A Novel Hunger Games Search Optimization-Based Artificial Neural Network for Predicting Ground Vibration Intensity Induced by Mine Blasting

Innovation efforts in developing soft computing models (SCMs) of researchers and scholars are significant in recent years, especially for problems in the mining industry. So far, many SCMs have been proposed and applied to practical engineering to predict ground vibration intensity (BIGV) induced by mine blasting with high accuracy and reliability. These models significantly contributed to mitigate the adverse effects of blasting operations in mines. Despite the fact that many SCMs have been introduced with promising results, but ambitious goals of researchers are still novel SCMs with the accuracy improved. They aim to prevent the damages caused by blasting operations to the surrounding environment. This study, therefore, proposed a novel SCM based on a robust meta-heuristic algorithm, namely Hunger Games Search (HGS) and artificial neural network (ANN), abbreviated as HGS–ANN model, for predicting BIGV. Three benchmark models based on three other meta-heuristic algorithms (i.e., particle swarm optimization (PSO), firefly algorithm (FFA), and grasshopper optimization algorithm (GOA)) and ANN, named as PSO–ANN, FFA–ANN, and GOA–ANN, were also examined to have a comprehensive evaluation of the HGS–ANN model. A set of data with 252 blasting operations was collected to evaluate the effects of BIGV through the mentioned models. The data were then preprocessed and normalized before splitting into individual parts for training and validating the models. In the training phase, the HGS algorithm with the optimal parameters was fine-tuned to train the ANN model to optimize the ANN model's weights. Based on the statistical criteria, the HGS–ANN model showed its best performance with an MAE of 1.153, RMSE of 1.761, R² of 0.922, and MAPE of 0.156, followed by the GOA–ANN, FFA–ANN and PSO–ANN models with the lower performances (i.e., MAE?=?1.186, 1.528, 1.505; RMSE?=?1.772, 2.085, 2.153; R²?=?0.921, 0.899, 0.893; MAPE?=?0.231, 0.215, 0.225, respectively). Based on the outstanding performance, the HGS–ANN model should be applied broadly and across a swath of open-pit mines to predict BIGV, aiming to optimize blast patterns and reduce the environmental effects.

     

Intelligent Prediction of Blasting-Induced Ground Vibration Using ANFIS Optimized by GA and PSO

Ground vibration induced by rock blasting is one of the most crucial problems in surface mines and tunneling projects. Hence, accurate prediction of ground vibration is an important prerequisite in the minimization of its environmental impacts. This study proposes hybrid intelligent models to predict ground vibration using adaptive neuro-fuzzy inference system (ANFIS) optimized by particle swarm optimization (PSO) and genetic algorithms (GAs). To build prediction models using ANFIS, ANFIS–GA, and ANFIS–PSO, a database was established, consisting of 86 data samples gathered from two quarries in Iran. The input parameters of the proposed models were the burden, spacing, stemming, powder factor, maximum charge per delay (MCD), and distance from the blast points, while peak particle velocity (PPV) was considered as the output parameter. Based on the sensitivity analysis results, MCD was found as the most effective parameter of PPV. To check the applicability and efficiency of the proposed models, several traditional performance indices such as determination coefficient (R²) and root-mean-square error (RMSE) were computed. The obtained results showed that the proposed ANFIS–GA and ANFIS–PSO models were capable of statistically predicting ground vibration with excellent levels of accuracy. Compared to the ANFIS, the ANFIS–GA model showed an approximately 61% decrease in RMSE and 10% increase in R². Also, the ANFIS–PSO model showed an approximately 53% decrease in RMSE and 9% increase in R² compared to ANFIS. In other words, the ANFIS performance was optimized with the use of GA and PSO.

