Characterising information gains and losses when collecting multiple epidemic model outputs.

BACKGROUND: Collaborative comparisons and combinations of epidemic models are used as policy-relevant evidence during epidemic outbreaks. In the process of collecting multiple model projections, such collaborations may gain or lose relevant information. Typically, modellers contribute a probabilistic summary at each time-step. We compared this to directly collecting simulated trajectories. We aimed to explore information on key epidemic quantities; ensemble uncertainty; and performance against data, investigating potential to continuously gain information from a single cross-sectional collection of model results. METHODS: We compared projections from the European COVID-19 Scenario Modelling Hub. Five teams modelled incidence in Belgium, the Netherlands, and Spain. We compared July 2022 projections by incidence, peaks, and cumulative totals. We created a probabilistic ensemble drawn from all trajectories, and compared to ensembles from a median across each model's quantiles, or a linear opinion pool. We measured the predictive accuracy of individual trajectories against observations, using this in a weighted ensemble. We repeated this sequentially against increasing weeks of observed data. We evaluated these ensembles to reflect performance with varying observed data. RESULTS: By collecting modelled trajectories, we showed policy-relevant epidemic characteristics. Trajectories contained a right-skewed distribution well represented by an ensemble of trajectories or a linear opinion pool, but not models' quantile intervals. Ensembles weighted by performance typically retained the range of plausible incidence over time, and in some cases narrowed this by excluding some epidemic shapes. CONCLUSIONS: We observed several information gains from collecting modelled trajectories rather than quantile distributions, including potential for continuously updated information from a single model collection. The value of information gains and losses may vary with each collaborative effort's aims, depending on the needs of projection users. Understanding the differing information potential of methods to collect model projections can support the accuracy, sustainability, and communication of collaborative infectious disease modelling efforts.

Translating the COVID-19 epidemiological situation into policies and measures: the Belgian experience.

The COVID-19 pandemic led to sustained surveillance efforts, which made unprecedented volumes and types of data available. In Belgium, these data were used to conduct a targeted and regular assessment of the epidemiological situation. In addition, management tools were developed, incorporating key indicators and thresholds, to define risk levels and offer guidance to policy makers. Categorizing risk into various levels provided a stable framework to monitor the COVID-19 epidemiological situation and allowed for clear communication to authorities. Although translating risk levels into specific public health measures has remained challenging, this experience was foundational for future evaluation of the situation for respiratory infections in general, which, in Belgium, is now based on a management tool combining different data sources.

Cluster pattern analysis of environmental stressors and quantifying their impact on all-cause mortality in Belgium.

Environmental stress represents an important burden on health and leads to a considerable number of diseases, hospitalisations, and excess mortality. Our study encompasses a representative sample size drawn from the Belgian population in 2016 (n = 11.26 million, with a focus on n = 11.15 million individuals). The analysis is conducted at the geographical level of statistical sectors, comprising a total of n = 19,794 sectors, with a subset of n = 18,681 sectors considered in the investigation. We integrated multiple parameters at the finest spatial level and constructed three categories of environmental stress through clustering: air pollution, noise stress and stress related to specific land-use types. We observed identifiable patterns in the spatial distribution of stressors within each cluster category. We assessed the relationship between age-standardized all-cause mortality rates (ASMR) and environmental stressors. Our research found that especially very high air pollution values in areas where traffic is the dominant local component of air pollution (ASMR + 14,8%, 95% CI: 10,4 - 19,4%) and presence of industrial land (ASMR + 14,7%, 95% CI: 9,4 - 20,2%) in the neighbourhood are associated with an increased ASMR. Cumulative exposure to multiple sources of unfavourable environmental stress (simultaneously high air pollution, high noise, presence of industrial land or proximity of primary/secondary roads and lack of green space) is associated with an increase in ASMR (ASMR + 26,9%, 95% CI: 17,1 - 36,5%).

Trends in socioeconomic inequalities in cause-specific premature mortality in Belgium, 1998-2019.

