Lockdown measures and relative changes in the age-specific incidence of SARS-CoV-2 in Spain.

During the first months of the severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) epidemic in 2020, Spain implemented an initial lockdown period on 15 March followed by a strengthened lockdown period on 30 March when only essential workers continued to commute to work. However, little is known about the epidemic dynamics in different age groups during these periods.We used the daily number of coronavirus 2019 cases (by date of symptom onset) reported to the National Epidemiological Surveillance Network among individuals aged 15-19 years through 65-69 years. For each age group g, we computed the proportion PrE(g) of individuals in age group g among all reported cases aged 15-69 years during the pre-lockdown period (1-10 March 2020) and the corresponding proportion PrL(g) during two lockdown periods (initial: 25 March-3 April; strengthened: 8-17 April 2020). For each lockdown period, we computed the proportion ratios PR(g) = PrL(g)/PrE(g). For each pair of age groups g1, g2, PR(g1)>PR(g2) implies a relative increase in the incidence of detected SARS-CoV-2 infection in the age group g1 compared with g2 for the lockdown period vs. the pre-lockdown period.For the initial lockdown period, the highest PR values were in age groups 50-54 years (PR = 1.21; 95% CI: 1.12,1.30) and 55-59 years (PR = 1.19; 1.11,1.27). For the second lockdown period, the highest PR values were in age groups 15-19 years (PR = 1.26; 0.95,1.68) and 50-54 years (PR = 1.20; 1.09,1.31).Our results suggest that different outbreak control measures led to different changes in the relative incidence by age group. During the initial lockdown period, when non-essential work was allowed, individuals aged 40-64 years, particularly those aged 50-59 years, had a higher relative incidence compared with the pre-lockdown period. Younger adults/older adolescents had an increased relative incidence during the later, strengthened lockdown. The role of different age groups during the epidemic should be considered when implementing future mitigation efforts.

On the role of different age groups during pertussis epidemics in California, 2010 and 2014.

There is limited information on the roles of different age groups in propagating pertussis outbreaks, and the temporal changes in those roles since the introduction of acellular pertussis vaccines. The relative roles of different age groups in propagating the 2010 and the 2014 pertussis epidemics in California were evaluated using the relative risk (RR) statistic that measures the change in the group's proportion among all detected cases before vs. after the epidemic peak. For the 2010-11 epidemic, evidence for a predominant transmission age group was weak, with the largest RR estimates being 1.26 (95% CI 1.08-1.46) (aged 11-13 years); 1.19 (1.01-1.4) (aged 9-10 years); 1.17 (0.86-1.59) (aged 14-15 years); 1.12 (0.86-1.46) (aged 16-19 years) and 1.1 (0.89-1.36) (aged 7-8 years). The 2014 epidemic showed a strong signal of the role of older adolescents, with the highest RR estimate being in those aged 14-15 years (RR = 1.83, 1.61-2.07), followed by adolescents aged 16-19 years (RR = 1.41, 1.24-1.61) and 11-13 years (RR = 1.26, 1.12-1.41), with lower RR estimates in other age groups. As the time following introduction of acellular pertussis vaccines in California progressed, older adolescents played an increasing role in transmission during the major pertussis outbreaks. Booster pertussis vaccination for older adolescents with vaccines effective against pertussis transmission should be considered with the aim of mitigating future pertussis epidemics in the community.

Depletion-of-susceptibles bias in influenza vaccine waning studies: how to ensure robust results.

