaining coexistence between sensitive and resistant strains of commensal bacteria.
Although a number of alternative mechanisms that could explain coexistence between drug-sensitive and resistant pathogens have been proposed3–5, 20–23, some support only modest amounts of coexistence3, 5, while other proposed mechanisms may be difficult to generalize empirically, such as strongly age-assortative mixing4, independent mappings of balancing selection4, or specific immune responses to resistance-associated phenotypes3, 21–23. Our framework of within-host neutrality provides two advances on previous work: it harmonises pathogen dynamics occurring at the between-host and within-host levels, and it allows us to better and more parsimoniously capture observed patterns of resistance prevalence across a range of important bacteria-drug combinations.
Dual carriage of resistant and sensitive strains, a crucial factor for coexistence, is generated in our models via sequential colonisation. The empirical prevalence of dual carriage is not well known, but a study of S. aureus carriage in children found 21% of hosts carried both resistant and sensitive strains24 and—although resistance phenotypes were not measured—other studies have found up to 48% multiple carriage of genetically-distinct S. pneumoniae strains25, 26 and 42% multiple carriage of virulent E. coli strains27. These studies find that carriage is typically dominated by one strain with other strains carried at low frequency, consistent with our model’s carrying-capacity assumptions. Dual carriage could also occur through de novo mutation, which is likely to be especially important for long-lived chronic infections such as colonisations of the cystic fibrosis lung by Pseudomonas aeruginosa28, 29. While it is possible that coexistence is maintained by forces additional to dual carriage, we suggest that any model incorporating dual carriage should observe within-host neutrality to avoid biasing against coexistence.
Antibiotic resistance is one of the foremost threats to human health, and combating this threat will require the global deployment of coordinated interventions1, 2. Mathematical models of disease transmission will play a crucial role in this endeavour, because they can explicitly integrate the mechanisms that drive resistance evolution in a population-level framework and allow us to quantify long-term trends as well as the likely impact of any large-scale interventions for reducing resistance30. Providing a framework in which to answer public health questions will require a balance between mathematical tractability and identifiability of the models on one side, and necessary complexity on the other; building on the simple models proposed here will help to establish that balance. If mathematical models are able to incorporate a truly mechanistic understanding of resistance, they will be better able to explain common patterns of resistance and to accurately predict the effect of interventions at a national and global level30. With growing calls for an integrated and multifaceted approach to the problem of antimicrobial resistance1, 2, a new generation of mechanistic mathematical models will be uniquely placed to support the evidence-based adoption of impactful and cost-effective strategies.
Acknowledgements
We thank M. Davies for assistance. NGD, MJ and KEA were funded by the National Institute for Health Research Health Protection Research Unit (NIHR HPRU) in Immunisation at the London School of Hygiene and Tropical Medicine in partnership with Public Health England (PHE. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR, the Department of Health or PHE. The authors declare no competing financial interests. NGD, SF, MJ and KEA conceived the study; NGD performed the analyses; NGD and KEA drafted the manuscript, which all authors revised.