     

Comparison of dew point temperature estimation methods in Southwestern Georgia

Recent upward trends in acres irrigated have been linked to increasing near-surface moisture. Unfortunately, stations with dew point data for monitoring near-surface moisture are sparse. Thus, models that estimate dew points from more readily observed data sources are useful. Daily average dew temperatures were estimated and evaluated at 14 stations in Southwest Georgia using linear regression models and artificial neural networks (ANN). Estimation methods were drawn from simple and readily available meteorological observations, therefore only temperature and precipitation were considered as input variables. In total, three linear regression models and 27 ANN were analyzed. The two methods were evaluated using root mean square error (RMSE), mean absolute error (MAE), and other model evaluation techniques to assess the skill of the estimation methods. Both methods produced adequate estimates of daily averaged dew point temperatures, with the ANN displaying the best overall skill. The optimal performance of both models was during the warm season. Both methods had higher error associated with colder dew points, potentially due to the lack of observed values at those ranges. On average, the ANN reduced RMSE by 6.86% and MAE by 8.30% when compared to the best performing linear regression model.     

Estimation of Blast-Induced Air Overpressure in Quarry Mines Using Cubist-Based Genetic Algorithm

In the present work, blast-induced air overpressure is estimated by an innovative intelligence system based on the cubist algorithm (CA) and genetic algorithm (GA) with high accuracy, called GA–CA model. Herein, CA initialization model was developed first and the hyper-parameters of the CA model were selected randomly. Subsequently, the GA procedure was applied to perform a global search for the optimized values of the hyper-factors of the CA model. Root-mean-square error (RMSE) is utilized as a compatibility function to determine the optimal CA model with the lowest RMSE. Gaussian process (GP), conditional inference tree (CIT), principal component analysis (PCA), hybrid neural fuzzy inference system (HYFIS) and k-nearest neighbor (k-NN) models are also developed as the benchmark models in order to compare and analyze the quality of the proposed GA–CA algorithm; 164 blasting works were investigated at a quarry mine of Vietnam for this aim. The results revealed that GA significantly improved the performance of the CA model. Based on the statistical indices used for model assessment, the proposed GA–CA model was confirmed as the most superior model as compared to the other models (i.e., GP, CIT, HYFIS, PCA, k-NN). It can be applied as a robust soft computing tool for estimating blast-induced air overpressure.

     

Prediction of Blast-Induced Ground Vibration in an Open-Pit Mine by a Novel Hybrid Model Based on Clustering and Artificial Neural Network

Natural Resources Research - Ground vibration (PPV) is one of the hazard effects induced by blasting operations in open-pit mines, which can affect the surrounding structures, particularly the...     

A comparison between diatom-based pH inference models using Artificial Neural Networks (ANN), Weighted Averaging (WA) and Weighted Averaging Partial Least Squares (WA-PLS) regressions

We explored the possibility of using artificial neural networks (ANN) to develop quantitative inference models in paleolimnology. ANNs are dynamic computer systems able to learn the relations between input and output data. We developed ANN models to infer pH from fossil diatom assemblages using a calibration data set of 76 lakes in Quebec. We evaluated the predictive power of these models in comparison with the two most commonly methods used in paleolimnology: Weighted Averaging (WA) and Weighted Averaging Partial Least Squares (WA-PLS). Results show that the relationship between species assemblages and environmental variables of interest can be modelled by a 3-layer back-propagation network, with apparent R² and RMSE of 0.9 and 0.24 pH units, respectively. Leave-one-out cross-validation was used to access the reliabilities of the WA, WA-PLS and ANN models. Validation results show that the ANN model (R² _jackknife = 0.63, RMSE_jackknife = 0.45, mean bias = 0.14, maximum bias = 1.13) gives a better predictive power than the WA model (R² _jackknife = 0.56, RMSE_jackknife = 0.5, mean bias = –0.09, maximum bias = –1.07) or WA-PLS model (R² _jackknife = 0.58, RMSE_jackknife = 0.48, mean bias = –0.15, maximum bias = –1.08). We also evaluated whether the removal of certain taxa according to their tolerance changed the performance of the models. Overall, we found that the removal of taxa with high tolerances for pH improved the predictive power of WA-PLS models whereas the removal of low tolerance taxa lowered its performance. However, ANN models were generally much less affected by the removal of taxa of either low or high pH tolerance. Moreover, the best model was obtained by averaging the predictions of WA-PLS and ANN models. This implies that the two modelling approaches capture and extract complementary information from diatom assemblages. We suggest that future modelling efforts might achieve better results using analogous multi-model strategies.     

