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The effect of norovirus dose on outcomes such as virus shedding and symptoms after initial infection is not well understood. We performed a secondary analysis of a human challenge study by using Bayesian mixed-effects models. As the dose increased from 4.8 to 4,800 reverse transcription PCR units, the total amount of shed virus in feces increased from 4.5 × 1011 to 3.4 × 1012 genomic equivalent copies; in vomit, virus increased from 6.4 × 105 to 3.0 × 107 genomic equivalent copies. Onset time of viral shedding in feces decreased from 1.4 to 0.8 days, and time of peak viral shedding decreased from 2.3 to 1.5 days. Time to symptom onset decreased from 1.5 to 0.8 days. One type of symptom score increased. An increase in norovirus dose was associated with more rapid shedding and symptom onset and possibly increased severity. However, the effect on virus load and shedding was inconclusive.

To support decision-making and policy for managing epidemics of emerging pathogens, we present a model for inference and scenario analysis of SARS-CoV-2 transmission in the USA. The stochastic SEIR-type model includes compartments for latent, asymptomatic, detected and undetected symptomatic individuals, and hospitalized cases, and features realistic interval distributions for presymptomatic and symptomatic periods, time varying rates of case detection, diagnosis, and mortality. The model accounts for the effects on transmission of human mobility using anonymized mobility data collected from cellular devices, and of difficult to quantify environmental and behavioral factors using a latent process. The baseline transmission rate is the product of a human mobility metric obtained from data and this fitted latent process. We fit the model to incident case and death reports for each state in the USA and Washington D.C., using likelihood Maximization by Iterated particle Filtering (MIF). Observations (daily case and death reports) are modeled as arising from a negative binomial reporting process. We estimate time-varying transmission rate, parameters of a sigmoidal time-varying fraction of hospitalized cases that result in death, extra-demographic process noise, two dispersion parameters of the observation process, and the initial sizes of the latent, asymptomatic, and symptomatic classes. In a retrospective analysis covering March-December 2020, we show how mobility and transmission strength became decoupled across two distinct phases of the pandemic. The decoupling demonstrates the need for flexible, semi-parametric approaches for modeling infectious disease dynamics in real-time.

Abstract Background Recent approaches to TB control have focused on identifying and treating active cases to halt further transmission. Patients with TB symptoms often delay to seek care, get appropriate diagnosis, and initiate effective treatment. These delays are partly influenced by whom the patients contact within their community network. We aimed to evaluate the community drivers of diagnostic delay in an urban setting in Uganda. Methods In this study we analyze data from a retrospective cohort of 194 TB patients in Kampala, Uganda. We characterized the patterns of contacts made by patients seeking care for TB symptoms. The main outcome of interest was total community contact delay, defined as the time patients spent seeking care before visiting a provider capable of diagnosing TB. Results Visits to health providers without access to appropriate diagnostic services accounted for 56% of contacts made by cohort members, and were significantly associated with community contact delay, as were symptoms common to other prevalent illnesses, such as bone and joint pain. Conclusions Education programs aimed at primary care providers, as well as other community members, may benefit case identification, by informing them of rarer symptoms of TB, potential for co-infections of TB and other prevalent diseases, and the availability of diagnostic services.

Abstract University administrators face decisions about how to safely return and maintain students, staff and faculty on campus throughout the 2020–21 school year. We developed a susceptible-exposed-infectious-recovered (SEIR) deterministic compartmental transmission model of SARS-CoV-2 among university students, staff, and faculty. Our goals were to inform planning at our own university, Emory University, a medium-sized university with around 15,000 students and 15,000 faculty and staff, and to provide a flexible modeling framework to inform the planning efforts at similar academic institutions. Control strategies of isolation and quarantine are initiated by screening (regardless of symptoms) or testing (of symptomatic individuals). We explored a range of screening and testing frequencies and performed a probabilistic sensitivity analysis. We found that among students, monthly and weekly screening can reduce cumulative incidence by 59% and 87%, respectively, while testing with a 2-, 4- and 7-day delay between onset of infectiousness and testing results in an 84%, 74% and 55% reduction in cumulative incidence. Smaller reductions were observed among staff and faculty. Community-introduction of SARS-CoV-2 onto campus may be controlled with testing, isolation, contract tracing and quarantine. Screening would need to be performed at least weekly to have substantial reductions beyond disease surveillance. This model can also inform resource requirements of diagnostic capacity and isolation/quarantine facilities associated with different strategies.

