No coexistence for free: neutral null models for multistrain pathogens

An evolutionary model to predict the frequency of antibiotic resistance under seasonal antibiotic use, and an application to Streptococcus pneumoniae

The frequency of resistance to antibiotics in Streptococcus pneumoniae has been stable over recent decades. For example, penicillin non-susceptibility in Europe has fluctuated between 12% and 16% without any major time trend. In spite of long-term stability, resistance fluctuates over short time scales, presumably in part due to seasonal fluctuations in antibiotic prescriptions. Here, we develop a model that describes the evolution of antibiotic resistance under selection by multiple antibiotics prescribed at seasonally changing rates. This model was inspired by, and fitted to, published data on monthly antibiotics prescriptions and frequency of resistance in two communities in Israel over 5 years. Seasonal fluctuations in antibiotic usage translate into small fluctuations of the frequency of resistance around the average value. We describe these dynamics using a perturbation approach that encapsulates all ecological and evolutionary forces into a generic model, whose parameters quantify a force stabilizing the frequency of resistance around the equilibrium and the sensitivity of the population to antibiotic selection. Fitting the model to the data revealed a strong stabilizing force, typically two to five times stronger than direct selection due to antibiotics. The strong stabilizing force explains that resistance fluctuates in phase with usage, as antibiotic selection alone would result in resistance fluctuating behind usage with a lag of three months when antibiotic use is seasonal. While most antibiotics selected for increased resistance, intriguingly, cephalosporins selected for decreased resistance to penicillins and macrolides, an effect consistent in the two communities. One extra monthly prescription of cephalosporins per 1000 children decreased the frequency of penicillin-resistant strains by 1.7%. This model emerges under minimal assumptions, quantifies the forces acting on resistance and explains up to 43% of the temporal variation in resistance.

Why sensitive bacteria are resistant to hospital infection control

Background: Large reductions in the incidence of antibiotic-resistant strains of Staphylococcus aureus and Clostridium difficile have been observed in response to multifaceted hospital-based interventions. Reductions in antibiotic-sensitive strains have been smaller or non-existent. It has been argued that since infection control measures, such as hand hygiene, should affect resistant and sensitive strains equally, observed changes must have largely resulted from other factors, including changes in antibiotic use. We used a mathematical model to test the validity of this reasoning. Methods: We developed a mechanistic model of resistant and sensitive strains in a hospital and its catchment area. We assumed the resistant strain had a competitive advantage in the hospital and the sensitive strain an advantage in the community. We simulated a hospital hand hygiene intervention that directly affected resistant and sensitive strains equally. The annual incidence rate ratio ( IRR) associated with the intervention was calculated for hospital- and community-acquired infections of both strains. Results: For the resistant strain, there were large reductions in hospital-acquired infections (0.1 ≤ IRR ≤ 0.6) and smaller reductions in community-acquired infections (0.2 ≤ IRR ≤  0.9). These reductions increased in line with increasing importance of nosocomial transmission of the strain. For the sensitive strain, reductions in hospital acquisitions were much smaller (0.6 ≤ IRR ≤ 0.9), while communityacquisitions could increase or decrease (0.9 ≤ IRR ≤ 1.2). The greater the importance of the community environment for the transmission of the sensitive strain, the smaller the reductions. Conclusions: Counter-intuitively, infection control interventions, including hand hygiene, can have strikingly discordant effects on resistant and sensitive strains even though they target them equally, following differences in their adaptation to hospital and community-based transmission. Observed lack of effectiveness of control measures for sensitive strains does not provide evidence that infection control interventions have been ineffective in reducing resistant strains.

Why sensitive bacteria are resistant to hospital infection control

Background: Large reductions in the incidence of antibiotic-resistant strains of Staphylococcus aureus and Clostridium difficile have been observed in response to multifaceted hospital-based interventions. Reductions in antibiotic-sensitive strains have been smaller or non-existent. It has been argued that since infection control measures, such as hand hygiene, should affect resistant and sensitive strains equally, observed changes must have largely resulted from other factors, including changes in antibiotic use. We used a mathematical model to test the validity of this reasoning.

Methods: We developed a mechanistic model of resistant and sensitive strains in a hospital and its catchment area. We assumed the resistant strain had a competitive advantage in the hospital and the sensitive strain an advantage in the community. We simulated a hospital hand hygiene intervention that directly affected resistant and sensitive strains equally. The annual incidence rate ratio ( IRR) associated with the intervention was calculated for hospital- and community-acquired infections of both strains.

Results: For the resistant strain, there were large reductions in hospital-acquired infections (0.1 ≤ IRR ≤ 0.6) and smaller reductions in community-acquired infections (0.2 ≤ IRR ≤  0.9). These reductions increased in line with increasing importance of nosocomial transmission of the strain. For the sensitive strain, reductions in hospital acquisitions were much smaller (0.6 ≤ IRR ≤ 0.9), while communityacquisitions could increase or decrease (0.9 ≤ IRR ≤ 1.2). The greater the importance of the community environment for the transmission of the sensitive strain, the smaller the reductions.

Conclusions: Counter-intuitively, infection control interventions, including hand hygiene, can have strikingly discordant effects on resistant and sensitive strains even though they target them equally, following differences in their adaptation to hospital and community-based transmission. Observed lack of effectiveness of control measures for sensitive strains does not provide evidence that infection control interventions have been ineffective in reducing resistant strains.

Use of mathematical modelling to assess the impact of vaccines on antibiotic resistance

Antibiotic resistance is a major global threat to the provision of safe and effective health care. To control antibiotic resistance, vaccines have been proposed as an essential intervention, complementing improvements in diagnostic testing, antibiotic stewardship, and drug pipelines. The decision to introduce or amend vaccination programmes is routinely based on mathematical modelling. However, few mathematical models address the impact of vaccination on antibiotic resistance. We reviewed the literature using PubMed to identify all studies that used an original mathematical model to quantify the impact of a vaccine on antibiotic resistance transmission within a human population. We reviewed the models from the resulting studies in the context of a new framework to elucidate the pathways through which vaccination might impact antibiotic resistance. We identified eight mathematical modelling studies; the state of the literature highlighted important gaps in our understanding. Notably, studies are limited in the range of pathways represented, their geographical scope, and the vaccine-pathogen combinations assessed. Furthermore, to translate model predictions into public health decision making, more work is needed to understand how model structure and parameterisation affects model predictions and how to embed these predictions within economic frameworks.