ORELM: A Novel Machine Learning Approach for Prediction of Flyrock in Mine Blasting

Blast-induced flyrock is a hazardous and undesirable phenomenon that may occur in surface mines, especially when blasting takes place near residential areas. Therefore, accurate prediction of flyrock distance is of high significance in the determination of the statutory danger area. To this end, there is a practical need to propose an accurate model to predict flyrock. Aiming at this topic, this study presents two machine learning models, including extreme learning machine (ELM) and outlier robust ELM (ORELM), for predicting flyrock. To the best of our knowledge, this is the first work that investigates the use of ORELM model in the field of flyrock prediction. To construct and verify the proposed ELM and ORELM models, a database including 82 datasets has been collected from the three granite quarry sites in Malaysia. Additionally, artificial neural network (ANN) and multiple regression models were used for comparison. According to the results, both ELM and ORELM models performed satisfactorily, and their performances were far better compared to the performances of ANN and multiple regression models.

     

Time series forecasting of river flow using an integrated approach of wavelet multi-resolution analysis and evolutionary data-driven models. A case study: Sebaou River (Algeria)

The complexity of hydrological processes and lack of data for modeling require the use of specific tools for non-linear natural phenomenon. In this paper, an effort has been made to develop a conjunction model – wavelet transformation, data-driven models, and genetic algorithm (GA) – for forecasting the daily flow of a river in northern Algeria using the time series of runoff. This catchment has a semi-arid climate and strong variability in runoff. The original time series was decomposed into multi-frequency time series by wavelet transform algorithm and used as inputs to artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS) models. Several factors must be optimized to determine the best model structures. Wavelet-based data-driven models using a GA are designed to optimize model structure. The performances of wavelet-based data-driven models (i.e. WANFIS and WANN) were superior to those of conventional models. WANFIS (RMSE = 12.15 m³/s, EC = 87.32%, R = .934) and WANN (RMSE = 15.73 m³/s, EC = 78.83%, R = .888) models improved the performances of ANFIS (RMSE = 23.13 m³/s, EC = 54.11%, R = .748) and ANN (RMSE = 22.43 m³/s, EC = 56.90%, R = .755) during the test period.     

An optimized spatial proximity model for fine particulate matter air pollution exposure assessment in areas of sparse monitoring

GIS-based proximity models are one of the key tools for the assessment of exposure to air pollution when the density of spatial monitoring stations is sparse. Central to exposure assessment that utilizes proximity models is the ‘exposure intensity–distance’ hypothesis. A major weakness in the application of this hypothesis is that it does not account for the Gaussian processes that are at the core of the physical mechanisms inherent in the dispersion of air pollutants.

Building upon the utility of spatial proximity models and the theoretical reliability of Gaussian dispersion processes of air pollutants, this study puts forward a novel Gaussian weighting function-aided proximity model (GWFPM). The study area and data set for this work consisted of transport-related emission sources of PM_2.5 in the Houston-Baytown-Sugar Land metropolitan area. Performance of the GWFPM was validated by comparing on-site observed PM_2.5 concentrations with results from classical ordinary kriging (OK) interpolation and a robust emission-weighted proximity model (EWPM). Results show that the fitting R² between possible exposure intensity calculated by GWFPM and observed PM_2.5 concentrations was 0.67. A variety of statistical evidence (i.e., bias, root mean square error [RMSE], mean absolute error [MAE], and correlation coefficient) confirmed that GWFPM outperformed OK and EWPM in estimating annual PM_2.5 concentrations for all monitoring sites. These results indicate that a GWFPM utilizing the physical dispersing mechanisms integrated may more effectively characterize annual-scale exposure than traditional models. Using GWFPM, receptors’ exposure to air pollution can be assessed with sufficient accuracy, even in those areas with a low density of monitoring sites. These results may be of use to public health and planning officials in a more accurate assessment of the annual exposure risk to a population, especially in areas where monitoring sites are sparse.     