Objectives: Avian influenza virus A(H7N9) remains a threat to humans and has great potential to cause a pandemic in the foreseeable future. Antiviral treatment with neuraminidase inhibitors has been recommended to treat patients with H7N9 infection as early as possible, although evidence-based research on their effectiveness for H7N9 infection is lacking. Methods: Data from all laboratory-confirmed cases of H7N9 infection in Zhejiang Province between 2013 and 2017 were retrieved, and time-dependent survival models were used to evaluate the effectiveness of treatment with neuraminidase inhibitors to reduce the risk of mortality. Results: The final optimal model found no significant association (odds ratio 1.29, 95% confidence interval 0.78–2.15) between time to treatment with neuraminidase inhibitors and survival after controlling for age and white blood cell count. Sensitivity analyses with multiple imputation for missing data concurred with the primary analysis. Conclusions: No association was found between treatment with neuraminidase inhibitors and survival in patients with H7N9 infection using various adjusted models and sensitivity analyses of missing data imputations.

Norovirus is the leading cause of acute gastroenteritis outbreaks in the United States. We estimated the basic (R0) and effective (Re) reproduction numbers for 7,094 norovirus outbreaks reported to the National Outbreak Reporting System (NORS) during 2009–2017 and used regression models to assess whether transmission varied by outbreak setting. The median R0 was 2.75 (interquartile range [IQR] 2.38–3.65), and median Re was 1.29 (IQR 1.12–1.74). Long-term care and assisted living facilities had an R0 of 3.35 (95% CI 3.26–3.45), but R0 did not differ substantially for outbreaks in other settings, except for outbreaks in schools, colleges, and universities, which had an R0 of 2.92 (95% CI 2.82–3.03). Seasonally, R0 was lowest (3.11 [95% CI 2.97–3.25]) in summer and peaked in fall and winter. Overall, we saw little variability in transmission across different outbreaks settings in the United States.

Abstract Background As immunology continues to become more quantitative, increasingly sophisticated computational tools are commonly used. One useful toolset are simulation models. Becoming familiar with such models and their uses generally requires writing computer code early in the learning process. This poses a barrier for individuals who do not have prior coding experience. Results To help reduce this barrier, I wrote software that teaches the use of mechanistic simulation models to study infection and immune response dynamics, without the need to read or write computer code. The software, called Dynamical Systems Approach to Immune Response Modeling (DSAIRM), is implemented as a freely available package for the R programming language. The target audience are immunologists and other scientists with no or little coding experience. DSAIRM provides a hands-on introduction to simulation models, teaches the basics of those models and what they can be used for. Here, I describe the DSAIRM R package, explain the different ways the package can be used, and provide a few introductory examples. Conclusions Working through DSAIRM will equip individuals with the knowledge needed to critically assess studies using simulation models in the published literature and will help them understand when such a modeling approach might be suitable for their own research. DSAIRM also provides users a potential starting point towards development and use of simulation models in their own research.

Introduction: Most countries are dependent on nonpharmaceutical public health interventions such as social distancing, contact tracing, and case isolation to mitigate COVID-19 spread until medicines or vaccines widely available. Minimal research has been performed on the independent and combined impact of each of these interventions based on empirical case data. Methods: We obtained data from all confirmed COVID-19 cases from January 7th to February 22nd 2020 in Zhejiang Province, China, to fit an age-stratified compartmental model using human contact information before and during the outbreak. The effectiveness of social distancing, contact tracing, and case isolation was studied and compared in simulation. We also simulated a two-phase reopening scenario to assess whether various strategies combining nonpharmaceutical interventions are likely to achieve population-level control of a second-wave epidemic. Results: Our study sample included 1,218 symptomatic cases with COVID-19, of which 664 had no inter-province travel history. Results suggest that 36.5 % (95 % CI, 12.8–57.1) of contacts were quarantined, and approximately five days (95 % CI, 2.2–11.0) were needed to detect and isolate a case. As contact networks would increase after societal and economic reopening, avoiding a second wave without strengthening nonpharmaceutical interventions compared to the first wave it would be exceedingly difficult. Conclusions: Continuous attention and further improvement of nonpharmaceutical interventions are needed in second-wave prevention. Specifically, contact tracing merits further attention.