BACKGROUND: Higher levels of socioeconomic deprivation have been consistently associated with increased risk of premature mortality, but a detailed analysis by causes of death is lacking in Belgium. We aim to investigate the association between area deprivation and all-cause and cause-specific premature mortality in Belgium over the period 1998-2019. METHODS: We used the 2001 and 2011 Belgian Indices of Multiple Deprivation to assign statistical sectors, the smallest geographical units in the country, into deprivation deciles. All-cause and cause-specific premature mortality rates, population attributable fraction, and potential years of life lost due to inequality were estimated by period, sex, and deprivation deciles. RESULTS: Men and women living in the most deprived areas were 1.96 and 1.78 times more likely to die prematurely compared to those living in the least deprived areas over the period under study (1998-2019). About 28% of all premature deaths could be attributed to socioeconomic inequality and about 30% of potential years of life lost would be averted if the whole population of Belgium faced the premature mortality rates of the least deprived areas. CONCLUSION: Premature mortality rates have declined over time, but inequality has increased due to a faster pace of decrease in the least deprived areas compared to the most deprived areas. As the causes of death related to poor lifestyle choices contribute the most to the inequality gap, more effective, country-level interventions should be put in place to target segments of the population living in the most deprived areas as they are facing disproportionately high risks of dying.

The influence of resolution on the predictive power of spatial heterogeneity measures as biomarkers of liver fibrosis.

Spatial heterogeneity of cells in liver biopsies can be used as biomarker for disease severity of patients. This heterogeneity can be quantified by non-parametric statistics of point pattern data, which make use of an aggregation of the point locations. The method and scale of aggregation are usually chosen ad hoc, despite values of the aforementioned statistics being heavily dependent on them. Moreover, in the context of measuring heterogeneity, increasing spatial resolution will not endlessly provide more accuracy. The question then becomes how changes in resolution influence heterogeneity indicators, and subsequently how they influence their predictive abilities. In this paper, cell level data of liver biopsy tissue taken from chronic Hepatitis B patients is used to analyze this issue. Firstly, Morisita-Horn indices, Shannon indices and Getis-Ord statistics were evaluated as heterogeneity indicators of different types of cells, using multiple resolutions. Secondly, the effect of resolution on the predictive performance of the indices in an ordinal regression model was investigated, as well as their importance in the model. A simulation study was subsequently performed to validate the aforementioned methods. In general, for specific heterogeneity indicators, a downward trend in predictive performance could be observed. While for local measures of heterogeneity a smaller grid-size is outperforming, global measures have a better performance with medium-sized grids. In addition, the use of both local and global measures of heterogeneity is recommended to improve the predictive performance.

Reflections On Epidemiological Modeling To Inform Policy During The COVID-19 Pandemic In Western Europe, 2020-23.

We reflect on epidemiological modeling conducted throughout the COVID-19 pandemic in Western Europe, specifically in Belgium, France, Italy, the Netherlands, Portugal, Switzerland, and the United Kingdom. Western Europe was initially one of the worst-hit regions during the COVID-19 pandemic. Western European countries deployed a range of policy responses to the pandemic, which were often informed by mathematical, computational, and statistical models. Models differed in terms of temporal scope, pandemic stage, interventions modeled, and analytical form. This diversity was modulated by differences in data availability and quality, government interventions, societal responses, and technical capacity. Many of these models were decisive to policy making at key junctures, such as during the introduction of vaccination and the emergence of the Alpha, Delta, and Omicron variants. However, models also faced intense criticism from the press, other scientists, and politicians around their accuracy and appropriateness for decision making. Hence, evaluating the success of models in terms of accuracy and influence is an essential task. Modeling needs to be supported by infrastructure for systems to collect and share data, model development, and collaboration between groups, as well as two-way engagement between modelers and both policy makers and the public.

Key risk factors associated with fractal dimension based geographical clustering of COVID-19 data in the Flemish and Brussels region, Belgium.