Vaccine effectiveness studies are subject to biases due to depletion-of-persons at risk of infection, or at especially high risk of infection, at different rates from different groups (depletion-of-susceptibles bias), a problem that can also lead to biased estimates of waning effectiveness, including spurious inference of waning when none exists. An alternative study design to identify waning is to study only vaccinated persons, and compare for each day the incidence in persons with earlier or later dates of vaccination to assess waning in vaccine protection as a function of vaccination time (namely whether earlier vaccination would result in lower subsequent protection compared to later vaccination). Prior studies suggested under what conditions this alternative would yield correct estimates of waning. Here we define the depletion-of-susceptibles process formally and show mathematically that for influenza vaccine waning studies, a randomised trial or corresponding observational study that compares incidence at a specific calendar time among individuals vaccinated at different times before the influenza season begins will not be vulnerable to depletion-of-susceptibles bias in its inference of waning as a function of vaccination time under the null hypothesis that none exists, and will - if waning does actually occur - underestimate the extent of waning. Such a design is thus robust in the sense that a finding of waning in that inference framework reflects actual waning of vaccine-induced immunity. We recommend such a design for future studies of waning, whether observational or randomised.

Modelling the epidemiologic impact of achieving UNAIDS fast-track 90-90-90 and 95-95-95 targets in South Africa.

UNAIDS established fast-track targets of 73% and 86% viral suppression among human immunodeficiency virus (HIV)-positive individuals by 2020 and 2030, respectively. The epidemiologic impact of achieving these goals is unknown. The HIV-Calibrated Dynamic Model, a calibrated agent-based model of HIV transmission, is used to examine scenarios of incremental improvements to the testing and antiretroviral therapy (ART) continuum in South Africa in 2015. The speed of intervention availability is explored, comparing policies for their predicted effects on incidence, prevalence and achievement of fast-track targets in 2020 and 2030. Moderate (30%) improvements in the continuum will not achieve 2020 or 2030 targets and have modest impacts on incidence and prevalence. Improving the continuum by 80% and increasing availability reduces incidence from 2.54 to 0.80 per 100 person-years (-1.73, interquartile range (IQR): -1.42, -2.13) and prevalence from 26.0 to 24.6% (-1.4 percentage points, IQR: -0.88, -1.92) from 2015 to 2030 and achieves fast track targets in 2020 and 2030. Achieving 90-90-90 in South Africa is possible with large improvements to the testing and treatment continuum. The epidemiologic impact of these improvements depends on the balance between survival and transmission benefits of ART with the potential for incidence to remain high.

Near real-time surveillance of the SARS-CoV-2 epidemic with incomplete data.

Designing public health responses to outbreaks requires close monitoring of population-level health indicators in real-time. Thus, an accurate estimation of the epidemic curve is critical. We propose an approach to reconstruct epidemic curves in near real time. We apply this approach to characterize the early SARS-CoV-2 outbreak in two Spanish regions between March and April 2020. We address two data collection problems that affected the reliability of the available real-time epidemiological data, namely, the frequent missing information documenting when a patient first experienced symptoms, and the frequent retrospective revision of historical information (including right censoring). This is done by using a novel back-calculating procedure based on imputing patients' dates of symptom onset from reported cases, according to a dynamically-estimated "backward" reporting delay conditional distribution, and adjusting for right censoring using an existing package, NobBS , to estimate in real time (nowcast) cases by date of symptom onset. This process allows us to obtain an approximation of the time-varying reproduction number ( R t ) in real-time. At each step, we evaluate how different assumptions affect the recovered epidemiological events and compare the proposed approach to the alternative procedure of merely using curves of case counts, by report day, to characterize the time-evolution of the outbreak. Finally, we assess how these real-time estimates compare with subsequently documented epidemiological information that is considered more reliable and complete that became available later in time. Our approach may help improve accuracy, quantify uncertainty, and evaluate frequently unstated assumptions when recovering the epidemic curves from limited data obtained from public health surveillance systems in other locations.

On the effect of age on the transmission of SARS-CoV-2 in households, schools and the community.