CTL responses are critical in protection against pathogens. Here, using mass spectrometry and flow cytometry, the authors characterize the kinetics of influenza A virus class I MHC epitopes cross-presented in professional antigen presenting cells and identify new epitopes that elicit T cell responses in infected mice.

Background: The overall performance of a multiple component vaccine assessed by the vaccine-elicited immune responses across various strains in a repeated vaccination setting has not been well-studied, and the comparison between adults and teenagers is yet to be made.Methods: A human cohort study was conducted at the University of Georgia, with 140 subjects (86 adults and 54 teenagers) repeatedly vaccinated in the 2017/2018 and 2018/2019 influenza seasons. Host information was prospectively collected, and serum samples were collected before and after vaccination in each season. The association between host factors and repeated measures of hemagglutination inhibition (HAI) composite scores was assessed by generalized linear models with generalized estimating equations.Results: The mean HAI composite scores for the entire sample (t = 4.26, df = 139, p < 0.001) and the teenager group (t = 6.44, df = 53, p < 0.001) declined in the second season, while the changes in the adults were not statistically significant (t = −1.14, df = 85, p = 0.26). A mixture pattern of changes in both directions was observed in the adults when stratified by prior vaccination. In addition, the regression analysis suggested an interactive effect of age and BMI on the HAI composite scores in the overall population (beta = 0.005; 95% CI, 0.0008–0.01) and the adults (beta = 0.005; 95% CI, 0.0005–0.01).Conclusions: Our study found distinct vaccine-elicited immune responses between adults and teenagers when both were repeatedly vaccinated in consecutive years. An interactive effect of age and BMI on the HAI composite scores were identified in the overall population and the adults.

Directly observed therapy (DOT) is almost universally used for the treatment of TB. Several meta-analyses using different methods have assessed the effectiveness of DOT compared to self-administered therapy (SAT). The results of these meta-analyses often conflict with some concluding DOT is superior and others that there is little or no difference. Meta-analyses can guide policymaking, but such analyses must be reliable. To assess the validity of a previous meta-analysis, we tried to reproduce it. We encountered problems with the previous analysis that did not allow for a meaningful reproduction. We describe the issues we encountered here. We then performed a new meta-analysis comparing the treatment outcomes of adults given treatment with SAT versus DOT. Outcomes in the new analysis are loss to follow-up, treatment failure, cure, treatment completed, and all-cause mortality. All data, documentation, and code used to generate our results is provided. Our new analysis included four randomized and three observational studies with 1603 and 1626 individuals respectively. The pooled relative risks (RR) are as follows: Lost to follow-up (RR = 1.2, 95% CI 0.9, 1.7), Treatment Failure (RR = 1.1, 95% CI 0.6, 2), Cure (RR = 0.9, 95% CI 0.8, 1.1), Treatment Completion (RR = 1, 95% CI 0.9, 1.1), Mortality (RR = 0.9, 95% CI 0.6, 1.3). Based on data from our new meta-analysis, the magnitude of the difference between DOT and SAT for all reported outcomes is small, and none of the differences are statistically significant.

[This corrects the article DOI: 10.1371/journal.pone.0150568.].