Introduction: COVID-19 remains a major concern globally. Therefore, it is important to evaluate COVID-19's rapidly changing trends. The fractal dimension has been proposed as a viable method to characterize COVID-19 curves since epidemic data is often subject to considerable heterogeneity. In this study, we aim to investigate the association between various socio-demographic factors and the complexity of the COVID-19 curve as quantified through its fractal dimension. Methods: We collected population indicators data (ethnic composition, socioeconomic status, number of inhabitants, population density, the older adult population proportion, vaccination rate, satisfaction, and trust in the government) at the level of the statistical sector in Belgium. We compared these data with fractal dimension indicators of COVID-19 incidence between 1 January - 31 December 2021 using canonical correlation analysis. Results: Our results showed that these population indicators have a significant association with COVID-19 incidences, with the highest explanatory and predictive power coming from the number of inhabitants, population density, and ethnic composition. Conclusion: It is important to monitor these population indicators during a pandemic, especially when dealing with targeted interventions for a specific population.

Key performance indicators of COVID-19 contact tracing in Belgium from September 2020 to December 2021.

The goal of tracing, testing, and quarantining contacts of infected individuals is to contain the spread of infectious diseases, a strategy widely used during the COVID-19 pandemic. However, limited research exists on the effectiveness of contact tracing, especially with regard to key performance indicators (KPIs), such as the proportion of cases arising from previously identified contacts. In our study, we analyzed contact tracing data from Belgium collected between September 2020 and December 2021 to assess the impact of contact tracing on SARS-CoV-2 transmission and understand its characteristics. Among confirmed cases involved in contact tracing in the Flemish and Brussels-Capital regions, 19.1% were previously identified as close contacts and were aware of prior exposure. These cases, referred to as 'known' to contact tracing operators, reported on average fewer close contacts compared to newly identified individuals (0.80 versus 1.05), resulting in fewer secondary cases (0.23 versus 0.28). Additionally, we calculated the secondary attack rate, representing infections per contact, which was on average lower for the 'known' cases (0.22 versus 0.25) between December 2020 and August 2021. These findings indicate the effectiveness of contact tracing in Belgium in reducing SARS-CoV-2 transmission. Although we were unable to quantify the exact number of prevented cases, our findings emphasize the importance of contact tracing as a public health measure. In addition, contact tracing data provide indications of potential shifts in transmission patterns among different age groups associated with emerging variants of concern and increasing vaccination rates.

Measures of spatial heterogeneity in the liver tissue micro-environment as predictive factors for fibrosis score.

The organization and interaction between hepatocytes and other hepatic non-parenchymal cells plays a pivotal role in maintaining normal liver function and structure. Although spatial heterogeneity within the tumor micro-environment has been proven to be a fundamental feature in cancer progression, the role of liver tissue topology and micro-environmental factors in the context of liver damage in chronic infection has not been widely studied yet. We obtained images from 110 core needle biopsies from a cohort of chronic hepatitis B patients with different fibrosis stages according to METAVIR score. The tissue sections were immunofluorescently stained and imaged to determine the locations of CD45 positive immune cells and HBsAg-negative and HBsAg-positive hepatocytes within the tissue. We applied several descriptive techniques adopted from ecology, including Getis-Ord, the Shannon Index and the Morisita-Horn Index, to quantify the extent to which immune cells and different types of liver cells co-localize in the tissue biopsies. Additionally, we modeled the spatial distribution of the different cell types using a joint log-Gaussian Cox process and proposed several features to quantify spatial heterogeneity. We then related these measures to the patient fibrosis stage by using a linear discriminant analysis approach. Our analysis revealed that the co-localization of HBsAg-negative hepatocytes with immune cells and the co-localization of HBsAg-positive hepatocytes with immune cells are equally important factors for explaining the METAVIR score in chronic hepatitis B patients. Moreover, we found that if we allow for an error of 1 on the METAVIR score, we are able to reach an accuracy of around 80%. With this study we demonstrate how methods adopted from ecology and applied to the liver tissue micro-environment can be used to quantify heterogeneity and how these approaches can be valuable in biomarker analyses for liver topology.