BACKGROUND: There is limited information on the effect of age on the transmission of SARS-CoV-2 infection in different settings, including primary, secondary and high schools, households, and the whole community. We undertook a literature review of published studies/data on detection of SARS-CoV-2 infection in contacts of COVID-19 cases, as well as serological studies, and studies of infections in the school setting to examine those issues. RESULTS: Our literature review presents evidence for significantly lower susceptibility to infection for children aged under 10 years compared to adults given the same exposure, for elevated susceptibility to infection in adults aged over 60y compared to younger/middle aged adults, and for the risk of SARS-CoV-2 infection associated with sleeping close to an infected individual. Published serological studies also suggest that younger adults (particularly those aged under 35y) often have high cumulative rates of SARS-CoV-2 infection in the community. Additionally, there is some evidence of robust spread of SARS-CoV-2 in secondary/high schools, and there appears to be more limited spread in primary schools. Some countries with relatively large class sizes in primary schools (e.g. Chile and Israel) reported sizeable outbreaks in some of those schools, though routes of transmission of infection to both students and staff are not clear from current reports. CONCLUSIONS: Opening secondary/high schools is likely to contribute to the spread of SARS-CoV-2, and, if implemented, it should require both lower levels of community transmission and greater safeguards to reduce transmission. Compared to secondary/high schools, opening primary schools and daycare facilities may have a more limited effect on the spread of SARS-CoV-2 in the community, particularly under smaller class sizes and in the presence of mitigation measures. Efforts to avoid crowding in the classroom and other mitigation measures should be implemented, to the extent possible, when opening primary schools. Efforts should be undertaken to diminish the mixing in younger adults to mitigate the spread of the epidemic in the whole community.

Using predicted imports of 2019-nCoV cases to determine locations that may not be identifying all imported cases.

Cases from the ongoing outbreak of atypical pneumonia caused by the 2019 novel coronavirus (2019-nCoV) exported from mainland China can lead to self-sustained outbreaks in other populations. Internationally imported cases are currently being reported in several different locations. Early detection of imported cases is critical for containment of the virus. Based on air travel volume estimates from Wuhan to international destinations and using a generalized linear regression model we identify locations which may potentially have undetected internationally imported cases.

Population biology, evolution, and infectious disease: convergence and synthesis.

Traditionally, the interest of population and evolutionary biologists in infectious diseases has been almost exclusively in their role as agents of natural selection in higher organisms. Recently, this interest has expanded to include the genetic structure and evolution of microparasite populations, the mechanisms of pathogenesis and the immune response, and the population biology, ecology, and evolutionary consequences of medical and public health interventions. This article describes recent work in these areas, emphasizing the ways in which quantitative, population-biological approaches have been contributing to the understanding of infectious disease and the design and evaluation of interventions for their treatment and prevention.

Antigenic Variation in Streptococcus pneumoniae PspC Promotes Immune Escape in the Presence of Variant-Specific Immunity.

Genomic analysis reveals extensive sequence variation and hot spots of recombination in surface proteins of Streptococcus pneumoniae While this phenomenon is commonly attributed to diversifying selection by host immune responses, there is little mechanistic evidence for the hypothesis that diversification of surface protein antigens produces an immune escape benefit during infection with S. pneumoniae Here, we investigate the biological significance of sequence variation within the S. pneumoniae cell wall-associated pneumococcal surface protein C (PspC) protein antigen. Using pspC allelic diversity observed in a large pneumococcal collection, we produced variant-specific protein constructs that span the sequence variability within the pspC locus. We show that antibodies raised against these PspC constructs are variant specific and prevent association between PspC and the complement pathway mediator, human factor H. We found that PspC variants differ in their capacity to bind factor H, suggesting that sequence variation within pspC reflects differences in biological function. Finally, in an antibody-dependent opsonophagocytic assay, S. pneumoniae expressing a PspC variant matching the antibody specificity was killed efficiently. In contrast, killing efficacy was not evident against S. pneumoniae expressing mismatched PspC variants. Our data suggest that antigenic variation within the PspC antigen promotes immune evasion and could confer a fitness benefit during infection.IMPORTANCE Loci encoding surface protein antigens in Streptococcus pneumoniae are highly polymorphic. It has become a truism that these polymorphisms are the outcome of selective pressure on S. pneumoniae to escape host immunity. However, there is little mechanistic evidence to support the hypothesis that diversifying protein antigens produces a benefit for the bacteria. Using the highly diverse pspC locus, we have now characterized the functional and immune implications of sequence diversity within the PspC protein. We have characterized the spectrum of biological function among diverse PspC variants and show that pspC sequence diversity reflects functional differences. Further, we show that sequence variation in PspC confers an immune escape benefit in the presence of anti-PspC variant-specific immunity. Overall, the results of our studies provide insights into the functional implications of protein sequence diversity and the role of variant-specific immunity in its maintenance.