Artificial Neural Networks in Proglacial Discharge Simulation: Application and Efficiency Analysis in Comparison to the Multivariate Regression; A Case Study of Waldemar River (Svalbard)

Artificial neural networks were applied to simulate runoff from the glacierized part of the Waldemar River catchment (Svalbard) based on hydrometeorological data collected in the summer seasons of 2010, 2011 and 2012. Continuous discharge monitoring was performed at about 1 km from the glacier snout, in the place where the river leaves the marginal zone. Averaged daily values of discharge and selected meteorological variables in a number of combinations were used to create several models based on the feed‐forward multilayer perceptron architecture. Due to specific conditions of melt water storing and releasing, two groups of models were established: the first is based on meteorological inputs only, while second includes the preceding day's mean discharge. Analysis of the multilayer perceptron simulation performance was done in comparison to the other black‐box model type, a multivariate regression method based on the following efficiency criteria: coefficient of determination (R²) and its adjusted form (adj. R²), weighted coefficient of determination (wR²), Nash–Sutcliffe coefficient of efficiency, mean absolute error, and error analysis. Moreover, the predictors' importance analysis for both multilayer perceptron and multivariate regression models was done. The performed study showed that the nonlinear estimation realized by the multilayer perceptron gives more accurate results than the multivariate regression approach in both groups of models.     

Application and comparison of two prediction models for groundwater levels: A case study in Western Jilin Province,China

Evaluation and prediction of groundwater levels through specific model(s) helps in forecasting of groundwater resources. Among the different robust tools available, the Integrated Time Series (ITS) and Back-Propagation Artificial Neural Network (BPANN) models are commonly used to empirically forecast hydrological variables. Here, we discuss the modeling process and accuracy of these two methods in assessing their relative advantages and disadvantages based on Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and coefficient of efficiency (CE). The arid and semi-arid areas of western Jilin province of China were chosen as study area owing to the decline of groundwater levels during the past decade mainly due to overexploitation. The simulation results indicated that both ITS and BPANN are accurate in reproducing (fitting) the groundwater levels and the CE are 0.98 and 0.97, respectively. In the validation phase, the comparison of the prediction accuracy of the BPANN and ITS models indicated that the BPANN models is superior to the ITS in forecasting the groundwater levels time series in term of the RMSE, MAE and CE.     

Validation of WRF model on simulating forcing data for Heihe River Basin

The research of coupling WRF (Weather Research and Forecasting Model) with a land surface model is enhanced to explore the interaction of the atmosphere and land surface; however, regional applicability of WRF model is questioned. In order to do the validation of WRF model on simulating forcing data for the Heihe River Basin, daily meteorological observation data from 15 stations of CMA (China Meteorological Administration) and hourly meteorological observation data from seven sites of WATER (Watershed Airborne Telemetry Experimental Research) are used to compare with WRF simulations, with a time range of a whole year for 2008. Results show that the average MBE (Mean Bias Error) of daily 2-m surface temperature, surface pressure, 2-m relative humidity and 10-m wind speed were ?0.19 °C, ?4.49 hPa, 4.08% and 0.92 m/s, the average RMSE (Root Mean Square Error) of them were 2.11 °C, 5.37 hPa, 9.55% and 1.73 m/s, and the average R (correlation coefficient) of them were 0.99, 0.98, 0.80 and 0.55, respectively. The average MBE of hourly 2-m surface temperature, surface pressure, 2-m relative humidity, 10-m wind speed, downward shortwave radiation and downward longwave were ?0.16 °C, ?6.62 hPa, ?5.14%, 0.26 m/s, 33.0 W/m² and ?6.44 W/m², the average RMSE of them were 2.62 °C, 17.10 hPa, 20.71%, 2.46 m/s, 152.9 W/m² and 53.5 W/m², and the average R of them were 0.96, 0.97, 0.70, 0.26, 0.91 and 0.60, respectively. Thus, the following conclusions were obtained: (1) regardless of daily or hourly validation, WRF model simulations of 2-m surface temperature, surface pressure and relative humidity are more reliable, especially for 2-m surface air temperature and surface pressure, the values of MBE were small and R were more than 0.96; (2) the WRF simulating downward shortwave radiation was relatively good, the average R between WRF simulation and hourly observation data was above 0.9, and the average R of downward longwave radiation was 0.6; (3) both wind speed and rainfall simulated from WRF model did not agree well with observation data.     