Geographic variation in pneumococcal vaccine efficacy estimated from dynamic modeling of epidemiological data post-PCV7

Although mean efficacy of multivalent pneumococcus vaccines has been intensively studied, variance in vaccine efficacy (VE) has been overlooked. Different net individual protection across settings can be driven by environmental conditions, local serotype and clonal composition, as well as by socio-demographic and genetic host factors. Understanding efficacy variation has implications for population-level effectiveness and other eco-evolutionary feedbacks. Here I show that realized VE can vary across epidemiological settings, by applying a multi-site-one-model approach to data post-vaccination. I analyse serotype prevalence dynamics following PCV7, in asymptomatic carriage in children attending day care in Portugal, Norway, France, Greece, Hungary and Hong-Kong. Model fitting to each dataset provides site-specific estimates for vaccine efficacy against acquisition, and pneumococcal transmission parameters. According to this model, variable serotype replacement across sites can be explained through variable PCV7 efficacy, ranging from 40% in Norway to 10% in Hong-Kong. While the details of how this effect is achieved remain to be determined, here I report three factors negatively associated with the VE readout, including initial prevalence of serotype 19F, daily mean temperature, and the Gini index. The study warrants more attention on local modulators of vaccine performance and calls for predictive frameworks within and across populations.

Evolution of antibiotic resistance is linked to any genetic mechanism affecting bacterial duration of carriage

Understanding how changes in antibiotic consumption affect the prevalence of antibiotic resistance in bacterial pathogens is important for public health. In a number of bacterial species, including Streptococcus pneumoniae, the prevalence of resistance has remained relatively stable despite prolonged selection pressure from antibiotics. The evolutionary processes allowing the robust coexistence of antibiotic sensitive and resistant strains are not fully understood. While allelic diversity can be maintained at a locus by direct balancing selection, there is no evidence for such selection acting in the case of resistance. In this work, we propose a mechanism for maintaining coexistence at the resistance locus: linkage to a second locus that is under balancing selection and that modulates the fitness effect of resistance. We show that duration of carriage plays such a role, with long duration of carriage increasing the fitness advantage gained from resistance. We therefore predict that resistance will be more common in strains with a long duration of carriage and that mechanisms maintaining diversity in duration of carriage will also maintain diversity in antibiotic resistance. We test these predictions in S. pneumoniae and find that the duration of carriage of a serotype is indeed positively correlated with the prevalence of resistance in that serotype. These findings suggest heterogeneity in duration of carriage is a partial explanation for the coexistence of sensitive and resistant strains and that factors determining bacterial duration of carriage will also affect the prevalence of resistance.

Exploring the population-level impact of MenB vaccination via modeling: Potential for serogroup replacement

Various meningococcal conjugate vaccines exist against serogroups A, C, W and Y. A new protein-based vaccine targeting serogroup B (MenB) is also now available. The potential of such vaccines to drive serogroup replacement is considered a possible public health concern when implementing nationwide routine immunization programmes. The aim of this work was to investigate if and how serogroup replacement may occur following widespread vaccination with a MenB vaccine that may protect against carriage. To that end, we built a dynamic transmission model with age and serogroup stratification, focusing on European settings where most invasive meningococcal disease (IMD) cases are caused by serogroups B and C. For illustration purposes, the model was employed in 2 such settings: UK (England and Wales) and Czech Republic. Preliminary model-based projections suggest that, under strong serogroup competition for colonization, vaccine-induced serogroup replacement may occur even with a relatively low vaccine efficacy against serogroup B carriage (e.g., 20%), with potential subsequent increase in serogroup C IMD. The magnitude and speed of the model-projected serogroup C IMD increase depend on the MenB vaccination strategy, vaccine efficacy against carriage and the extent of any potential cross-protection against other serogroups. These analyses are neither exhaustive nor definitive, and focused on simulating potential population-level trends in IMD post-vaccination, under certain assumptions. Due to present inherent limitations and uncertainties, this study has limited quantitative value and is best regarded as an explorative qualitative modeling approach, to complement and challenge the current status quo, and suggest areas where collecting additional data may be essential.

Interim results of an ecological experiment - Conjugate vaccination against the pneumococcus and serotype replacement

Streptococcus pneumoniae has more than 95 serotypes, each of which presumably can cause sepsis, meningitis, pneumonia, and acute otitis media. Pneumococcal conjugate vaccines (PCV) targeted against a limited number of serotypes have nonetheless revealed an impressive impact on each manifestation of pneumococcal disease. At the same time, growing evidence of significant non-vaccine type (NVT) replacement disease following implementation of infant PCV programs has raised questions about the long-term viability of PCV immunization strategies and how to optimize PCV formulations. We discuss here theoretical and practical considerations regarding serotype replacement, and provide a snapshot of the most important NVT types seen to date after implementation of the 2 higher-valent PCVs.

Harnessing Intra-Host Strain Competition to Limit Antibiotic Resistance: Mathematical Model Results

Antibiotic overuse has promoted the spread of antibiotic resistance. To compound the issue, treating individuals dually infected with antibiotic-resistant and antibiotic-vulnerable strains can make their infections completely resistant through competitive release. We formulate mathematical models of transmission dynamics accounting for dual infections and extensions accounting for lag times between infection and treatment or between cure and ending treatment. Analysis using the Next-Generation Matrix reveals how competition within hosts and the costs of resistance determine whether vulnerable and resistant strains persist, coexist, or drive each other to extinction. Invasion analysis predicts that treatment of dually infected cases will promote resistance. By varying antibiotic strength, the models suggest that physicians have two ways to achieve a particular resistance target: prescribe relatively weak antibiotics to everyone infected with an antibiotic-vulnerable strain or give more potent prescriptions to only those patients singly infected with the vulnerable strain after ruling out the possibility of them being dually infected with resistance. Through selectivity and moderation in antibiotic prescription, resistance might be limited.

Evaluating the potential impact of enhancing HIV treatment and tuberculosis control programmes on the burden of tuberculosis

HIV has fuelled increasing tuberculosis (TB) incidence in sub-Saharan Africa. Better control of TB in this region may be achieved directly through TB programme improvements and indirectly through expanded use of antiretroviral therapy (ART) among those with HIV. We used a mathematical model of TB and HIV in South Africa to examine the potential epidemiological impact in scenarios involving improvements in three dimensions of TB programmes: coverage, diagnosis and treatment effectiveness, as well as expanded ART use through broadened eligibility. We projected the effect of alternative scenarios on TB prevalence, incidence and TB-related mortality over 20 years. Of the three dimensions of TB programme improvement, expanding coverage would produce the greatest reduction in TB burden. Compared with current performance, combined TB programme improvements were projected to decrease TB incidence by 30% over 5 years and 46% over 20 years, and decrease TB-related mortality by 45% over 5 years and 69% over 20 years. Expanded ART eligibility was projected to decrease TB incidence by 22% over 5 years and 45% over 20 years, and TB-related mortality by 22% over 5 years and 50% over 20 years. We found that over a 20-year horizon, TB-specific and HIV-specific programme changes contribute equally to incidence reductions, whereas the TB-specific changes produce a majority of the mortality benefits. An aggressive expansion of ART alongside traditional TB-specific control measures has the potential to greatly reduce TB burden, with the different elements of a combined approach having a synergistic effect in reducing long-term TB incidence and mortality.