Vaccination is an effective method to protect against infectious diseases. An important consideration in any vaccine formulation is the inoculum dose, i.e., amount of antigen or live attenuated pathogen that is used. Higher levels generally lead to better stimulation of the immune response but might cause more severe side effects and allow for less population coverage in the presence of vaccine shortages. Determining the optimal amount of inoculum dose is an important component of rational vaccine design. A combination of mathematical models with experimental data can help determine the impact of the inoculum dose. We illustrate the concept of using data and models to inform inoculum dose determination for vaccines, wby fitting a mathematical model to data from influenza A virus (IAV) infection of mice and human parainfluenza virus (HPIV) infection of cotton rats at different inoculum doses. We use the model to map inoculum dose to the level of immune protection and morbidity and to explore how such a framework might be used to determine an optimal inoculum dose. We show how a framework that combines mathematical models with experimental data can be used to study the impact of inoculum dose on important outcomes such as immune protection and morbidity. Our findings illustrate that the impact of inoculum dose on immune protection and morbidity can depend on the specific pathogen and that both protection and morbidity do not necessarily increase monotonically with increasing inoculum dose. Once vaccine design goals are specified with required levels of protection and acceptable levels of morbidity, our proposed framework can help in the rational design of vaccines and determination of the optimal amount of inoculum.

Determining the duration of protective immunity requires quantifying the magnitude and rate of loss of antibodies to different virus and vaccine antigens. A key complication is heterogeneity in both the magnitude and decay rate of responses of different individuals to a given vaccine, as well as of a given individual to different vaccines. We analyzed longitudinal data on antibody titers in 45 individuals to characterize the extent of this heterogeneity and used models to determine how it affected the longevity of protective immunity to measles, rubella, vaccinia, tetanus, and diphtheria. Our analysis showed that the magnitude of responses in different individuals varied between 12- and 200-fold (95% coverage) depending on the antigen. Heterogeneity in the magnitude and decay rate contribute comparably to variation in the longevity of protective immunity between different individuals. We found that some individuals have, on average, slightly longer-lasting memory than others-on average, they have higher antibody levels with slower decay rates. We identified different patterns for the loss of protective levels of antibodies to different vaccine and virus antigens. Specifically, we found that for the first 25 to 50 years, virtually all individuals have protective antibody titers against diphtheria and tetanus, respectively, but about 10% of the population subsequently lose protective immunity per decade. In contrast, at the outset, not all individuals had protective titers against measles, rubella, and vaccinia. However, these antibody titers wane much more slowly, with a loss of protective immunity in only 1% to 3% of the population per decade. Our results highlight the importance of long-term longitudinal studies for estimating the duration of protective immunity and suggest both how vaccines might be improved and how boosting schedules might be reevaluated.

For most pathogens, vaccination reduces the spread of the infection and total number of cases; thus, public policy usually advocates maximizing vaccination coverage. We use simple mathematical models to explore how this may be different for pathogens, such as influenza, which exhibit strain variation. Our models predict that the total number of seasonal influenza infections is minimized at an intermediate (rather than maximal) level of vaccination, and, somewhat counter-intuitively, further increasing the level of the vaccination coverage may lead to higher number of influenza infections and be detrimental to the public interest. This arises due to the combined effects of: competition between multiple co-circulating strains; limited breadth of protection afforded by the vaccine; and short-term strain-transcending immunity following natural infection. The study highlights the need for better quantification of the components of vaccine efficacy and longevity of strain-transcending cross-immunity in order to generate nuanced recommendations for influenza vaccine coverage levels.

