The influence of cross-border mobility on the COVID-19 epidemic in Nordic countries.

Restrictions of cross-border mobility are typically used to prevent an emerging disease from entering a country in order to slow down its spread. However, such interventions can come with a significant societal cost and should thus be based on careful analysis and quantitative understanding on their effects. To this end, we model the influence of cross-border mobility on the spread of COVID-19 during 2020 in the neighbouring Nordic countries of Denmark, Finland, Norway and Sweden. We investigate the immediate impact of cross-border travel on disease spread and employ counterfactual scenarios to explore the cumulative effects of introducing additional infected individuals into a population during the ongoing epidemic. Our results indicate that the effect of inter-country mobility on epidemic growth is non-negligible essentially when there is sizeable mobility from a high prevalence country or countries to a low prevalence one. Our findings underscore the critical importance of accurate data and models on both epidemic progression and travel patterns in informing decisions related to inter-country mobility restrictions.

On realized serial and generation intervals given control measures: The COVID-19 pandemic case.

The SARS-CoV-2 pathogen is currently spreading worldwide and its propensity for presymptomatic and asymptomatic transmission makes it difficult to control. The control measures adopted in several countries aim at isolating individuals once diagnosed, limiting their social interactions and consequently their transmission probability. These interventions, which have a strong impact on the disease dynamics, can affect the inference of the epidemiological quantities. We first present a theoretical explanation of the effect caused by non-pharmaceutical intervention measures on the mean serial and generation intervals. Then, in a simulation study, we vary the assumed efficacy of control measures and quantify the effect on the mean and variance of realized generation and serial intervals. The simulation results show that the realized serial and generation intervals both depend on control measures and their values contract according to the efficacy of the intervention strategies. Interestingly, the mean serial interval differs from the mean generation interval. The deviation between these two values depends on two factors. First, the number of undiagnosed infectious individuals. Second, the relationship between infectiousness, symptom onset and timing of isolation. Similarly, the standard deviations of realized serial and generation intervals do not coincide, with the former shorter than the latter on average. The findings of this study are directly relevant to estimates performed for the current COVID-19 pandemic. In particular, the effective reproduction number is often inferred using both daily incidence data and the generation interval. Failing to account for either contraction or mis-specification by using the serial interval could lead to biased estimates of the effective reproduction number. Consequently, this might affect the choices made by decision makers when deciding which control measures to apply based on the value of the quantity thereof.

Drug Use Changes at the Individual Level: Results from a Longitudinal, Multisite Survey in Young Europeans Frequenting the Nightlife Scene.

BACKGROUND: Monitoring emerging trends in the increasingly dynamic European drug market is vital; however, information on change at the individual level is scarce. In the current study, we investigated changes in drug use over 12 months in European nightlife attendees. METHOD: In this longitudinal online survey, changes in substances used, use frequency in continued users, and relative initiation of use at follow-up were assessed for 20 different substances. To take part, participants had to be aged 18-34 years; be from Belgium, Italy, the Netherlands, Sweden, or the UK; and have attended at least 6 electronic music events in the past 12 months at baseline. Of 8,045 volunteers at baseline, 2,897 completed the survey at both time points (36% follow-up rate), in 2017 and 2018. RESULTS: The number of people using ketamine increased by 21% (p < 0.001), and logarithmized frequency of use in those continuing use increased by 15% (p < 0.001; 95% CI: 0.07-0.23). 4-Fluoroamphetamine use decreased by 27% (p < 0.001), and logarithmized frequency of use in continuing users decreased by 15% (p < 0.001, 95% CI: -0.48 to -0.23). The drugs with the greatest proportion of relative initiation at follow-up were synthetic cannabinoids (73%, N = 30), mephedrone (44%, N = 18), alkyl nitrites (42%, N = 147), synthetic dissociatives (41%, N = 15), and prescription opioids (40%, N = 48). CONCLUSIONS: In this European nightlife sample, ketamine was found to have the biggest increase in the past 12 months, which occurred alongside an increase in frequency of use in continuing users. The patterns of uptake and discontinuation of alkyl nitrates, novel psychoactive substances, and prescription opioids provide new information that has not been captured by existing cross-sectional surveys. These findings demonstrate the importance of longitudinal assessments of drug use and highlight the dynamic nature of the European drug landscape.

Quantitative Assessment of High School Students' Poly-drug Use: Related Social Aspects and School Dropout.

