Approximation of Bayesian Hawkes process with inlabru

Hawkes process are very popular mathematical tools for modeling phenomena exhibiting a self-exciting or self-correcting behavior. Typical examples are earthquakes occurrence, wild-fires, drought, capture-recapture, crime violence, trade exchange, and social network activity. The widespread use of Hawkes process in different fields calls for fast, reproducible, reliable, easy-to-code techniques to implement such models. We offer a technique to perform approximate Bayesian inference of Hawkes process parameters based on the use of the R-package inlabru . The inlabru R-package, in turn, relies on the INLA methodology to approximate the posterior of the parameters. Our Hawkes process approximation is based on a decomposition of the log-likelihood in three parts, which are linearly approximated separately. The linear approximation is performed with respect to the mode of the parameters' posterior distribution, which is determined with an iterative gradient-based method. The approximation of the posterior parameters is therefore deterministic, ensuring full reproducibility of the results. The proposed technique only requires the user to provide the functions to calculate the different parts of the decomposed likelihood, which are internally linearly approximated by the R-package inlabru . We provide a comparison with the bayesianETAS R-package which is based on an MCMC method. The two techniques provide similar results but our approach requires two to ten times less computational time to converge, depending on the amount of data.

Identifying extreme COVID-19 mortality risks in English small areas: a disease cluster approach.

The COVID-19 pandemic is having a huge impact worldwide and has highlighted the extent of health inequalities between countries but also in small areas within a country. Identifying areas with high mortality is important both of public health mitigation in COVID-19 outbreaks, and of longer term efforts to tackle social inequalities in health. In this paper we consider different statistical models and an extension of a recent method to analyze COVID-19 related mortality in English small areas during the first wave of the epidemic in the first half of 2020. We seek to identify hotspots, and where they are most geographically concentrated, taking account of observed area factors as well as spatial correlation and clustering in regression residuals, while also allowing for spatial discontinuities. Results show an excess of COVID-19 mortality cases in small areas surrounding London and in other small areas in North-East and and North-West of England. Models alleviating spatial confounding show ethnic isolation, air quality and area morbidity covariates having a significant and broadly similar impact on COVID-19 mortality, whereas nursing home location seems to be slightly less important.

Mapping ex ante risks of COVID-19 in Indonesia using a Bayesian geostatistical model on airport network data.

A rapid response to global infectious disease outbreaks is crucial to protect public health. Ex ante information on the spatial probability distribution of early infections can guide governments to better target protection efforts. We propose a two-stage statistical approach to spatially map the ex ante importation risk of COVID-19 and its uncertainty across Indonesia based on a minimal set of routinely available input data related to the Indonesian flight network, traffic and population data, and geographical information. In a first step, we use a generalised additive model to predict the ex ante COVID-19 risk for 78 domestic Indonesian airports based on data from a global model on the disease spread and covariates associated with Indonesian airport network flight data prior to the global COVID-19 outbreak. In a second step, we apply a Bayesian geostatistical model to propagate the estimated COVID-19 risk from the airports to all of Indonesia using freely available spatial covariates including traffic density, population and two spatial distance metrics. The results of our analysis are illustrated using exceedance probability surface maps, which provide policy-relevant information accounting for the uncertainty of the estimates on the location of areas at risk and those that might require further data collection.

Spread of COVID-19 Deaths in Jakarta: Cluster and Regression Analysis

Jakarta as the center of the capital city of Indonesia has a very high mobility and population density. This has resulted in the spread of COVID-19 cases also have a very high increasing trend. Regional clustering and the detection of variables that affect COVID-19 deaths can be an early warning or the basis for government policies in handling the spread of disease outbreaks. This study aims to classify areas at the subdistrict level in Jakarta based on distribution of COVID-19 cases using the K-Means method. After the regional clusters were formed, Bayesian regression analysis was carried in each cluster and sub-district to identify variables that had an effect on COVID-19 deaths. The number of deaths is assumed to have Normal distribution, and statistical inference in Bayesian regression using the Integrated Nested Laplace Approximation (INLA) approach. This study produced several interesting results including: (1) there are 4 clusters that indicate areas prone to spread with a high case rate, fairly high risk, low risk to very low risk areas. (2) most of Jakarta's sub-districts, which is about 45%, are included in areas with a fairly high risk of spreading. (3) In general, the number of recovered cases is a significant variable on the majority decrease number of COVID-19 deaths in each cluster. © 2021 IEEE.

A spatiotemporal analysis of NO 2 concentrations during the Italian 2020 COVID-19 lockdown.