Background: The post-2015 End TB Strategy proposes targets of 50% reduction in tuberculosis incidence and 75% reduction in mortality from tuberculosis by 2025. We aimed to assess whether these targets are feasible in three high-burden countries with contrasting epidemiology and previous programmatic achievements. Methods: 11 independently developed mathematical models of tuberculosis transmission projected the epidemiological impact of currently available tuberculosis interventions for prevention, diagnosis, and treatment in China, India, and South Africa. Models were calibrated with data on tuberculosis incidence and mortality in 2012. Representatives from national tuberculosis programmes and the advocacy community provided distinct country-specific intervention scenarios, which included screening for symptoms, active case finding, and preventive therapy. Findings: Aggressive scale-up of any single intervention scenario could not achieve the post-2015 End TB Strategy targets in any country. However, the models projected that, in the South Africa national tuberculosis programme scenario, a combination of continuous isoniazid preventive therapy for individuals on antiretroviral therapy, expanded facility-based screening for symptoms of tuberculosis at health centres, and improved tuberculosis care could achieve a 55% reduction in incidence (range 31–62%) and a 72% reduction in mortality (range 64–82%) compared with 2015 levels. For India, and particularly for China, full scale-up of all interventions in tuberculosis-programme performance fell short of the 2025 targets, despite preventing a cumulative 3·4 million cases. The advocacy scenarios illustrated the high impact of detecting and treating latent tuberculosis. Interpretation: Major reductions in tuberculosis burden seem possible with current interventions. However, additional interventions, adapted to country-specific tuberculosis epidemiology and health systems, are needed to reach the post-2015 End TB Strategy targets at country level. Funding: Bill and Melinda Gates Foundation

Background: The post-2015 End TB Strategy sets global targets of reducing tuberculosis incidence by 50% and mortality by 75% by 2025. We aimed to assess resource requirements and cost-effectiveness of strategies to achieve these targets in China, India, and South Africa. Methods: We examined intervention scenarios developed in consultation with country stakeholders, which scaled up existing interventions to high but feasible coverage by 2025. Nine independent modelling groups collaborated to estimate policy outcomes, and we estimated the cost of each scenario by synthesising service use estimates, empirical cost data, and expert opinion on implementation strategies. We estimated health effects (ie, disability-adjusted life-years averted) and resource implications for 2016–35, including patient-incurred costs. To assess resource requirements and cost-effectiveness, we compared scenarios with a base case representing continued current practice. Findings: Incremental tuberculosis service costs differed by scenario and country, and in some cases they more than doubled existing funding needs. In general, expansion of tuberculosis services substantially reduced patient-incurred costs and, in India and China, produced net cost savings for most interventions under a societal perspective. In all three countries, expansion of access to care produced substantial health gains. Compared with current practice and conventional cost-effectiveness thresholds, most intervention approaches seemed highly cost-effective. Interpretation: Expansion of tuberculosis services seems cost-effective for high-burden countries and could generate substantial health and economic benefits for patients, although substantial new funding would be required. Further work to determine the optimal intervention mix for each country is necessary. Funding: Bill & Melinda Gates Foundation.

The threat of an influenza A virus pandemic stems from continual virus spillovers from reservoir species, a tiny fraction of which spark sustained transmission in humans. To date, no pandemic emergence of a new influenza strain has been preceded by detection of a closely related precursor in an animal or human. Nonetheless, influenza surveillance efforts are expanding, prompting a need for tools to assess the pandemic risk posed by a detected virus. The goal would be to use genetic sequence and/or biological assays of viral traits to identify those non-human influenza viruses with the greatest risk of evolving into pandemic threats, and/or to understand drivers of such evolution, to prioritize pandemic prevention or response measures. We describe such efforts, identify progress and ongoing challenges, and discuss three specific traits of influenza viruses (hemagglutinin receptor binding specificity, hemagglutinin pH of activation, and polymerase complex efficiency) that contribute to pandemic risk.

The World Health Organization identifies influenza as a major public health problem. While the strains commonly circulating in humans usually do not cause severe pathogenicity in healthy adults, some strains that have infected humans, such as H5N1, can cause high morbidity and mortality. Based on the severity of the disease, influenza viruses are sometimes categorized as either being highly pathogenic (HP) or having low pathogenicity (LP). The reasons why some strains are LP and others HP are not fully understood. While there are likely multiple mechanisms of interaction between the virus and the immune response that determine LP versus HP outcomes, we focus here on one component, namely macrophages (MP). There is some evidence that MP may both help fight the infection and become productively infected with HP influenza viruses. We developed mathematical models for influenza infections which explicitly included the dynamics and action of MP. We fit these models to viral load and macrophage count data from experimental infections of mice with LP and HP strains. Our results suggest that MP may not only help fight an influenza infection but may contribute to virus production in infections with HP viruses. We also explored the impact of combination therapies with antivirals and anti-inflammatory drugs on HP infections. Our study suggests a possible mechanism of MP in determining HP versus LP outcomes, and how different interventions might affect infection dynamics.