INTRODUCTION: Poly-drug use has increased in recent decades, especially in young drugusing groups. Classic epidemiological indicators of drug use, such as prevalence and incidence of users of specific substances, are not adequate as measures of the possible harms of poly-drug use. We applied poly-drug use indicators, based on substance-specific harm scores reported by van Amsterdam and Nutt in 2015, to data from high school student surveys, showing their usefulness in identifying high-risk drug consumption. Analysing the 'correlation' between high-risk drug use of high school students and school dropout allows the evaluation of adopted prevention policies and may suggest more suitable approaches. METHODS: Each drug user is characterized by two specific scores: overall frequency of use of substances during the period of interest (FUS) and poly-drug use score (PDS). The poly-drug use score is a weighted average of the harm scores of the individual substances used multiplied by their respective frequencies of use. The PDS increases with the frequency of use, with the number of substances used, and with the specific harm scores of each substance. This indicator consists of two components, one representing the health harm score toward self and the other the social harm score toward others. RESULTS: The indicators have been applied to sample data involving youth population, specifically the ESPAD®Italia survey data on high school students conducted annually in Italy. The trends of poly-drug use at different ages of students, 15-19 years, over time, and gender have been studied. The results have been linked to educational outcomes, early school leaving and social aspects, making it possible to assess present prevention interventions and suggest appropriate planning of future prevention interventions. CONCLUSION: Poly-drug use indicators allow a comprehensive quantitative evaluation of the risks of drug use. The analysis of the links between heavy use of drugs, school performance and dropout, and the social variables that influence them, shown in this work, suggests how best to plan secondary or indicated prevention interventions at school. The problem of including "new" NPS in analyses is also briefly discussed.

Modelling preventive measures and their effect on generation times in emerging epidemics.

We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing community. The model is based on an infectivity process, which we define through stochastic contact and infectiousness processes, so that each individual has an independent infectivity profile. In particular, we monitor variations of the reproduction number and of the distribution of generation times. We show that some interventions, i.e. uniform reduction and vaccination, affect the former while leaving the latter unchanged, whereas other interventions, i.e. isolation, screening and contact tracing, affect both quantities. We provide a theoretical analysis of the variation of these quantities, and we show that, in practice, the variation of the generation time distribution can be significant and that it can cause biases in the estimation of reproduction numbers. The framework, because of its general nature, captures the properties of many infectious diseases, but particular emphasis is on COVID-19, for which numerical results are provided.

Commentary on the use of the reproduction number R during the COVID-19 pandemic.

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

Cost-effectiveness of varicella and herpes zoster vaccination in Sweden: An economic evaluation using a dynamic transmission model.

OBJECTIVES: Comprehensive cost-effectiveness analyses of introducing varicella and/or herpes zoster vaccination in the Swedish national vaccination programme. DESIGN: Cost-effectiveness analyses based on epidemiological results from a specifically developed transmission model. SETTING: National vaccination programme in Sweden, over an 85- or 20-year time horizon depending on the vaccination strategy. PARTICIPANTS: Hypothetical cohorts of people aged 12 months and 65-years at baseline. INTERVENTIONS: Four alternative vaccination strategies; 1, not to vaccinate; 2, varicella vaccination with one dose of the live attenuated vaccine at age 12 months and a second dose at age 18 months; 3, herpes zoster vaccination with one dose of the live attenuated vaccine at 65 years of age; and 4, both vaccine against varicella and herpes zoster with the before-mentioned strategies. MAIN OUTCOME MEASURES: Accumulated cost and quality-adjusted life years (QALY) for each strategy, and incremental cost-effectiveness ratios (ICER). RESULTS: It would be cost-effective to vaccinate against varicella (dominant), but not to vaccinate against herpes zoster (ICER of EUR 200,000), assuming a cost-effectiveness threshold of EUR 50,000 per QALY. The incremental analysis between varicella vaccination only and the combined programme results in a cost per gained QALY of almost EUR 1.6 million. CONCLUSIONS: The results from this study are central components for policy-relevant decision-making, and suggest that it was cost-effective to introduce varicella vaccination in Sweden, whereas herpes zoster vaccination with the live attenuated vaccine for the elderly was not cost-effective-the health effects of the latter vaccination cannot be considered reasonable in relation to its costs. Future observational and surveillance studies are needed to make reasonable predictions on how boosting affects the herpes zoster incidence in the population, and thus the cost-effectiveness of a vaccination programme against varicella. Also, the link between herpes zoster and sequelae need to be studied in more detail to include it suitably in health economic evaluations.

Estimating the incidence, prevalence and clinical burden of hepatitis C over time in Italy.