How generation intervals shape the relationship between growth rates and reproductive numbers.

Mathematical models of transmission have become invaluable management tools in planning for the control of emerging infectious diseases. A key variable in such models is the reproductive number R. For new emerging infectious diseases, the value of the reproductive number can only be inferred indirectly from the observed exponential epidemic growth rate r. Such inference is ambiguous as several different equations exist that relate the reproductive number to the growth rate, and it is unclear which of these equations might apply to a new infection. Here, we show that these different equations differ only with respect to their assumed shape of the generation interval distribution. Therefore, the shape of the generation interval distribution determines which equation is appropriate for inferring the reproductive number from the observed growth rate. We show that by assuming all generation intervals to be equal to the mean, we obtain an upper bound to the range of possible values that the reproductive number may attain for a given growth rate. Furthermore, we show that by taking the generation interval distribution equal to the observed distribution, it is possible to obtain an empirical estimate of the reproductive number.

Exploring the role of competition induced by non-vaccine serotypes for herd protection following pneumococcal vaccination.

The competitive pressure from non-vaccine serotypes may have helped pneumococcal conjugate vaccines (PCVs) to limit vaccine-type (VT) serotype prevalence. We aimed to investigate if, consequently, the indirect protection of vaccines targeting most pneumococcal serotypes could fall short of the profound effects of current formulations. We compared three previously described pneumococcal models harmonized to simulate 20 serotypes with a combined pre-vaccination prevalence in children younger than 5-years-old of 40%. We simulated vaccines of increasing valency by adding serotypes in order of their competitiveness and explored their ability to reduce VT carriage by 95% within 10 years after introduction. All models predicted that additional valency will reduce indirect vaccine effects and hence the overall vaccine impact on carriage both in children and adults. Consequently, the minimal effective coverage (efficacy against carriage×vaccine coverage) needed to eliminate VT carriage increased with increasing valency. One model predicted this effect to be modest, while the other two predicted that high-valency vaccines may struggle to eliminate VT pneumococci unless vaccine efficacy against carriage can be substantially improved. Similar results were obtained when settings of higher transmission intensity and different PCV formulations were explored. Failure to eliminate carriage as a result of increased valency could lead to overall decreased impact of vaccination if the disease burden caused by the added serotypes is low. Hence, a comparison of vaccine formulations of varying valency, and pan-valent formulations in particular, should consider the invasiveness of targeted serotypes, as well as efficacy against carriage.

The rise and fall of antimicrobial resistance.

Antimicrobial resistance is a growing problem in nearly every infectious disease, but the extent and rate of increase of the problem varies widely with different pathogen-drug combinations. The rate of increase of resistance depends primarily on the availability of resistant variants and the intensity of selection imposed by antimicrobial treatment (appropriately measured). Declines in resistance following antimicrobial control measures are typically faster in hospital-acquired infections than in community-acquired ones, probably owing to the dependence in the latter case on the fitness cost of resistance. Open questions and approaches for testing the hypotheses proposed here are outlined.

Virulence and transmissibility of pathogens: what is the relationship?

The fitness of most pathogenic microorganisms depends on transmission from host to host. This requires adaptation for dissemination, translocation and survival between hosts, as well as for colonization. A complex relationship exists between these components of microbial fitness and virulence. Understanding this relationship has important implications for research and public health.