CD8(+) T cells directed against conserved viral regions elicit broad immunity against distinct influenza viruses, promote rapid virus elimination and enhanced host recovery. The influenza neuraminidase inhibitor, oseltamivir, is prescribed for therapy and prophylaxis, although it remains unclear how the drug impacts disease severity and establishment of effector and memory CD8(+) T cell immunity. We dissected the effects of oseltamivir on viral replication, inflammation, acute CD8(+) T cell responses and the establishment of immunological CD8(+) T cell memory. In mice, ferrets and humans, the effect of osteltamivir on viral titre was relatively modest. However, prophylactic oseltamivir treatment in mice markedly reduced morbidity, innate responses, inflammation and, ultimately, the magnitude of effector CD8(+) T cell responses. Importantly, functional memory CD8(+) T cells established during the drug-reduced effector phase were capable of mounting robust recall responses. Moreover, influenza-specific memory CD4(+) T cells could be also recalled after the secondary challenge, while the antibody levels were unaffected. This provides evidence that long-term memory T cells can be generated during an oseltamivir-interrupted infection. The anti-inflammatory effect of oseltamivir was verified in H1N1-infected patients. Thus, in the case of an unpredicted influenza pandemic, while prophylactic oseltamivir treatment can reduce disease severity, the capacity to generate memory CD8(+) T cells specific for the newly emerged virus is uncompromised. This could prove especially important for any new influenza pandemic which often occurs in separate waves.

Tuberculosis (TB) is an infectious disease with a peculiar feature: Upon infection with the causative agent, Mycobacterium Tuberculosis (MTB), most hosts enter a latent state during which no transmission of MTB to new hosts occurs. Only a fraction of latently infected hosts develop TB disease and can potentially infect new hosts. At first glance, this seems like a waste of transmission potential and therefore an evolutionary suboptimal strategy for MTB. It might be that the human immune response keeps MTB in check in most hosts, thereby preventing it from achieving its evolutionary optimum. Another possible explanation is that long latency and progression to disease in only a fraction of hosts are evolutionary beneficial to MTB by allowing it to persist better in small host populations. Given that MTB has co-evolved with human hosts for millenia or longer, it likely encountered small host populations for a large share of its evolutionary history and had to evolve strategies of persistence. Here, we use a mathematical model to show that indeed, MTB persistence is optimal for an intermediate duration of latency and level of activation. The predicted optimal level of activation is above the observed value, suggesting that human co-evolution has lead to host immunity, which keeps MTB below its evolutionary optimum.

Successful replication within an infected host and successful transmission between hosts are key to the continued spread of most pathogens. Competing selection pressures exerted at these different scales can lead to evolutionary trade-offs between the determinants of fitness within and between hosts. Here, we examine such a trade-off in the context of influenza A viruses and the differential pressures exerted by temperature-dependent virus persistence. For a panel of avian influenza A virus strains, we find evidence for a trade-off between the persistence at high versus low temperatures. Combining a within-host model of influenza infection dynamics with a between-host transmission model, we study how such a trade-off affects virus fitness on the host population level. We show that conclusions regarding overall fitness are affected by the type of link assumed between the within- and between-host levels and the main route of transmission (direct or environmental). The relative importance of virulence and immune response mediated virus clearance are also found to influence the fitness impacts of virus persistence at low versus high temperatures. Based on our results, we predict that if transmission occurs mainly directly and scales linearly with virus load, and virulence or immune responses are negligible, the evolutionary pressure for influenza viruses to evolve toward good persistence at high within-host temperatures dominates. For all other scenarios, influenza viruses with good environmental persistence at low temperatures seem to be favored.