Our objective was to estimate HCV clinical burden over time in Italy. A national age-specific HCV prevalence in 1995 was obtained from studies conducted in general population samples and intravenous drug users. Age profile of new HCV infections and trend of incidence since 1985 were derived from a database of reported acute HCV infections. These incidence and prevalence data were used to estimate HCV burden from 1950 to 2030 by mathematical modelling. Different rates of HCV related liver disease progression were tested to assess the robustness of estimates. It is estimated that HCV had a major spread in Italy in 1945-1969. HCV RNA-positive subjects peaked around 1970; their prevalence in 2005 was 3.2%, 58% of them being >65 y of age. The number of individuals with HCV related cirrhosis and that of HCV liver related deaths peaked in 1980-1985. In 2005, they were approximately 230,000 (range 150,000-240,000, according to lower or higher disease progression rates) and approximately 7,000 (range 2200-12,300), respectively: both will be halved by 2025. In conclusion, unlike other industrialized countries, the burden of clinically relevant HCV-positive cases in Italy is already on the decline and will further reduce in the future. This is due to differences in the age-specific prevalence, most of HCV-positive Italians currently being >65 y of age.

Estimation in emerging epidemics: biases and remedies.

When analysing new emerging infectious disease outbreaks, one typically has observational data over a limited period of time and several parameters to estimate, such as growth rate, the basic reproduction number R0, the case fatality rate and distributions of serial intervals, generation times, latency and incubation times and times between onset of symptoms, notification, death and recovery/discharge. These parameters form the basis for predicting a future outbreak, planning preventive measures and monitoring the progress of the disease outbreak. We study inference problems during the emerging phase of an outbreak, and point out potential sources of bias, with emphasis on: contact tracing backwards in time, replacing generation times by serial intervals, multiple potential infectors and censoring effects amplified by exponential growth. These biases directly affect the estimation of, for example, the generation time distribution and the case fatality rate, but can then propagate to other estimates such as R0 and growth rate. We propose methods to remove or at least reduce bias using statistical modelling. We illustrate the theory by numerical examples and simulations.

Effect of textured insoles on postural control during static upright posture following lower limb muscle fatigue.

BACKGROUND: The purpose of this study was to assess the effects of textured insoles on static upright posture before and after lower limb muscle fatigue. Textured insoles used contained small and non-deformable pebbles of various sizes that are able to stimulate a major number of mechanoreceptors. It was inserted inside footwear. METHODS: Ten healthy young adults participated in the study (mean age 26.1±3.07 years). They were asked to stand on a force platform in four sensory states: vision, no vision, with and without natural plantar stimulation. For each sensory state the subjects underwent a single 30-second trial in pre-fatigue and post-fatigue conditions. Muscle fatigue was induced by 60 seconds of continuous jumping. Center of pressure displacement, sway velocity, antero-posterior and medio-lateral sway velocity were measured using force platform. RESULTS: Textured insoles had a stabilizing effect on balance compared to control insoles. Textured insoles significantly reduced CoPDISP and VA/P levels in closed eyes pre-fatigue condition. Post-fatigue all postural parameters improved in both vision and no vision conditions. CONCLUSIONS: Textured insoles with rigid stimulation significantly improved CoPDISP, independently of vision, supplying relevant and complete sensory information and improving balance in fatigue conditions.

A simple explanation for the low impact of border control as a countermeasure to the spread of an infectious disease.

A simple model for the effect of border control or travel restrictions is proposed. It can be used to predict the corresponding results in quite complex disease spread models and has the advantage of providing easy qualitative understanding of the effects of this kind of intervention.

Modeling the impact of combined vaccination programs against varicella and herpes zoster in Norway.

BACKGROUND: Adoption of varicella immunization in Europe is limited due to a predicted increase in the incidence of herpes zoster (HZ) resulting from a removal of exogenous boosting by varicella vaccination. Most available assessments of immunization strategies only considered universal varicella vaccination (alone or in combination with HZ by the live vaccine). The development of a new subunit recombinant zoster vaccine may provide new perspectives of HZ control. METHODS: We used a mathematical model for VZV in Norway based on the progressive immunity formulation of exogenous boosting. We evaluated a complete range of alternative immunization options against varicella and HZ including both universal and targeted varicella vaccination, either alone or with zoster immunization, and zoster immunization alone. We considered all values of the boosting intensity consistent with the Norwegian HZ incidence and compared the performance of the currently available live vaccine vs. a new recombinant vaccine. RESULTS: Universal varicella vaccination alone resulted in a marked increase in the incidence of HZ under all scenarios considered. Even under the most favorable hypotheses on the magnitude of the boosting intensity, this increase could be mitigated only by a parallel HZ immunization with a recombinant vaccine, assuming a long duration of protection. Targeted varicella immunization of adolescents resulted in a modest increase in the HZ incidence which could be counterbalanced by both the live and, especially, the recombinant vaccine. CONCLUSIONS: Given current knowledge on HZ pathogenesis and exogenous boosting, targeted varicella vaccination of adolescents was the only strategy that was not predicted to impact the epidemiology of HZ, and therefore it may represent a suitable alternative to universal vaccination. These results are aimed to support vaccine policy decisions in Norway and other countries with a similar VZV epidemiology.