The influence of COVID-19 risk perception and vaccination status on the number of social contacts across Europe: insights from the CoMix study.

BACKGROUND: The SARS-CoV-2 transmission dynamics have been greatly modulated by human contact behaviour. To curb the spread of the virus, global efforts focused on implementing both Non-Pharmaceutical Interventions (NPIs) and pharmaceutical interventions such as vaccination. This study was conducted to explore the influence of COVID-19 vaccination status and risk perceptions related to SARS-CoV-2 on the number of social contacts of individuals in 16 European countries. METHODS: We used data from longitudinal surveys conducted in the 16 European countries to measure social contact behaviour in the course of the pandemic. The data consisted of representative panels of participants in terms of gender, age and region of residence in each country. The surveys were conducted in several rounds between December 2020 and September 2021 and comprised of 29,292 participants providing a total of 111,103 completed surveys. We employed a multilevel generalized linear mixed effects model to explore the influence of risk perceptions and COVID-19 vaccination status on the number of social contacts of individuals. RESULTS: The results indicated that perceived severity played a significant role in social contact behaviour during the pandemic after controlling for other variables (p-value < 0.001). More specifically, participants who had low or neutral levels of perceived severity reported 1.25 (95% Confidence intervals (CI) 1.13 - 1.37) and 1.10 (95% CI 1.00 - 1.21) times more contacts compared to those who perceived COVID-19 to be a serious illness, respectively. Additionally, vaccination status was also a significant predictor of contacts (p-value < 0.001), with vaccinated individuals reporting 1.31 (95% CI 1.23 - 1.39) times higher number of contacts than the non-vaccinated. Furthermore, individual-level factors played a more substantial role in influencing contact behaviour than country-level factors. CONCLUSION: Our multi-country study yields significant insights on the importance of risk perceptions and vaccination in behavioral changes during a pandemic emergency. The apparent increase in social contact behaviour following vaccination would require urgent intervention in the event of emergence of an immune escaping variant.

Longitudinal social contact data analysis: insights from 2 years of data collection in Belgium during the COVID-19 pandemic.

BACKGROUND: During the COVID-19 pandemic, the CoMix study, a longitudinal behavioral survey, was designed to monitor social contacts and public awareness in multiple countries, including Belgium. As a longitudinal survey, it is vulnerable to participants' "survey fatigue", which may impact inferences. METHODS: A negative binomial generalized additive model for location, scale, and shape (NBI GAMLSS) was adopted to estimate the number of contacts reported between age groups and to deal with under-reporting due to fatigue within the study. The dropout process was analyzed with first-order auto-regressive logistic regression to identify factors that influence dropout. Using the so-called next generation principle, we calculated the effect of under-reporting due to fatigue on estimating the reproduction number. RESULTS: Fewer contacts were reported as people participated longer in the survey, which suggests under-reporting due to survey fatigue. Participant dropout is significantly affected by household size and age categories, but not significantly affected by the number of contacts reported in any of the two latest waves. This indicates covariate-dependent missing completely at random (MCAR) in the dropout pattern, when missing at random (MAR) is the alternative. However, we cannot rule out more complex mechanisms such as missing not at random (MNAR). Moreover, under-reporting due to fatigue is found to be consistent over time and implies a 15-30% reduction in both the number of contacts and the reproduction number ([Formula: see text]) ratio between correcting and not correcting for under-reporting. Lastly, we found that correcting for fatigue did not change the pattern of relative incidence between age groups also when considering age-specific heterogeneity in susceptibility and infectivity. CONCLUSIONS: CoMix data highlights the variability of contact patterns across age groups and time, revealing the mechanisms governing the spread/transmission of COVID-19/airborne diseases in the population. Although such longitudinal contact surveys are prone to the under-reporting due to participant fatigue and drop-out, we showed that these factors can be identified and corrected using NBI GAMLSS. This information can be used to improve the design of similar, future surveys.

A practical illustration of spatial smoothing methods for disconnected regions with INLA: spatial survey on overweight and obesity in Malaysia.