How could preventive therapy affect the prevalence of drug resistance? Causes and consequences

Various forms of preventive and prophylactic antimicrobial therapies have been proposed to combat HIV (e.g. pre-exposure prophylaxis), tuberculosis (e.g. isoniazid preventive therapy) and malaria (e.g. intermittent preventive treatment). However, the potential population-level effects of preventative therapy (PT) on the prevalence of drug resistance are not well understood. PT can directly affect the rate at which resistance is acquired among those receiving PT. It can also indirectly affect resistance by altering the rate at which resistance is acquired through treatment for active disease and by modifying the level of competition between transmission of drug-resistant and drug-sensitive pathogens. We propose a general mathematical model to explore the ways in which PT can affect the long-term prevalence of drug resistance. Depending on the relative contributions of these three mechanisms, we find that increasing the level of coverage of PT may result in increases, decreases or non-monotonic changes in the overall prevalence of drug resistance. These results demonstrate the complexity of the relationship between PT and drug resistance in the population. Care should be taken when predicting population-level changes in drug resistance from small pilot studies of PT or estimates based solely on its direct effects.

Carriage burden, multiple colonization and antibiotic pressure promote emergence of resistant vaccine escape pneumococci

Pneumococcal conjugate vaccines target the limited subset of the more than 90 known serotypes of Streptococcus pneumoniae responsible for the greatest burden of pneumococcal disease and antibiotic resistance. Following the introduction of these vaccines, serotypes not targeted were able to expand and resistance became more common within these types. Here we use a stochastic dynamic model of pediatric pneumococcal carriage to evaluate potential influences on the emergence of new resistant lineages following the introduction of a vaccine targeting more common resistant types. Antibiotic pressure was the strongest driver, with no emergence at low levels and universal emergence at high levels. At intermediate levels of antibiotic pressure, higher carriage burden and a greater degree of dual carriage promoted emergence. This may have implications for current plans to introduce childhood pneumococcal vaccination in several high-burden countries.

Estimation and interpretation of heterogeneous vaccine efficacy against recurrent infections

Vaccine-induced protection may not be homogeneous across individuals. It is possible that a vaccine gives complete protection for a portion of individuals, while the rest acquire only incomplete (leaky) protection of varying magnitude. If vaccine efficacy is estimated under wrong assumptions about such individual level heterogeneity, the resulting estimates may be difficult to interpret. For instance, population-level predictions based on such estimates may be biased. We consider the problem of estimating heterogeneous vaccine efficacy against an infection that can be acquired multiple times (susceptible-infected-susceptible model). The estimation is based on a limited number of repeated measurements of the current status of each individual, a situation commonly encountered in practice. We investigate how the placement of consecutive samples affects the estimability and efficiency of vaccine efficacy parameters. The same sampling frequency may not be optimal for efficient estimation of all components of heterogeneous vaccine protection. However, we suggest practical guidelines allowing estimation of all components. For situations in which the estimability of individual components fails, we suggest to use summary measures of vaccine efficacy.

How direct competition shapes coexistence and vaccine effects in multi-strain pathogen systems

We describe an integrated modeling framework for understanding strain coexistence in polymorphic pathogen systems. Previous studies have debated the utility of neutral formulations and focused on cross-immunity between strains as a major stabilizing mechanism. Here we convey that direct competition for colonization mediates stable coexistence only when competitive abilities amongst pathogen clones satisfy certain pairwise asymmetries. We illustrate our ideas with nested SIS models of single and dual colonization, applied to polymorphic pneumococcal bacteria. By fitting the models to cross-sectional prevalence data from Portugal (before and after the introduction of a seven-valent pneumococcal conjugate vaccine), we are able to not only statistically compare neutral and non-neutral epidemiological formulations, but also estimate vaccine efficacy, transmission and competition parameters simultaneously. Our study highlights that the response of polymorphic pathogen populations to interventions holds crucial information about strain interactions, which can be extracted by suitable nested modeling.

How competition governs whether moderate or aggressive treatment minimizes antibiotic resistance

Understanding how our use of antimicrobial drugs shapes future levels of drug resistance is crucial. Recently, there has been debate over whether an aggressive (i.e., high dose) or more moderate (i.e., lower dose) treatment of individuals will most limit the emergence and spread of resistant bacteria. In this study, we demonstrate how one can understand and resolve these apparently contradictory conclusions. We show that a key determinant of which treatment strategy will perform best at the individual level is the extent of effective competition between resistant and sensitive pathogens within a host. We extend our analysis to the community level, exploring the spectrum between strict inter-strain competition and strain independence. From this perspective as well, we find that the magnitude of effective competition between resistant and sensitive strains determines whether an aggressive approach or moderate approach minimizes the burden of resistance in the population.

DOI:http://dx.doi.org/10.7554/eLife.10559.001

Antibiotics are chemical compounds used to treat bacterial infections. The discovery of antibiotics, starting with penicillin in 1929, revolutionized medicine, making it possible to cure or prevent life-threatening infections such as tetanus and pneumonia. However, many bacteria have become resistant to one or more antibiotics and so can no longer be killed by these drugs.

The emergence of antibiotic resistance reflects an evolutionary process that occurs during antibiotic treatment. While the antibiotic will kill most bacteria, some bacteria may naturally have a feature or genetic mutation that allows them to survive in the presence of the antibiotic. These bacteria then reproduce and pass on their resistant traits, eventually leading to the emergence of a new antibiotic-resistant strain of bacteria. Once a resistant strain exists it may be able to spread from one person to another.

There is conflicting evidence about how best to prevent antibiotic-resistant bacteria from evolving and spreading. The results of some experiments suggest that treating bacteria with large doses of antibiotics early in an infection is the most effective way to optimize treatment and minimize the risk of an antibiotic-resistant strain developing. However, other studies suggest that exposing bacteria to high levels of antibiotics more efficiently selects for resistance; in this case a more moderate approach should be used when treating bacterial infections.

Here, Colijn and Cohen present a mathematical model that suggests that the natural competition between the antibiotic-resistant and antibiotic-sensitive strains of bacteria influence which treatment strategy should be taken. Strains were modeled both within individual hosts and spreading in a community of individuals. In the models, aggressive antibiotic treatment is most effective (in that it minimizes antibiotic resistance) when the antibiotic-resistant strain either does not experience strong competition from the non-resistant strains of bacteria or is not fit enough to be a good competitor. However, a more moderate treatment is appropriate when the two strains are competing and the antibiotic-resistant strain is a fit competitor. Competition may mean that moderate treatment is best to avoid resistance at the community level, even in situations when aggressive treatment is likely best for individuals.

Two important future challenges are to better understand the diversity of strains in bacterial infections, and to develop tools to measure to what extent strains are effectively competing with each other.

DOI:http://dx.doi.org/10.7554/eLife.10559.002

The adaptive evolution of virulence: a review of theoretical predictions and empirical tests

Why is it that some parasites cause high levels of host damage (i.e. virulence) whereas others are relatively benign? There are now numerous reviews of virulence evolution in the literature but it is nevertheless still difficult to find a comprehensive treatment of the theory and data on the subject that is easily accessible to non-specialists. Here we attempt to do so by distilling the vast theoretical literature on the topic into a set of relatively few robust predictions. We then provide a comprehensive assessment of the available empirical literature that tests these predictions. Our results show that there have been some notable successes in integrating theory and data but also that theory and empiricism in this field do not ‘speak’ to each other very well. We offer a few suggestions for how the connection between the two might be improved.