False occurrences of functional motifs in protein sequences highlight evolutionary constraints.

BACKGROUND: False occurrences of functional motifs in protein sequences can be considered as random events due solely to the sequence composition of a proteome. Here we use a numerical approach to investigate the random appearance of functional motifs with the aim of addressing biological questions such as: How are organisms protected from undesirable occurrences of motifs otherwise selected for their functionality? Has the random appearance of functional motifs in protein sequences been affected during evolution? RESULTS: Here we analyse the occurrence of functional motifs in random sequences and compare it to that observed in biological proteomes; the behaviour of random motifs is also studied. Most motifs exhibit a number of false positives significantly similar to the number of times they appear in randomized proteomes (=expected number of false positives). Interestingly, about 3% of the analysed motifs show a different kind of behaviour and appear in biological proteomes less than they do in random sequences. In some of these cases, a mechanism of evolutionary negative selection is apparent; this helps to prevent unwanted functionalities which could interfere with cellular mechanisms. CONCLUSION: Our thorough statistical and biological analysis showed that there are several mechanisms and evolutionary constraints both of which affect the appearance of functional motifs in protein sequences.

[Two methods to analyze trends in the incidence of heroin and cocaine use in Barcelona [Spain]]. / Dos métodos para analizar la evolución de la incidencia de consumo de heroína y cocaína en Barcelona.

OBJECTIVES: To describe 2 statistical methods for estimating trends in the incidence of heroin and cocaine use in Barcelona. METHODS: Admissions for treatment of heroin and cocaine consumption recorded by the Barcelona Drug Information System between 1991 and 2003 were used. We selected 4,367 subjects initiating treatment for the first time for heroin use, and 2,147 for cocaine use. Two statistical techniques were employed: Reporting Delay Adjustment (RDA) and the Log-linear Model (LLM). RDA was used in subjects who initiated drug consumption between 1991 and 2003, and LLM for those who began heroin use between 1967 and 2003 and cocaine use between 1971 and 2003. In addition, for each drug and method the latency period (LP) was determined (years between first consumption and first treatment). RESULTS: Comparison of the distributions of the LP for each drug revealed that heroin users initiated treatment for the first time sooner than cocaine users, regardless of the method employed. In general, the estimated incidence of heroin use in Barcelona fell progressively after 1982. In contrast, the incidence of cocaine use rose rapidly until 1998, and has been irregular since. The incidence of cocaine use began to be substantial in the early 1990s, but took several years to manifest itself as problematic. CONCLUSION: The estimated incidence was underestimated by RDA compared with LLM, but the incidence of heroin use could be biased before 1991 due to changes in treatment provisions. Although the estimated incidence is relative to individuals who are admitted for treatment at some time in their life, trends in incidence can be used to plan future actions.

The natural history of varicella zoster virus infection in Norway: Further insights on exogenous boosting and progressive immunity to herpes zoster.

We use age-structured models for VZV transmission and reactivation to reconstruct the natural history of VZV in Norway based on available pre-vaccination serological data, contact matrices, and herpes zoster incidence data. Depending on the hypotheses on contact and transmission patterns, the basic reproduction number of varicella in Norway ranges between 3.7 and 5.0, implying a vaccine coverage between 73 and 80% to effectively interrupt transmission with a 100% vaccine efficacy against infection. The varicella force of infection peaks during early childhood (3-5 yrs) and shows a prolonged phase of higher risk during the childbearing period, though quantitative variations can occur depending on contact patterns. By expressing the magnitude of exogenous boosting as a proportion of the force of infection, it is shown that reactivation is well described by a progressive immunity mechanism sustained by a large, though possibly below 100%, degree of exogenous boosting, in agreement with findings from other Nordic countries, implying large reproduction numbers of boosting. Moreover, magnitudes of exogenous boosting below 40% are robustly disconfirmed by data. These results bring further insight on the magnitude of immunity boosting and its relationship with reactivation.

Estimating Age-Specific Immunity and Force of Infection of Varicella Zoster Virus in Norway Using Mixture Models.