If repeated interventions against multiple outbreaks are not feasible, there is an optimal level of control during the first outbreak. Any control measures above that optimal level will lead to an outcome that may be as sub-optimal as that achieved by an intervention that is too weak. We studied this scenario in more detail.An age-stratified ordinary-differential-equation model was constructed to study infectious disease outbreaks and control in a population made up of two groups, adults and children. The model was parameterized using influenza as an example. This model was used to simulate two consecutive outbreaks of the same infectious disease, with an intervention applied only during the first outbreak, and to study how cumulative attack rates were influenced by population composition, strength of inter-group transmission, and different ways of triggering and implementing the interventions. We assumed that recovered individuals are fully immune and the intervention does not confer immunity.The optimal intervention depended on coupling between the two population sub-groups, the length, strength and timing of the intervention, and the population composition. Population heterogeneity affected intervention strategies only for very low cross-transmission between groups. At more realistic values, coupling between the groups led to synchronization of outbreaks and therefore intervention strategies that were optimal in reducing the attack rates for each subgroup and the population overall coincided. For a sustained intervention of low efficacy, early intervention was found to be best, while at high efficacies, a delayed start was better. For short interventions, a delayed start was always advantageous, independent of the intervention efficacy. For most scenarios, starting the intervention after a certain cumulative proportion of children were infected seemed more robust in achieving close to optimal outcomes compared to a strategy that used a specified duration after an outbreak's beginning as the trigger.

Small populations are thought to be adaptively handicapped, not only because they suffer more from deleterious mutations but also because they have limited access to new beneficial mutations, particularly those conferring large benefits.Here, we test this widely held conjecture using both simulations and experiments with small and large bacterial populations evolving in either a simple or a complex nutrient environment. Consistent with expectations, we find that small populations are adaptively constrained in the simple environment; however, in the complex environment small populations not only follow more heterogeneous adaptive trajectories, but can also attain higher fitness than the large populations. Large populations are constrained to near deterministic fixation of rare large-benefit mutations. While such determinism speeds adaptation on the smooth adaptive landscape represented by the simple environment, it can limit the ability of large populations from effectively exploring the underlying topography of rugged adaptive landscapes characterized by complex environments.Our results show that adaptive constraints often faced by small populations can be circumvented during evolution on rugged adaptive landscapes.

Neuraminidase Inhibitors (NI) are currently the most effective drugs against influenza. Recent cases of NI resistance are a cause for concern. To assess the danger of NI resistance, a number of studies have reported the fraction of treated patients from which resistant strains could be isolated. Unfortunately, those results strongly depend on the details of the experimental protocol. Additionally, knowing the fraction of patients harboring resistance is not too useful by itself. Instead, we want to know how likely it is that an infected patient can generate a resistant infection in a secondary host, and how likely it is that the resistant strain subsequently spreads. While estimates for these parameters can often be obtained from epidemiological data, such data is lacking for NI resistance in influenza. Here, we use an approach that does not rely on epidemiological data. Instead, we combine data from influenza infections of human volunteers with a mathematical framework that allows estimation of the parameters that govern the initial generation and subsequent spread of resistance. We show how these parameters are influenced by changes in drug efficacy, timing of treatment, fitness of the resistant strain, and details of virus and immune system dynamics. Our study provides estimates for parameters that can be directly used in mathematical and computational models to study how NI usage might lead to the emergence and spread of resistance in the population. We find that the initial generation of resistant cases is most likely lower than the fraction of resistant cases reported. However, we also show that the results depend strongly on the details of the within-host dynamics of influenza infections, and most importantly, the role the immune system plays. Better knowledge of the quantitative dynamics of the immune response during influenza infections will be crucial to further improve the results.

Pathogens that evolve resistance to drugs usually have reduced fitness. However, mutations that largely compensate for this reduction in fitness often arise. We investigate how these compensatory mutations affect population-wide resistance emergence as a function of drug treatment. Using a model of gonorrhea transmission dynamics, we obtain generally applicable, qualitative results that show how compensatory mutations lead to more likely and faster resistance emergence. We further show that resistance emergence depends on the level of drug use in a strongly nonlinear fashion. We also discuss what data need to be obtained to allow future quantitative predictions of resistance emergence.