Modeling multiple infection of cells by viruses: Challenges and insights

The multiple infection of cells with several copies of a given virus has been demonstrated in experimental systems, and has been subject to previous mathematical modeling approaches. Such models, especially those based on ordinary differential equations, can be characterized by difficulties and pitfalls. One such difficulty arises from what we refer to as multiple infection cascades. That is, such models subdivide the infected cell population into sub-populations that are carry i viruses, and each sub-population can in principle always be further infected to contain i + 1 viruses. In order to study the model with numerical simulations, the infection cascade needs to be cut artificially, and this can influence the results. This is shown here in the context of the simplest setting that involves a single, homogeneous virus population. If the viral replication rate is sufficiently fast, then most infected cells will accumulate in the last member of the infection cascade, leading to incorrect numerical results. This can be observed even with relatively long infection cascades, and in this case computational costs associated with a sufficiently long infection cascade can render this approach impractical. We subsequently examine a more complex scenario where two virus types/strains with different fitness are allowed to compete. Again, we find that the length of the infection cascade can have a crucial influence on the results. Competitive exclusion can be observed for shorter infection cascades, while coexistence can be observed for longer infection cascades. More subtly, the length of the infection cascade can influence the equilibrium level of the populations in numerical simulations. Studying the model in a parameter regime where an increase in the infection cascade length does not influence the results, we examine the effect of multiple infection on the outcome of competition. We find that multiple infection can promote coexistence of virus types if there is a degree of intracellular niche separation. If this is not the case, the only outcome is competitive exclusion, similar to equivalent models that do not take into account multiple infection of cells. We further find that multiple infection has a reduced ability to allow coexistence if virus spread is spatially restricted compared to a well-mixed system. These results provide important insights when analyzing and interpreting multiple infection models.

The community ecology of pathogens: coinfection, coexistence and community composition

Disease and community ecology share conceptual and theoretical lineages, and there has been a resurgence of interest in strengthening links between these fields. Building on recent syntheses focused on the effects of host community composition on single pathogen systems, we examine pathogen (microparasite) communities using a stochastic metacommunity model as a starting point to bridge community and disease ecology perspectives. Such models incorporate the effects of core community processes, such as ecological drift, selection and dispersal, but have not been extended to incorporate host-pathogen interactions, such as immunosuppression or synergistic mortality, that are central to disease ecology. We use a two-pathogen susceptible-infected (SI) model to fill these gaps in the metacommunity approach; however, SI models can be intractable for examining species-diverse, spatially structured systems. By placing disease into a framework developed for community ecology, our synthesis highlights areas ripe for progress, including a theoretical framework that incorporates host dynamics, spatial structuring and evolutionary processes, as well as the data needed to test the predictions of such a model. Our synthesis points the way for this framework and demonstrates that a deeper understanding of pathogen community dynamics will emerge from approaches working at the interface of disease and community ecology.

Nine challenges for deterministic epidemic models

Deterministic models have a long history of being applied to the study of infectious disease epidemiology. We highlight and discuss nine challenges in this area. The first two concern the endemic equilibrium and its stability. We indicate the need for models that describe multi-strain infections, infections with time-varying infectivity, and those where super infection is possible. We then consider the need for advances in spatial epidemic models, and draw attention to the lack of models that explore the relationship between communicable and non-communicable diseases. The final two challenges concern the uses and limitations of deterministic models as approximations to stochastic systems.

Pathogen evolution and the immunological niche

Host immunity is a major driver of pathogen evolution and thus a major determinant of pathogen diversity. Explanations for pathogen diversity traditionally assume simple interactions between pathogens and the immune system, a view encapsulated by the susceptible-infected-recovered (SIR) model. However, there is growing evidence that the complexity of many host-pathogen interactions is dynamically important. This revised perspective requires broadening the definition of a pathogen's immunological phenotype, or what can be thought of as its immunological niche. After reviewing evidence that interactions between pathogens and host immunity drive much of pathogen evolution, I introduce the concept of a pathogen's immunological phenotype. Models that depart from the SIR paradigm demonstrate the utility of this perspective and show that it is particularly useful in understanding vaccine-induced evolution. This paper highlights questions in immunology, evolution, and ecology that must be answered to advance theories of pathogen diversity.

Co-infection and super-infection models in evolutionary epidemiology

Multiple infections are intensively studied because of their consequences for the health of the host but also because they can radically alter the selective pressures acting on parasites. I discuss how multiple infections have been modelled in evolutionary epidemiology. First, I briefly mention within-host models, which are at the root of these epidemiological models. Then, I present the super-infection framework, with an original focus on how the definition of the super-infection function can lead to evolutionary branching. There are several co-infection models and, for each of them, I briefly go through the underlying mathematics (especially the invasion fitness of a mutant strain) and I discuss the biological assumptions they make and the questions they consequently may ask. In particular, I show that a widely used co-infection model should not be invoked for invasion analyses because it confers a frequency-dependent advantage to rare neutral mutants. Finally, I present more recent frameworks, such as the Price equation framework in epidemiology, that can account for increased parasite diversity. To conclude, I discuss some perspectives for the study of multiple infections in evolutionary epidemiology.

The impact of coinfections and their simultaneous transmission on antigenic diversity and epidemic cycling of infectious diseases

Epidemic cycling in human infectious diseases is common; however, its underlying mechanisms have been poorly understood. Much effort has been made to search for external mechanisms. Multiple strains of an infectious agent were usually observed and coinfections were frequent; further, empirical evidence indicates the simultaneous transmission of coinfections. To explore intrinsic mechanisms for epidemic cycling, in this study we consider a multistrain Susceptible-Infected-Recovered-Susceptible epidemic model by including coinfections and simultaneous transmission. We show that coinfections and their simultaneous transmission widen the parameter range for coexistence and coinfections become popular when strains enhance each other and the immunity wanes quickly. However, the total prevalence is nearly independent of these characteristics and approximated by that of one-strain model. With sufficient simultaneous transmission and antigenic diversity, cyclical epidemics can be generated even when strains interfere with each other by reducing infectivity. This indicates that strain interactions within coinfections and cross-immunity during subsequent infection provide a possible intrinsic mechanism for epidemic cycling.

Modeling the spread of multiple concurrent contagions on networks

Many contagions spread over various types of communication networks and their spreading dynamics have been extensively studied in the literature. Here we propose a general model for the concurrent spread of an arbitrary number of contagions in complex networks. The model is stochastic and runs in discrete time, and includes two widely used mechanisms by which a node can change its state. The first, termed the spontaneous state change mechanism, describes spontaneous transition to another state, while the second, termed the contact-induced state change mechanism, describes acquiring other contagions due to contact with the neighbors. We consider reactive discrete-time spreading processes of multiple concurrent contagions where time steps are of finite size without neglecting the possibility of multiple infecting events in a single time step. An essential element for making the model numerically tractable is the use of an approximation for the probability that a node transits to a specific state given any set of neighboring states. Different transmission probabilities may be present between each pair of states. We also derive corresponding continuous–time equations that are simple and intuitive. The model includes many well-known epidemic and rumor spreading models as a special case and it naturally captures spreading processes in multiplex networks.