BACKGROUND: National prevalence could mask subnational heterogeneity in disease occurrence, and disease mapping is an important tool to illustrate the spatial pattern of disease. However, there is limited information on techniques for the specification of conditional autoregressive models in disease mapping involving disconnected regions. This study explores available techniques for producing district-level prevalence estimates for disconnected regions, using as an example childhood overweight in Malaysia, which consists of the Peninsular and Borneo regions separated by the South China Sea. We used data from Malaysia National Health and Morbidity Survey conducted in 2015. We adopted Bayesian hierarchical modelling using the integrated nested Laplace approximation (INLA) program in R-software to model the spatial distribution of overweight among 6301 children aged 5-17 years across 144 districts located in two disconnected regions. We illustrate different types of spatial models for prevalence mapping across disconnected regions, taking into account the survey design and adjusting for district-level demographic and socioeconomic covariates. RESULTS: The spatial model with split random effects and a common intercept has the lowest Deviance and Watanabe Information Criteria. There was evidence of a spatial pattern in the prevalence of childhood overweight across districts. An increasing trend in smoothed prevalence of overweight was observed when moving from the east to the west of the Peninsular and Borneo regions. The proportion of Bumiputera ethnicity in the district had a significant negative association with childhood overweight: the higher the proportion of Bumiputera ethnicity in the district, the lower the prevalence of childhood overweight. CONCLUSION: This study illustrates different available techniques for mapping prevalence across districts in disconnected regions using survey data. These techniques can be utilized to produce reliable subnational estimates for any areas that comprise of disconnected regions. Through the example, we learned that the best-fit model was the one that considered the separate variations of the individual regions. We discovered that the occurrence of childhood overweight in Malaysia followed a spatial pattern with an east-west gradient trend, and we identified districts with high prevalence of overweight. This information could help policy makers in making informed decisions for targeted public health interventions in high-risk areas.

How contact patterns during the COVID-19 pandemic are related to pre-pandemic contact patterns and mobility trends.

BACKGROUND: Non-pharmaceutical interventions (NPIs) were adopted in Belgium in order to decrease social interactions between people and as such decrease viral transmission of SARS-CoV-2. With the aim to better evaluate the impact of NPIs on the evolution of the pandemic, an estimation of social contact patterns during the pandemic is needed when social contact patterns are not available yet in real time. METHODS: In this paper we use a model-based approach allowing for time varying effects to evaluate whether mobility and pre-pandemic social contact patterns can be used to predict the social contact patterns observed during the COVID-19 pandemic between November 11, 2020 and July 4, 2022. RESULTS: We found that location-specific pre-pandemic social contact patterns are good indicators for estimating social contact patterns during the pandemic. However, the relationship between both changes with time. Considering a proxy for mobility, namely the change in the number of visitors to transit stations, in interaction with pre-pandemic contacts does not explain the time-varying nature of this relationship well. CONCLUSION: In a situation where data from social contact surveys conducted during the pandemic are not yet available, the use of a linear combination of pre-pandemic social contact patterns could prove valuable. However, translating the NPIs at a given time into appropriate coefficients remains the main challenge of such an approach. In this respect, the assumption that the time variation of the coefficients can somehow be related to aggregated mobility data seems unacceptable during our study period for estimating the number of contacts at a given time.

The impact of national and international travel on spatio-temporal transmission of SARS-CoV-2 in Belgium in 2021.