Natural selection, infectious transfer and the existence conditions for bacterial plasmids.

Despite the near-ubiquity of plasmids in bacterial populations and the profound contribution of infectious gene transfer to the adaptation and evolution of bacteria, the mechanisms responsible for the maintenance of plasmids in bacterial populations are poorly understood. In this article, we address the question of how plasmids manage to persist over evolutionary time. Empirical studies suggest that plasmids are not infectiously transmitted at a rate high enough to be maintained as genetic parasites. In part i, we present a general mathematical proof that if this is the case, then plasmids will not be able to persist indefinitely solely by carrying genes that are beneficial or sometimes beneficial to their host bacteria. Instead, such genes should, in the long run, be incorporated into the bacterial chromosome. If the mobility of host-adaptive genes imposes a cost, that mobility will eventually be lost. In part ii, we illustrate a pair of mechanisms by which plasmids can be maintained indefinitely even when their rates of transmission are too low for them to be genetic parasites. First, plasmids may persist because they can transfer locally adapted genes to newly arriving strains bearing evolutionary innovations, and thereby preserve the local adaptations in the face of background selective sweeps. Second, plasmids may persist because of their ability to shuttle intermittently favored genes back and forth between various (noncompeting) bacterial strains, ecotypes, or even species.

The population dynamics of vertically and horizontally transmitted parasites.

We analyse a model of the transmission dynamics of a parasite transmitted both vertically and horizontally. The basic reproductive ratio (R0) of the parasite is shown to be a sum of horizontal and vertical components. We derive expressions for the equilibrium prevalence of infection for a mixture of horizontal and vertical transmission; prevalence can reach 100% if transmission is sufficiently high. At the endemic equilibrium, if prevalence is high, most transmission will in general be vertical, but horizontal transmission rates must be high to reach and stably maintain such an equilibrium. Surprisingly, for such parasites the highest equilibrium rates of vertical transmission are observed when horizontal transmission is very effective. We discuss the implications for assessing the importance of horizontal v. vertical transmission from field data, and we suggest some implications for the evolution of virulence.

Population dynamics of tuberculosis treatment: mathematical models of the roles of non-compliance and bacterial heterogeneity in the evolution of drug resistance.

SETTING: Patient non-compliance and/or spatial heterogeneity in drug concentration or effectiveness may contribute to the emergence of drug resistance during multiple-drug chemotherapy of tuberculosis. OBJECTIVE: Using mathematical models of mycobacterial population dynamics under antimicrobial treatment, to assess the effects of non-compliance, heterogeneity and other factors on the success of treatment. DESIGN: A mathematical model is used to generate predictions about the ascent of drug resistance in treated hosts with non-compliance and/or a 'protected compartment' of bacteria where only one drug is active; simulations of a more realistic version of this model take into account random mutation, and different assumptions about the size of, and growth rate of bacteria in, the protected compartment. RESULTS: The existence of a protected compartment can increase the likelihood of resistance to the single drug active in that compartment, but only if bacteria resistant to that drug can grow in the protected compartment or if the host is non-adherent to the treatment regimen. However, the protected compartment may also slow the ascent of bacteria resistant to drugs not active in it (e.g. isoniazid) by providing a reservoir of non-selected mycobacteria. The model predicts that relative rates of killing are more important than mutation rates in determining the order in which resistant mutants ascend. Model predictions, in combination with data about drug resistance patterns, suggest that non-compliance, but not heterogeneity, is an important cause of treatment failure. CONCLUSION: Patterns of acquired drug resistance may be used to infer processes of selection during treatment; mathematical models can aid in generating predictions about the relative impacts of treatment parameters in the evolution of resistance, and eventually in suggesting improved treatment protocols.

Resistance to antimicrobial chemotherapy: a prescription for research and action.