Emergence and spread of antibiotic resistance: setting a parameter space

The emergence and spread of antibiotic resistance among human pathogens is a relevant problem for human health and one of the few evolution processes amenable to experimental studies. In the present review, we discuss some basic aspects of antibiotic resistance, including mechanisms of resistance, origin of resistance genes, and bottlenecks that modulate the acquisition and spread of antibiotic resistance among human pathogens. In addition, we analyse several parameters that modulate the evolution landscape of antibiotic resistance. Learning why some resistance mechanisms emerge but do not evolve after a first burst, whereas others can spread over the entire world very rapidly, mimicking a chain reaction, is important for predicting the evolution, and relevance for human health, of a given mechanism of resistance. Because of this, we propose that the emergence and spread of antibiotic resistance can only be understood in a multi-parameter space. Measuring the effect on antibiotic resistance of parameters such as contact rates, transfer rates, integration rates, replication rates, diversification rates, and selection rates, for different genes and organisms, growing under different conditions in distinct ecosystems, will allow for a better prediction of antibiotic resistance and possibilities of focused interventions.

Neutrality, cross-immunity and subtype dominance in avian influenza viruses

Avian influenza viruses (AIVs) are considered a threat for their potential to seed human influenza pandemics. Despite their acknowledged importance, there are significant unknowns regarding AIV transmission dynamics in their natural hosts, wild birds. Of particular interest is the difference in subtype dynamics between human and bird populations-in human populations, typically only two or three subtypes cocirculate, while avian populations are capable of simultaneously hosting a multitude of subtypes. One species in particular-ruddy turnstones (Arenaria interpres)--has been found to harbour a very wide range of AIV subtypes, which could make them a key player in the spread of new subtypes in wild bird populations. Very little is known about the mechanisms that drive subtype dynamics in this species, and here we address this gap in our knowledge. Taking advantage of two independent sources of data collected from ruddy turnstones in Delaware Bay, USA, we examine patterns of subtype diversity and dominance at this site. We compare these patterns to those produced by a stochastic, multi-strain transmission model to investigate possible mechanisms that are parsimonious with the observed subtype dynamics. We find, in agreement with earlier experimental work, that subtype differences are unnecessary to replicate the observed dynamics, and that neutrality alone is sufficient. We also evaluate the role of subtype cross-immunity and find that it is not necessary to generate patterns consistent with observations. This work offers new insights into the mechanisms behind subtype diversity and dominance in a species that has the potential to be a key player in AIV dynamics in wild bird populations.

Revising ecological assumptions about Human papillomavirus interactions and type replacement

The controversy over whether vaccine-targeted HPV types will be replaced by other oncogenic, non-vaccine-targeted types remains unresolved. This is in part because little is known about the ecology of HPV types. Patient data has been interpreted to suggest independence or facilitative interactions between types and therefore replacement is believed to be unlikely. With a novel mathematical model, we investigated which HPV type interactions and their immune responses gave qualitatively similar patterns frequently observed in patients. To assess the possibility of type replacement, vaccination was added to see if non-vaccine-targeted types increased their 'niche'. Our model predicts that independence and facilitation are not necessary for the coexistence of types inside hosts, especially given the patchy nature of HPV infection. In fact, independence and facilitation inadequately represented co-infected patients. We found that some form of competition is likely in natural co-infections. Hence, non-vaccine-targeted types that are not cross-reactive with the vaccine could spread to more patches and can increase their viral load in vaccinated hosts. The degree to which this happens will depend on replication and patch colonization rates. Our results suggest that independence between types could be a fallacy, and so without conclusively untangling HPV within-host ecology, type replacement remains theoretically viable. More ecological thinking is needed in future studies.

The impact of specific and non-specific immunity on the ecology of Streptococcus pneumoniae and the implications for vaccination

More than 90 capsular serotypes of Streptococcus pneumoniae coexist despite competing for nasopharyngeal carriage and a gradient in fitness. The underlying mechanisms for this are poorly understood and make assessment of the likely population impact of vaccination challenging. We use an individual-based simulation model to generalize widely used deterministic models for pneumococcal competition and show that in these models short-term serotype-specific and serotype non-specific immunity could constitute the mechanism governing between-host competition and coexistence. We find that non-specific immunity induces between-host competition and that serotype-specific immunity limits a type's competitive advantage and allows stable coexistence of multiple serotypes. Serotypes carried at low prevalence show high variance in carriage levels, which would result in apparent outbreaks if they were highly pathogenic. Vaccination against few serotypes can lead to elimination of the vaccine types and induces replacement by others. However, in simulations where the elimination of the targeted types is achieved only by a combination of vaccine effects and the competitive pressure of the non-vaccine types, a universal vaccine with similar-type-specific effectiveness can fail to eliminate pneumococcal carriage and offers limited herd immunity. Hence, if vaccine effects are insufficient to control the majority of serotypes at the same time, then exploiting the competitive pressure by selective vaccination can help control the most pathogenic serotypes.

Breaking the symmetry: immune enhancement increases persistence of dengue viruses in the presence of asymmetric transmission rates

The dengue viruses exist as four antigenically distinct serotypes. These four serotypes co-circulate and interact with each other through multiple immune-mediated mechanisms. Though the majority of previous efforts to understand the transmission dynamics of dengue have assumed identical characteristics for these four serotypes, empirical data suggests that they differ from one another in important ways. Here, we examine dynamics and persistence in models that do not assume symmetry between the dengue viruses. We find that for serotype transmission rates that are only slightly asymmetric, increased transmissibility of secondary infections through immune enhancement increases the persistence of all dengue viruses in opposition to findings in symmetric models. We identify an optimal magnitude of immune enhancement that maximizes the probability of persistence of all four serotypes. In contrast to other pathogen systems where heterogeneity between serotypes in transmissibility facilitates competitive exclusion (Bremmermann and Thieme, 1989), here we find that in the presence of Antibody Dependent Enhancement (ADE) heterogeneity can increase the persistence of multiple serotypes of dengue.

A basic dynamic transmission model of Staphylococcus aureus in the US population

We present a basic mathematical model of Staphylococcus aureus transmission in the USA based on natural history of infection and nationally representative data. We employed a Susceptible-Colonized-Infected-Recovered-Susceptible compartmental modelling framework with two different phenotypes of S. aureus: methicillin-susceptible (MSSA) and methicillin-resistant (MRSA). The model is dynamic and accounts for the US population growth. For model calibration/validation, we used published 1999–2005 S. aureus infection data in conjunction with the 2001–2004 National Health and Nutrition Examination Survey colonization data. Baseline model projections illustrated how MRSA might continue to expand and gradually replace MSSA over time, in the absence of intervention, if there is strong competition for colonization. The model-based estimate of the basic reproduction number (R₀) highlights the need for infection control. We illustrate the potential population-level impact of intervention with a hypothetical S. aureus vaccination component.