BACKGROUND: The Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has rapidly spread over the world and caused tremendous impacts on global health. Understanding the mechanism responsible for the spread of this pathogen and the impact of specific factors, such as human mobility, will help authorities to tailor interventions for future SARS-CoV-2 waves or newly emerging airborne infections. In this study, we aim to analyze the spatio-temporal transmission of SARS-CoV-2 in Belgium at municipality level between January and December 2021 and explore the effect of different levels of human travel on disease incidence through the use of counterfactual scenarios. METHODS: We applied the endemic-epidemic modelling framework, in which the disease incidence decomposes into endemic, autoregressive and neighbourhood components. The spatial dependencies among areas are adjusted based on actual connectivity through mobile network data. We also took into account other important factors such as international mobility, vaccination coverage, population size and the stringency of restriction measures. RESULTS: The results demonstrate the aggravating effect of international travel on the incidence, and simulated counterfactual scenarios further stress the alleviating impact of a reduction in national and international travel on epidemic growth. It is also clear that local transmission contributed the most during 2021, and municipalities with a larger population tended to attract a higher number of cases from neighboring areas. CONCLUSIONS: Although transmission between municipalities was observed, local transmission was dominant. We highlight the positive association between the mobility data and the infection spread over time. Our study provides insight to assist health authorities in decision-making, particularly when the disease is airborne and therefore likely influenced by human movement.

Spatio-temporal model to investigate COVID-19 spread accounting for the mobility amongst municipalities.

The rapid spread of COVID-19 worldwide led to the implementation of various non-pharmaceutical interventions to limit transmission and hence reduce the number of infections. Using telecom-operator-based mobility data and a spatio-temporal dynamic model, the impact of mobility on the evolution of the pandemic at the level of the 581 Belgian municipalities is investigated. By decomposing incidence, particularly into within- and between-municipality components, we noted that the global epidemic component is relatively more important in larger municipalities (e.g., cities), while the local component is more relevant in smaller (rural) municipalities. Investigation of the effect of mobility on the pandemic spread showed that reduction of mobility has a significant impact in reducing the number of new infections.

Measuring small-area level deprivation in Belgium: The Belgian Index of Multiple Deprivation.

BACKGROUND: In the past, deprivation has been mostly captured through simple and univariate measures such as low income or poor educational attainment in research on health and social inequalities in Belgium. This paper presents a shift towards a more complex, multidimensional measure of deprivation at the aggregate level and describes the development of the first Belgian Indices of Multiple Deprivation (BIMDs) for the years 2001 and 2011. METHODS: The BIMDs are constructed at the level of the smallest administrative unit in Belgium, the statistical sector. They are a combination of six domains of deprivation: income, employment, education, housing, crime and health. Each domain is built on a suite of relevant indicators representing individuals that suffer from a certain deprivation in an area. The indicators are combined to create the domain deprivation scores, and these scores are then weighted to create the overall BIMDs scores. The domain and BIMDs scores can be ranked and assigned to deciles from 1 (the most deprived) to 10 (the least deprived). RESULTS: We show geographical variations in the distribution of the most and least deprived statistical sectors in terms of individual domains and overall BIMDs, and we identify hotspots of deprivation. The majority of the most deprived statistical sectors are located in Wallonia, whereas most of the least deprived statistical sectors are in Flanders. CONCLUSION: The BIMDs offer a new tool for researches and policy makers for analyzing patterns of deprivation and identifying areas that would benefit from special initiatives and programs.

Spatio-temporal dynamic of the COVID-19 epidemic and the impact of imported cases in Rwanda.

INTRODUCTION: Africa was threatened by the coronavirus disease 2019 (COVID-19) due to the limited health care infrastructure. Rwanda has consistently used non-pharmaceutical strategies, such as lockdown, curfew, and enforcement of prevention measures to control the spread of COVID-19. Despite the mitigation measures taken, the country has faced a series of outbreaks in 2020 and 2021. In this paper, we investigate the nature of epidemic phenomena in Rwanda and the impact of imported cases on the spread of COVID-19 using endemic-epidemic spatio-temporal models. Our study provides a framework for understanding the dynamics of the epidemic in Rwanda and monitoring its phenomena to inform public health decision-makers for timely and targeted interventions. RESULTS: The findings provide insights into the effects of lockdown and imported infections in Rwanda's COVID-19 outbreaks. The findings showed that imported infections are dominated by locally transmitted cases. The high incidence was predominant in urban areas and at the borders of Rwanda with its neighboring countries. The inter-district spread of COVID-19 was very limited due to mitigation measures taken in Rwanda. CONCLUSION: The study recommends using evidence-based decisions in the management of epidemics and integrating statistical models in the analytics component of the health information system.