This study applies mixture modelling to examine age-specific immunity to varicella zoster virus (VZV) infection in Norway based on the first large-scale serological study in the general population. We estimated the seropositive proportions at different ages and calculated the underlying force of infection by using a sample of 2103 residual sera obtained from patients seeking primary and hospital care. A rapid increase in the VZV-associated immunity is observed in the first years of life with 63% of children being immune by age 5. The increase in the immunity levels slows down thereafter, with a large proportion of adults still susceptible by age 20 (around 14.5%), thus at risk of serious sequelae of varicella infection. The corresponding force of infection peaks during the preschool period, subsequently declines to a minimum between ages 10 and 20 years, and afterwards moderately increases to reach a plateau lasting throughout the childbearing period. In comparison with the traditional cut-off approach, mixture modelling used the whole data without producing any inconclusive cases, led to an unbiased classification of individuals between susceptible and immune, and provided a smoother immune profile by age. These findings represent an important step towards any decision about the introduction of varicella vaccination in Norway, as they are a primary input for mathematical transmission models aimed at evaluating potential vaccination scenarios.

[Prevalence of the use of old and new drugs among new entrants in Italian prisons]. / "Prevalenza" di uso di vecchie e nuove droghe nei nuovi ingressi in strutture penitenziarie italiane.

An epidemiological survey was conducted to evaluate the prevalence of drug use among new entrants in Italian prisons. Overall, 1267 inmates were recruited by 9 prisons. Drug use before imprisonment was reported by 55.8% of the participants. Cocaine was the most commonly used drug (42%), followed by heroin (34%), marijuana/cannabis (33%), ecstasy (7%), hallucinogens (6%), amphetamines (5%); more than one drug was reported by 68% of abusers. Recent use (1 month before imprisonment) was admitted by up to 27% of inmates. Alcohol or tobacco use was reported by 38 and 77% of the inmates, respectively. Our findings indicate that a high proportion of inmates has ever used drugs; adequate intervention is needed to reduce the risk of addictive behaviour in this population group.

Seven challenges for metapopulation models of epidemics, including households models.

This paper considers metapopulation models in the general sense, i.e. where the population is partitioned into sub-populations (groups, patches,...), irrespective of the biological interpretation they have, e.g. spatially segregated large sub-populations, small households or hosts themselves modelled as populations of pathogens. This framework has traditionally provided an attractive approach to incorporating more realistic contact structure into epidemic models, since it often preserves analytic tractability (in stochastic as well as deterministic models) but also captures the most salient structural inhomogeneity in contact patterns in many applied contexts. Despite the progress that has been made in both the theory and application of such metapopulation models, we present here several major challenges that remain for future work, focusing on models that, in contrast to agent-based ones, are amenable to mathematical analysis. The challenges range from clarifying the usefulness of systems of weakly-coupled large sub-populations in modelling the spread of specific diseases to developing a theory for endemic models with household structure. They include also developing inferential methods for data on the emerging phase of epidemics, extending metapopulation models to more complex forms of human social structure, developing metapopulation models to reflect spatial population structure, developing computationally efficient methods for calculating key epidemiological model quantities, and integrating within- and between-host dynamics in models.

Quantifying the re-exposure process to an infectious agent. Measles and varicella as examples.

BACKGROUND AND OBJECTIVES: For viral infections conferring what is usually considered as permanent immunity, re-exposure to the pathogen due to contacts with infectious individuals might be critical for immunity boosting. A major example is represented by the varicella-zoster virus (VZV) where re-exposure is thought to lead to boosting of cell mediated immunity (CMI), which plays a protective role against the development of herpes zoster (HZ). Similar concerns have recently been raised also in relation to measles. However, while the first effective exposure, i.e. infection, has been the object of many studies, both theoretical and epidemiological, there has been no corresponding investigation of the re-exposure process. METHODOLOGY AND DATA: By combining basic concepts from deterministic and stochastic modelling of infection, we develop a basic model for quantifying the timing and number of re-exposures and, consequently, the potential for immune boosting at any given age. The model is then applied to measles, mumps and rubella (MMR) in the UK, and to varicella in Italy, using literature estimates of the pre-vaccination forces of infection. RESULTS: We supply analytical expressions for the expected number of lifetime re-exposures and for underlying age-patterns, including the average age at which the last re-exposure occurs. Based on updated estimates of the force of VZV infection, we show that the expected number of boosting opportunities of CMI might be in the range 2-3, which is consistent with recent findings about the development of herpes zoster. We also show that the estimate of the age at which the last re-exposure to VZV occurs is highly sensitive to the underlying form of age dependence of the force of infection. CONCLUSIONS: Our results contribute to the study of the potential immunity boosting effect of re-exposures to an infective agent by quantifying the re-exposure process.