Virus dynamics in the presence of synaptic transmission

Traditionally, virus dynamics models consider populations of infected and target cells, and a population of free virus that can infect susceptible cells. In recent years, however, it has become. clear that direct cell-to-cell transmission can also play an important role for the in vivo spread of viruses, especially retroviruses such as human T lymphotropic virus-1 (HTLV-1) and Human immunodeficiency virus (HIV). Such cell-to-cell transmission is thought to occur through the formation of virological synapses that are formed between an infected source cell and a susceptible target cell. Here we formulate and analyze a class of virus dynamics models that include such cell-cell synaptic transmission. We explore different "strategies" of the virus defined by the number of viruses passed per synapse, and determine how the choice of strategy influences the basic reproductive ratio, R0, of the virus and thus its ability to establish a persistent infection. We show that depending on specific assumptions about the viral kinetics, strategies with low or intermediate numbers of viruses transferred may correspond to the highest values of R0. We also explore the evolutionary competition of viruses of different strains, which differ by their synaptic strategy, and show that viruses characterized by synaptic strategies with the highest R0 win the evolutionary competition and exclude other, inferior, strains.

Hospital-community interactions foster coexistence between methicillin-resistant strains of Staphylococcus aureus

Methicillin-resistant Staphylococcus aureus (MRSA) is an important cause of morbidity and mortality in both hospitals and the community. Traditionally, MRSA was mainly hospital-associated (HA-MRSA), but in the past decade community-associated strains (CA-MRSA) have spread widely. CA-MRSA strains seem to have significantly lower biological costs of resistance, and hence it has been speculated that they may replace HA-MRSA strains in the hospital. Such a replacement could potentially have major consequences for public health, as there are differences in the resistance spectra of the two strains as well as possible differences in their clinical effects. Here we assess the impact of competition between HA- and CA-MRSA using epidemiological models which integrate realistic data on drug-usage frequencies, resistance profiles, contact, and age structures. By explicitly accounting for the differing antibiotic usage frequencies in the hospital and the community, we find that coexistence between the strains is a possible outcome, as selection favors CA-MRSA in the community, because of its lower cost of resistance, while it favors HA-MRSA in the hospital, because of its broader resistance spectrum. Incorporating realistic degrees of age- and treatment-structure into the model significantly increases the parameter ranges over which coexistence is possible. Thus, our results indicate that the large heterogeneities existing in human populations make coexistence between hospital- and community-associated strains of MRSA a likely outcome.

One of the most notorious cases of antibiotic-resistant bacteria is methicillin-resistant Staphylococcus aureus (MRSA), which causes diseases ranging from skin and soft-tissue infections to pneumonia and septicemia. Traditionally, MRSA was mainly hospital-associated, but in the past decade community-associated strains have spread widely. Typically drug-resistant bacteria have lower reproduction or transmission rates, called a fitness cost. Because this cost is estimated to be significantly lower for community-associated strains, it has been predicted that these will eventually replace the hospital-associated strains. However, hospital-associated strains are resistant against a greater variety of antibiotics, which may compensate for the higher fitness cost. Here, we integrate realistic data on drug-usage, resistance profiles, contact, and age structures into a mathematical model of MRSA transmission to predict the competition between hospital- and community-associated strains. We find that for a realistic degree of population structure it is likely that both strains of MRSA will coexist in the long term. This results from significantly different hospitalization and antibiotic consumption rates between age groups. In particular, elderly individuals have much higher rates of antibiotic usage and hospitalizations than other age groups. This generates a situation where community-associated strains can predominate in the community but are outcompeted in the hospital, resulting in coexistence in the population.

Multiple infections and the evolution of virulence

Infections that consist of multiple parasite strains or species are common in the wild and are a major public health concern. Theory suggests that these infections have a key influence on the evolution of infectious diseases and, more specifically, on virulence evolution. However, we still lack an overall vision of the empirical support for these predictions. We argue that within-host interactions between parasites largely determine how virulence evolves and that experimental data support model predictions. Then, we explore the main limitation of the experimental study of such 'mixed infections', which is that it draws conclusions on evolutionary outcomes from studies conducted at the individual level. We also discuss differences between coinfections caused by different strains of the same species or by different species. Overall, we argue that it is possible to make sense out of the complexity inherent to multiple infections and that experimental evolution settings may provide the best opportunity to further our understanding of virulence evolution.

Exploring individual HPV coinfections is essential to predict HPV-vaccination impact on genotype distribution: a model-based approach

INTRODUCTION

As for other vaccines that only target a subset of circulating pathogen types, human papillomavirus (HPV) immunization raises the concern of a potential risk of genotype replacement. Potential interactions between HPV types may affect infection acquisition and clearance. However, the existence and the nature of these interactions are still largely unknown. Here, we assess how such interactions might affect the impact of HPV vaccination on genotype distribution in the long term.

METHODS

We develop two mathematical models of the transmission of oncogenic HPV infections that include interactions between vaccine and nonvaccine genotypes to examine the influence of different coinfection dynamics (simultaneous vs. sequential clearance of coinfections) on the evolution of nonvaccine prevalences postimmunization.

RESULTS

After introducing vaccination, the two models give contrasting genotype-replacement outcomes. When hypothesizing that coinfections clear sequentially, genotype replacement depends on whether vaccine and nonvaccine genotypes reduce or favor the acquisition by one or the other. Interestingly, the hypothesis that coinfections clear simultaneously always leads to genotype replacement, even when infections with vaccine types favor the acquisition of infections with nonvaccine types.

CONCLUSION

Our results suggest that predictions regarding HPV genotype replacement strongly depend on the assumptions describing the dynamics (acquisition and clearance) of coinfections. In particular, HPV genotype replacement could be compatible with synergistic interactions between types affecting infections acquisition, contrary to previous suggestions. Understanding better how concurrent infections with multiple types change the acquisition and time to clearance of type-specific infections is essential to be able to predict the impact of vaccination on genotype distribution. Longitudinal data collection in populations, particularly examining infection and coinfection acquisition and clearance, is needed to better predict HPV-vaccine impact.

Parasite co-transmission and the evolutionary epidemiology of virulence

Hosts are often co-infected by several parasite genotypes of the same species or even by different species and this is known to affect virulence evolution. However, epidemiological models typically assume that only one of the co-infecting strains can be transmitted at the same time, which is often at odds with the observed biology. Here, I study the effect of co-transmission on virulence evolution in a case where parasites compete for host resources. For co-infections by strains of the same species, increased co-transmission selects for less virulent strains. This is because co-transmission aligns the interests of co-infecting strains, thus decreasing the selective pressure for increased within-host competitiveness. For co-infection caused by different parasite species, the evolutionary outcome depends on the respective virulence of the two parasite species. Finally, I investigate asymmetric scenarios, for example that of plant viruses that require "helper" molecules produced by viruses from another species to be transmitted. These results show that even if parasite strains compete for host resources, the prevalence of co-infections can be a poor predictor of virulence evolution.