The growing problem of resistance to antimicrobial chemotherapy was discussed by participants at the February 1995 workshop at Emory University on population biology, evolution, and control of infectious diseases. They discussed the nature and source of this problem and identified areas of research in which information is lacking for the development of programs to control of the emergence and spread of resistant bacteria. Particular attention was given to theoretical (mathematical modeling) and empirical studies of the within and between-host population biology (epidemiology) and the evolution of microbial resistance to chemotherapeutic agents. Suggestions were made about the kinds of models and data needed, and the procedures that could be employed to stem the ascent and dissemination of resistant bacteria. This article summarizes the observations and recommendations made at the 1995 meeting and in the correspondence between participants that followed. It concludes with an update on the theoretical and empirical research on the between- and within-host population biology and evolution of resistance to antimicrobial chemotherapy most of which has been done since that meeting.

Broad conditions favor the evolution of phase-variable loci.

UNLABELLED: Simple sequence repeat (SSR) tracts produce stochastic on-off switching, or phase variation, in the expression of a panoply of surface molecules in many bacterial commensals and pathogens. A change to the number of repeats in a tract may alter the phase of the translational reading frame, which toggles the on-off state of the switch. Here, we construct an in silico SSR locus with mutational dynamics calibrated to those of the Haemophilus influenzae mod locus. We simulate its evolution in a regimen of two alternating environments, simultaneously varying the selection coefficient, s, and the epoch length, T. Some recent work in a simpler (two-locus) model suggested that stochastic switching in a regimen of two alternating environments may be evolutionarily favored only if the selection coefficients in the two environments are nearly equal ("symmetric") or selection is very strong. This finding was puzzling, as it greatly restricted the conditions under which stochastic switching might evolve. Instead, we find agreement with other recent theoretical work, observing selective utility for stochastic switching if the product sT is large enough for the favored state to nearly fix in both environments. Symmetry is required neither in s nor in sT. Because we simulate finite populations and use a detailed model of the SSR locus, we are also able to examine the impact of population size and of several SSR locus parameters. Our results indicate that conditions favoring evolution and maintenance of SSR loci in bacteria are quite broad. IMPORTANCE: Bacteria experience frequent changes of environment during the infection cycle. One means to rapidly adapt is stochastic switching: a bacterial lineage will stochastically produce a variety of genotypes, so that some descendants will survive if the environment changes. Stochastic switching mediated by simple sequence repeat (SSR) loci is widespread among bacterial commensals and pathogens and influences critical interactions with host surfaces or immune effectors, thereby affecting host persistence, transmission, and virulence. Here, we use the most detailed in silico model of an SSR locus to date, with its phase variation calibrated to match the mod locus of Haemophilus influenzae. The type III restriction-modification system encoded by mod participates in the regulation of multiple other genes; thus, SSR-mediated phase variation of mod has far-reaching cis-regulatory effects. This coupling of phase-variable switching to complex phenotypic effects has been described as the "phasevarion" and is central to understanding the infection cycle of bacterial commensals and pathogens.

Vaccine allocation in a declining epidemic.

Sizeable quantities of 2009 pandemic influenza A/H1N1 (H1N1pdm) vaccine in the USA became available at the end of 2009 when the autumn wave of the epidemic was declining. At that point, risk factors for H1N1-related mortality for some of the high-risk groups, particularly adults with underlying health conditions, could be estimated. Although those high-risk groups are natural candidates for being in the top priority tier for vaccine allocation, another candidate group is school-aged children through their role as vectors for transmission affecting the whole community. In this paper, we investigate the question of prioritization for vaccine allocation in a declining epidemic between two groups-a group with a high risk of mortality versus a 'core' group with a relatively low risk of mortality but fuelling transmission in the community. We show that epidemic data can be used, under certain assumptions on future decline, seasonality and vaccine efficacy in different population groups, to give a criterion when initial prioritization of a population group with a sufficiently high risk of epidemic-associated mortality is advisable over the policy of prioritizing the core group.