When a new environmental policy or a specific intervention is taken in order to improve air quality, it is paramount to assess and quantify-in space and time-the effectiveness of the adopted strategy. The lockdown measures taken worldwide in 2020 to reduce the spread of the SARS-CoV-2 virus can be envisioned as a policy intervention with an indirect effect on air quality. In this paper we propose a statistical spatiotemporal model as a tool for intervention analysis, able to take into account the effect of weather and other confounding factor, as well as the spatial and temporal correlation existing in the data. In particular, we focus here on the 2019/2020 relative change in nitrogen dioxide (NO 2 ) concentrations in the north of Italy, for the period of March and April during which the lockdown measure was in force. We found that during March and April 2020 most of the studied area is characterized by negative relative changes (median values around - 25%), with the exception of the first week of March and the fourth week of April (median values around 5%). As these changes cannot be attributed to a weather effect, it is likely that they are a byproduct of the lockdown measures. There are two aspects of our research that are equally interesting. First, we provide a unique statistical perspective for calculating the relative change in the NO 2 by jointly modeling pollutant concentrations time series. Second, as an output we provide a collection of weekly continuous maps, describing the spatial pattern of the NO 2 2019/2020 relative changes.

MAPPING SUB-DISTRICTS-LEVEL AND PREDICTING SPATIAL SPREAD OF COVID-19 DEATH CASE IN JAKARTA

Currently, the number of deaths caused by COVID-19 continues to increase significantly, especially in areas with high population density and mobility such as Jakarta, Indonesia. Spread of infectious diseases has a spatial closeness which results in cases of COVID-19 deaths also have a spatial dependency which is influenced by cases of deaths in the surrounding area. This study aims to map and predict the number of COVID-19 deaths using the Bayes Linear Mixed Model (LMM) method involving spatial random effects. The response variable is number of deaths and the explanatory variable are number of positive cases of COVID-19 and population density with sub-district area units in Jakarta. Response variable is divided into 6 schemes (PSBB 1, PSBB Transition 1, PSBB 2, PSBB Transition 2, PPKM 1 and PPKM 2) which is adjusted to the policies and social distancing activities from Jakarta provincial government, and assumed to have a normal distribution with INLA (Integrated Nested Laplace Approximation) inference approach. Some important results from this study are: in all 6 social distancing schemes, the number of positive cases of Covid-19 has a significant effect on the increase in number of deaths, while population density has a significant effect along with the increasing variance value of response data. The Bayes LMM has successfully mapped the spread of COVID-19 cases with the best RMSE value of 3.31. The mapping results show that several sub-districts with high population density and sub-districts located on Jakarta border have a high risk of death. Furthermore, the PSBB and PSBB Transition social distancing schemes are considered to be quite effective in suppressing the diversity number of deaths. However, it is different from the PPKM scheme where it is predicted that there will be an increase in the number of high-risk districts for COVID-19 up to 51% per day.

A practical approach for geographic prioritization and targeting of insecticide-treated net distribution campaigns during public health emergencies and in resource-limited settings.

BACKGROUND: The use of data in targeting malaria control efforts is essential for optimal use of resources. This work provides a practical mechanism for prioritizing geographic areas for insecticide-treated net (ITN) distribution campaigns in settings with limited resources. METHODS: A GIS-based weighted approach was adopted to categorize and rank administrative units based on data that can be applied in various country contexts where Plasmodium falciparum transmission is reported. Malaria intervention and risk factors were used to rank local government areas (LGAs) in Nigeria for prioritization during mass ITN distribution campaigns. Each factor was assigned a unique weight that was obtained through application of the analytic hierarchy process (AHP). The weight was then multiplied by a value based on natural groupings inherent in the data, or the presence or absence of a given intervention. Risk scores for each factor were then summated to generate a composite unique risk score for each LGA. This risk score was translated into a prioritization map which ranks each LGA from low to high priority in terms of timing of ITN distributions. RESULTS: A case study using data from Nigeria showed that a major component that influenced the prioritization scheme was ITN access. Sensitivity analysis results indicate that changes to the methodology used to quantify ITN access did not modify outputs substantially. Some 120 LGAs were categorized as 'extremely high' or 'high' priority when a spatially interpolated ITN access layer was used. When prioritization scores were calculated using DHS-reported state level ITN access, 108 (90.0%) of the 120 LGAs were also categorized as being extremely high or high priority. The geospatial heterogeneity found among input risk factors suggests that a range of variables and covariates should be considered when using data to inform ITN distributions. CONCLUSION: The authors provide a tool for prioritizing regions in terms of timing of ITN distributions. It serves as a base upon which a wider range of vector control interventions could be targeted. Its value added can be found in its potential for application in multiple country contexts, expediated timeframe for producing outputs, and its use of systematically collected malaria indicators in informing prioritization.

The association of wildfire air pollution with COVID-19 incidence in New South Wales, Australia.