Superinfection and the evolution of resistance to antimalarial drugs

A major issue in the control of malaria is the evolution of drug resistance. Ecological theory has demonstrated that pathogen superinfection and the resulting within-host competition influences the evolution of specific traits. Individuals infected with Plasmodium falciparum are consistently infected by multiple parasites; however, while this probably alters the dynamics of resistance evolution, there are few robust mathematical models examining this issue. We developed a general theory for modelling the evolution of resistance with host superinfection and examine: (i) the effect of transmission intensity on the rate of resistance evolution; (ii) the importance of different biological costs of resistance; and (iii) the best measure of the frequency of resistance. We find that within-host competition retards the ability and slows the rate at which drug-resistant parasites invade, particularly as the transmission rate increases. We also find that biological costs of resistance that reduce transmission are less important than reductions in the duration of drug-resistant infections. Lastly, we find that random sampling of the population for resistant parasites is likely to significantly underestimate the frequency of resistance. Considering superinfection in mathematical models of antimalarial drug resistance may thus be important for generating accurate predictions of interventions to contain resistance.

Estimating rates of carriage acquisition and clearance and competitive ability for pneumococcal serotypes in Kenya with a Markov transition model

BACKGROUND

There are more than 90 serotypes of Streptococcus pneumoniae, with varying biologic and epidemiologic properties. Animal studies suggest that carriage induces an acquired immune response that reduces duration of colonization in a nonserotype-specific fashion.

METHODS

We studied pneumococcal nasopharyngeal carriage longitudinally in Kenyan children 3-59 months of age, following up positive swabs at days 2, 4, 8, 16, and 32 and then monthly thereafter until 2 swabs were negative for the original serotype. As previously reported, 1868/2840 (66%) of children swabbed at baseline were positive. We estimated acquisition, clearance, and competition parameters for 27 serotypes using a Markov transition model.

RESULTS

Point estimates of type-specific acquisition rates ranged from 0.00025/d (type 1) to 0.0031/d (type 19F). Point estimates of time to clearance (inverse of type-specific immune clearance rate) ranged from 28 days (type 20) to 124 days (type 6A). For the serotype most resistant to competition (type 19F), acquisition of other serotypes was 52% less likely (95% confidence interval = 37%-63%) than in an uncolonized host. Fitness components (carriage duration, acquisition rate, lack of susceptibility to competition) were positively correlated with each other and with baseline prevalence, and were associated with biologic properties previously shown to associate with serotype. Duration of carriage declined with age for most serotypes.

CONCLUSIONS

Common S. pneumoniae serotypes appear superior in many dimensions of fitness. Differences in rate of immune clearance are attenuated as children age and become capable of more rapid clearance of the longest-lived serotypes. These findings provide information for comparison after introduction of pneumococcal conjugate vaccine.

Niche and neutral effects of acquired immunity permit coexistence of pneumococcal serotypes

Over 90 capsular serotypes of Streptococcus pneumoniae, a common nasopharyngeal colonizer and major cause of pneumonia, bacteremia, and meningitis, are known. It is unclear why some serotypes can persist at all: They are more easily cleared from carriage and compete poorly in vivo. Serotype-specific immune responses, which could promote diversity in principle, are weak enough to allow repeated colonizations by the same type. We show that weak serotype-specific immunity and an acquired response not specific to the capsule can together reproduce observed diversity. Serotype-specific immunity stabilizes competition, and acquired immunity to noncapsular antigens reduces fitness differences. Our model can be used to explain the effects of pneumococcal vaccination and indicates general factors that regulate the diversity of pathogens.

Serotype replacement in disease after pneumococcal vaccination

Vaccination with heptavalent pneumococcal conjugate vaccine (PCV7) has significantly reduced the burden of pneumococcal disease and has had an important public health benefit. Because this vaccine targets only seven of the more than 92 pneumococcal serotypes, concerns have been raised that non-vaccine serotypes (NVTs) could increase in prevalence and reduce the benefits of vaccination. Indeed, among asymptomatic carriers, the prevalence of NVTs has increased substantially, and consequently, there has been little or no net change in the bacterial carriage prevalence. In many populations, pneumococcal disease caused by NVT has increased, but in most cases this increase has been less than the increase in NVT carriage. We review the evidence for serotype replacement in carriage and disease, and address the surveillance biases that might affect these findings. We then discuss possible reasons for the discrepancy between near-complete replacement in carriage and partial replacement for disease, including differences in invasiveness between vaccine serotypes. We contend that the magnitude of serotype replacement in disease can be attributed, in part, to a combination of lower invasiveness of the replacing serotypes, biases in the pre-vaccine carriage data (unmasking), and biases in the disease surveillance systems that could underestimate the true amount of replacement. We conclude by discussing the future potential for serotype replacement in disease and the need for continuing surveillance.

7-Valent pneumococcal conjugate vaccination in England and Wales: is it still beneficial despite high levels of serotype replacement?

Background

The UK introduced the 7-valent pneumococcal conjugate vaccine (PCV7) into the national vaccination program in September 2006. Previous modelling assumed that the likely impact of PCV7 on invasive pneumococcal disease (IPD) would be similar to the US experience with PCV7. However, recent surveillance data show a more rapid replacement of PCV7 IPD cases by non-PCV7 IPD cases than was seen in the US.

Methods and Findings

A previous model of pneumococcal vaccination was re-parameterised using data on vaccine coverage and IPD from England and Wales between 2006 and 2009. Disease incidence was adjusted for the increasing trend in reported IPD cases prior to vaccination. Using this data we estimated that individuals carrying PCV7 serotypes have much higher protection (96%;95% CI 72%-100%) against acquisition of NVT carriage than the 15% previously estimated from US data, which leads to greater replacement. However, even with this level of replacement, the annual number of IPD cases may be 560 (95% CI, -100 to 1230) lower ten years after vaccine introduction compared to what it may have been without vaccination. A particularly marked fall of 39% in children under 15 years by 2015/6 is predicted.

Conclusion

Our model suggests that PCV7 vaccination could result in a decrease in overall invasive pneumococcal disease, particularly in children, even in an environment of rapid replacement with non-PCV7 serotypes within 5 years of vaccine introduction at high coverage.

Contribution of mathematical modeling to the fight against bacterial antibiotic resistance

PURPOSE OF REVIEW

Modeling of antibiotic resistance in pathogenic bacteria responsible for human disease has developed considerably over the last decade. Herein, we summarize the main published studies to illustrate the contribution of models for understanding both within-host and population-based phenomena. We then suggest possible topics for future studies.

RECENT FINDINGS

Model building of bacterial resistance has involved epidemiologists, biologists and modelers with two different objectives. First, modeling has helped largely in identifying and understanding the factors and biological phenomena responsible for the emergence and spread of resistant strains. Second, these models have become important decision support tools for medicine and public health.

SUMMARY

Major improvements of models in the coming years should take into account specific pathogen characteristics (resistance mechanisms, multiple colonization phenomena, cooperation and competition among species) and better description of the contacts associated with transmission risk within populations.