Social contact patterns during the COVID-19 pandemic in 21 European countries - evidence from a two-year study.

BACKGROUND: Most countries have enacted some restrictions to reduce social contacts to slow down disease transmission during the COVID-19 pandemic. For nearly two years, individuals likely also adopted new behaviours to avoid pathogen exposure based on personal circumstances. We aimed to understand the way in which different factors affect social contacts - a critical step to improving future pandemic responses. METHODS: The analysis was based on repeated cross-sectional contact survey data collected in a standardized international study from 21 European countries between March 2020 and March 2022. We calculated the mean daily contacts reported using a clustered bootstrap by country and by settings (at home, at work, or in other settings). Where data were available, contact rates during the study period were compared with rates recorded prior to the pandemic. We fitted censored individual-level generalized additive mixed models to examine the effects of various factors on the number of social contacts. RESULTS: The survey recorded 463,336 observations from 96,456 participants. In all countries where comparison data were available, contact rates over the previous two years were substantially lower than those seen prior to the pandemic (approximately from over 10 to < 5), predominantly due to fewer contacts outside the home. Government restrictions imposed immediate effect on contacts, and these effects lingered after the restrictions were lifted. Across countries, the relationships between national policy, individual perceptions, or personal circumstances determining contacts varied. CONCLUSIONS: Our study, coordinated at the regional level, provides important insights into the understanding of the factors associated with social contacts to support future infectious disease outbreak responses.

Fractal dimension based geographical clustering of COVID-19 time series data.

Understanding the local dynamics of COVID-19 transmission calls for an approach that characterizes the incidence curve in a small geographical unit. Given that incidence curves exhibit considerable day-to-day variation, the fractal structure of the time series dynamics is investigated for the Flanders and Brussels Regions of Belgium. For each statistical sector, the smallest administrative geographical entity in Belgium, fractal dimensions of COVID-19 incidence rates, based on rolling time spans of 7, 14, and 21 days were estimated using four different estimators: box-count, Hall-Wood, variogram, and madogram. We found varying patterns of fractal dimensions across time and location. The fractal dimension is further summarized by its mean, variance, and autocorrelation over time. These summary statistics are then used to cluster regions with different incidence rate patterns using k-means clustering. Fractal dimension analysis of COVID-19 incidence thus offers important insight into the past, current, and arguably future evolution of an infectious disease outbreak.

Cohort-based smoothing methods for age-specific contact rates.

The use of social contact rates is widespread in infectious disease modeling since it has been shown that they are key driving forces of important epidemiological parameters. Quantification of contact patterns is crucial to parameterize dynamic transmission models and to provide insights on the (basic) reproduction number. Information on social interactions can be obtained from population-based contact surveys, such as the European Commission project POLYMOD. Estimation of age-specific contact rates from these studies is often done using a piecewise constant approach or bivariate smoothing techniques. For the latter, typically, smoothness is introduced in the dimensions of the respondent's and contact's age (i.e., the rows and columns of the social contact matrix). We propose a smoothing constrained approach-taking into account the reciprocal nature of contacts-introducing smoothness over the diagonal (including all subdiagonals) of the social contact matrix. This modeling approach is justified assuming that when people age their contact behavior changes smoothly. We call this smoothing from a cohort perspective. Two approaches that allow for smoothing over social contact matrix diagonals are proposed, namely (i) reordering of the diagonal components of the contact matrix and (ii) reordering of the penalty matrix ensuring smoothness over the contact matrix diagonals. Parameter estimation is done in the likelihood framework by using constrained penalized iterative reweighted least squares. A simulation study underlines the benefits of cohort-based smoothing. Finally, the proposed methods are illustrated on the Belgian POLYMOD data of 2006. Code to reproduce the results of the article can be downloaded on this GitHub repository https://github.com/oswaldogressani/Cohort_smoothing.