The 2020 COVID-19 outbreak in New South Wales (NSW), Australia, followed an unprecedented wildfire season that exposed large populations to wildfire smoke. Wildfires release particulate matter (PM), toxic gases and organic and non-organic chemicals that may be associated with increased incidence of COVID-19. This study estimated the association of wildfire smoke exposure with the incidence of COVID-19 in NSW. A Bayesian mixed-effect regression was used to estimate the association of either the average PM10 level or the proportion of wildfire burned area as proxies of wildfire smoke exposure with COVID-19 incidence in NSW, adjusting for sociodemographic risk factors. The analysis followed an ecological design using the 129 NSW Local Government Areas (LGA) as the ecological units. A random effects model and a model including the LGA spatial distribution (spatial model) were compared. A higher proportional wildfire burned area was associated with higher COVID-19 incidence in both the random effects and spatial models after adjustment for sociodemographic factors (posterior mean = 1.32 (99% credible interval: 1.05-1.67) and 1.31 (99% credible interval: 1.03-1.65), respectively). No evidence of an association between the average PM10 level and the COVID-19 incidence was found. LGAs in the greater Sydney and Hunter regions had the highest increase in the risk of COVID-19. This study identified wildfire smoke exposures were associated with increased risk of COVID-19 in NSW. Research on individual responses to specific wildfire airborne particles and pollutants needs to be conducted to further identify the causal links between SARS-Cov-2 infection and wildfire smoke. The identification of LGAs with the highest risk of COVID-19 associated with wildfire smoke exposure can be useful for public health prevention and or mitigation strategies.

Long-term exposure to air pollution and COVID-19 incidence: A multi-country study.

The study of the impacts of air pollution on COVID-19 has gained increasing attention. However, most of the existing studies are based on a single country, with a high degree of variation in the results reported in different papers. We attempt to inform the debate about the long-term effects of air pollution on COVID-19 by conducting a multi-country analysis using a spatial ecological design, including Canada, Italy, England and the United States. The model allows the residual spatial autocorrelation after accounting for covariates. It is concluded that the effects of PM2.5 and NO2 are inconsistent across countries. Specifically, NO2 was not found to be an important factor affecting COVID-19 infection, while a large effect for PM2.5 in the US is not found in the other three countries. The Population Attributable Fraction for COVID-19 incidence ranges from 3.4% in Canada to 45.9% in Italy, although with considerable uncertainty in these estimates.

Association between the New COVID-19 Cases and Air Pollution with Meteorological Elements in Nine Counties of New York State.

The principal objective of this article is to assess the possible association between the number of COVID-19 infected cases and the concentrations of fine particulate matter (PM2.5) and ozone (O3), atmospheric pollutants related to people's mobility in urban areas, taking also into account the effect of meteorological conditions. We fit a generalized linear mixed model which includes spatial and temporal terms in order to detect the effect of the meteorological elements and COVID-19 infected cases on the pollutant concentrations. We consider nine counties of the state of New York which registered the highest number of COVID-19 infected cases. We implemented a Bayesian method using integrated nested Laplace approximation (INLA) with a stochastic partial differential equation (SPDE). The results emphasize that all the components used in designing the model contribute to improving the predicted values and can be included in designing similar real-world data (RWD) models. We found only a weak association between PM2.5 and ozone concentrations with COVID-19 infected cases. Records of COVID-19 infected cases and other covariates data from March to May 2020 were collected from electronic health records (EHRs) and standard RWD sources.

Population-weighted exposure to air pollution and COVID-19 incidence in Germany.

Many countries have enforced social distancing to stop the spread of COVID-19. Within countries, although the measures taken by governments are similar, the incidence rate varies among areas (e.g., counties, cities). One potential explanation is that people in some areas are more vulnerable to the coronavirus disease because of their worsened health conditions caused by long-term exposure to poor air quality. In this study, we investigate whether long-term exposure to air pollution increases the risk of COVID-19 infection in Germany. The results show that nitrogen dioxide (NO 2 ) is significantly associated with COVID-19 incidence, with a 1 µ g  m - 3 increase in long-term exposure to NO 2 increasing the COVID-19 incidence rate by 5.58% (95% credible interval [CI]: 3.35%, 7.86%). This result is consistent across various models. The analyses can be reproduced and updated routinely using public data sources and shared R code.

Effectiveness of the measures to flatten the epidemic curve of COVID-19. The case of Spain.

After the cases of COVID-19 skyrocketed, showing that it was no longer possible to contain the spread of the disease, the governments of many countries launched mitigation strategies, trying to slow the spread of the epidemic and flatten its curve. The Spanish Government adopted physical distancing measures on March 14; 13 days after the epidemic outbreak started its exponential growth. Our objective in this paper was to evaluate ex-ante (before the flattening of the curve) the effectiveness of the measures adopted by the Spanish Government to mitigate the COVID-19 epidemic. Our hypothesis was that the behavior of the epidemic curve is very similar in all countries. We employed a time series design, using information from January 17 to April 5, 2020 on the new daily COVID-19 cases from Spain, China and Italy. We specified two generalized linear mixed models (GLMM) with variable response from the Gaussian family (i.e. linear mixed models): one to explain the shape of the epidemic curve of accumulated cases and the other to estimate the effect of the intervention. Just one day after implementing the measures, the variation rate of accumulated cases decreased daily, on average, by 3.059 percentage points, (95% credibility interval: -5.371, -0.879). This reduction will be greater as time passes. The reduction in the variation rate of the accumulated cases, on the last day for which we have data, has reached 5.11 percentage points. The measures taken by the Spanish Government on March 14, 2020 to mitigate the epidemic curve of COVID-19 managed to flatten the curve and although they have not (yet) managed to enter the decrease phase, they are on the way to do so.