A mathematical model for the spread of Strepotococcus pneumoniae with transmission dependent on serotype

We examine a mathematical model for the transmission of Streptococcus Pneumoniae amongst young children when the carriage transmission coefficient depends on the serotype. Carriage means pneumococcal colonization. There are two sequence types (STs) spreading in a population each of which can be expressed as one of two serotypes. We derive the differential equation model for the carriage spread and perform an equilibrium and global stability analysis on it. A key parameter is the effective reproduction number R (e). For R (e) ≤ 1,  there is only the carriage-free equilibrium (CFE) and the carriage will die out whatever be the starting values. For R (e) > 1, unless the effective reproduction numbers of the two STs are equal, in addition to the CFE there are two carriage equilibria, one for each ST. If the ST with the largest effective reproduction number is initially present, then in the long-term the carriage will tend to the corresponding equilibrium.

Within-host parasite cooperation and the evolution of virulence

Infections by multiple genotypes are common in nature and are known to select for higher levels of virulence for some parasites. When parasites produce public goods (PGs) within the host, such co-infections have been predicted to select for lower levels of virulence. However, this prediction is based on simplifying assumptions regarding epidemiological feedbacks on the multiplicity of infections (MOI). Here, we analyse the case of parasites producing a PG (for example, siderophore-producing bacteria) using a nested model that ties together within-host and epidemiological processes. We find that the prediction that co-infection should select for less virulent strains for PG-producing parasites is only valid if both parasite transmission and virulence are linear functions of parasite density. If there is a trade-off relationship such that virulence increases more rapidly than transmission, or if virulence also depends on the total amount of PGs produced, then more complex relationships between virulence and the MOI are predicted. Our results reveal that explicitly taking into account the distribution of parasite strains among hosts could help better understand the selective pressures faced by parasites at the population level.

The curse of the Pharaoh revisited: evolutionary bi-stability in environmentally transmitted pathogens

It is increasingly evident that for a number of high-profile pathogens, transmission involves both direct and environmental pathways. Much of the distinguished evolutionary theory has, however, focused on each of transmission component separately. Herein, we use the framework of adaptive dynamics to study the evolutionary consequences of mixed transmission. We find that environmental transmission can select for increased virulence when direct transmission is low. Increasing the efficiency of direct transmission gives rise to an evolutionary bi-stability, with coexistence of different levels of virulence. We conclude that the overlooked contribution of environmental transmission may explain the curious appearance of high virulence in pathogens that are typically only moderately pathogenic, as observed for avian influenza viruses and cholera.

Models to understand the population-level impact of mixed strain M. tuberculosis infections

Over the past decade, numerous studies have identified tuberculosis patients in whom more than one distinct strain of Mycobacterium tuberculosis is present. While it has been shown that these mixed strain infections can reduce the probability of treatment success for individuals simultaneously harboring both drug-sensitive and drug-resistant strains, it is not yet known if and how this phenomenon impacts the long-term dynamics for tuberculosis within communities. Strain-specific differences in immunogenicity and associations with drug resistance suggest that a better understanding of how strains compete within hosts will be necessary to project the effects of mixed strain infections on the future burden of drug-sensitive and drug-resistant tuberculosis. In this paper, we develop a modeling framework that allows us to investigate mechanisms of strain competition within hosts and to assess the long-term effects of such competition on the ecology of strains in a population. These models permit us to systematically evaluate the importance of unknown parameters and to suggest priority areas for future experimental research. Despite the current scarcity of data to inform the values of several model parameters, we are able to draw important qualitative conclusions from this work. We find that mixed strain infections may promote the coexistence of drug-sensitive and drug-resistant strains in two ways. First, mixed strain infections allow a strain with a lower basic reproductive number to persist in a population where it would otherwise be outcompeted if has competitive advantages within a co-infected host. Second, some individuals progressing to phenotypically drug-sensitive tuberculosis from a state of mixed drug-sensitive and drug-resistant infection may retain small subpopulations of drug-resistant bacteria that can flourish once the host is treated with antibiotics. We propose that these types of mixed infections, by increasing the ability of low fitness drug-resistant strains to persist, may provide opportunities for compensatory mutations to accumulate and for relatively fit, highly drug-resistant strains of M. tuberculosis to emerge.

What is the mechanism for persistent coexistence of drug-susceptible and drug-resistant strains of Streptococcus pneumoniae?

The rise of antimicrobial resistance in many pathogens presents a major challenge to the treatment and control of infectious diseases. Furthermore, the observation that drug-resistant strains have risen to substantial prevalence but have not replaced drug-susceptible strains despite continuing (and even growing) selective pressure by antimicrobial use presents an important problem for those who study the dynamics of infectious diseases. While simple competition models predict the exclusion of one strain in favour of whichever is 'fitter', or has a higher reproduction number, we argue that in the case of Streptococcus pneumoniae there has been persistent coexistence of drug-sensitive and drug-resistant strains, with neither approaching 100 per cent prevalence. We have previously proposed that models seeking to understand the origins of coexistence should not incorporate implicit mechanisms that build in stable coexistence 'for free'. Here, we construct a series of such 'structurally neutral' models that incorporate various features of bacterial spread and host heterogeneity that have been proposed as mechanisms that may promote coexistence. We ask to what extent coexistence is a typical outcome in each. We find that while coexistence is possible in each of the models we consider, it is relatively rare, with two exceptions: (i) allowing simultaneous dual transmission of sensitive and resistant strains lets coexistence become a typical outcome, as does (ii) modelling each strain as competing more strongly with itself than with the other strain, i.e. self-immunity greater than cross-immunity. We conclude that while treatment and contact heterogeneity can promote coexistence to some extent, the in-host interactions between strains, particularly the interplay between coinfection, multiple infection and immunity, play a crucial role in the long-term population dynamics of pathogens with drug resistance.

Environmental transmission scrambles coexistence patterns of avian influenza viruses

Despite the recent accumulation of theoretical and empirical studies on avian influenza viruses (AIVs), the interactions among the diverse pool of strains remain poorly understood. One potential reason is multiple transmission routes. In this paper, we explore the behavior of a two-strain mathematical model of AIV dynamics with lifelong immunity to understand how the combination of direct and environmental transmission (via a persistent viral reservoir) determines strains coexistence and dominance. We find that coexistence requires the magnitude of basic reproductive ratios of the strains to be identical for each transmission route (R(0)(dir) and R(0)(env)) when cross-immunity is assumed to be perfect. Coexistence may be also possible when one strain is only directly transmitted and the contribution by environmental transmission is high. When we relax this assumption, the level of cross-protection does not modify coexistence criteria when strains are mainly environmentally transmitted, in contrast to the case where direct transmission dominates. Finally, when competitive exclusion is observed, the strain with the largest contribution from direct transmission outcompetes the other through competition for viral particle acquisition. Overall, we conclude that environmental transmission can affect the patterns of coexistence predicted by direct transmission models in complex ways.