The value of a physically based model versus an empirical approach in the prediction of ephemeral gully erosion for loess-derived soils

A data set on soil losses and controlling factors for 58 ephemeral gullies has been collected in the Belgian loess belt from March 1997 to March 1999. Of the observed ephemeral gullies, 32 developed at the end of winter or in early spring (winter gullies) and 26 ephemeral gullies developed during summer (summer gullies). The assessed data have been used to test the physically based Ephemeral Gully Erosion Model (EGEM) and to compare its performance with the value of simple topographical and morphological indices in the prediction of ephemeral gully erosion.Analysis shows that EGEM is not capable of predicting ephemeral gully cross-sections well. Although conditions for input parameter assessment were ideal, some parameters such as channel erodibility, critical flow shear stress and local rainfall depth showed great uncertainty. Rather than revealing EGEM's inability of predicting ephemeral gully erosion, this analysis stresses the problematic nature of physically based models, since they often require input parameters that are not available or can hardly be obtained.With respect to the value of simple topographical and morphological indices in predicting ephemeral gully erosion, this study shows that for winter gullies and summer gullies, respectively, over 80% and about 75% of the variation in ephemeral gully volume can be explained when ephemeral gully length is known. Moreover, when previously collected data for ephemeral gullies in two Mediterranean study areas and the data for summer gullies formed in the Belgian loess belt are pooled, it appears that one single length (L)–volume (V) relation exists (V=0.048 L^1.29; R²=0.91). These findings imply that predicting ephemeral gully length is a valuable alternative for the prediction of ephemeral gully volume. A simple procedure to predict ephemeral gully length based on topographical thresholds is presented here. Secondly, the empirical length–volume relation can also be used to convert ephemeral gully length data extracted from aerial photos into ephemeral gully volumes.     

On the use of dimensioned measures of error to evaluate the performance of spatial interpolators

Spatial cross‐validation and average‐error statistics are examined with respect to their abilities to evaluate alternate spatial interpolation methods. A simple cross‐validation methodology is described, and the relative abilities of three, dimensioned error statistics—the root‐mean‐square error (RMSE), the mean absolute error (MAE), and the mean bias error (MBE)—to describe average interpolator performance are examined. To illustrate our points, climatologically averaged weather‐station temperatures were obtained from the Global Historical Climatology Network (GHCN), Version 2, and then alternately interpolated spatially (gridded) using two spatial‐interpolation procedures. Substantial differences in the performance of our two spatial interpolators are evident in maps of the cross‐validation error fields, in the average‐error statistics, as well as in estimated land‐surface‐average air temperatures that differ by more than 2°C. The RMSE and its square, the mean‐square error (MSE), are of particular interest, because they are the most widely reported average‐error measures, and they tend to be misleading. It (RMSE) is an inappropriate measure of average error because it is a function of three characteristics of a set of errors, rather than of one (the average error). Our findings indicate that MAE and MBE are natural measures of average error and that (unlike RMSE) they are unambiguous.     

一种改进的生成区域日降水场的方法及精度分析

利用全国687个气象站点11年的日降水数据,对基于地理特征和统计回归的函数拟合类模型DAYMET生成中国区域日降水场的能力进行了验证。交叉验证表明,DAYMET模型估计日降水累计得到的年降水量的绝对偏差11年平均为29.8%,年降水总量估计偏差低于20％的站点占48.3％。鉴于中国陆地区域降水深受季风的影响,不同方位气象站点对插值点的影响也有所不同,引入了站点不同方位对插值的影响权重,对DAYMET模型进行了改进,改进后年降水量的绝对偏差降为27%。与梯度距离平方反比法相比,该方法具有较高的区域降水插值精度。还以无定河流域降水插值为例,说明降水插值精度的高低与区域内雨量站点的多寡紧密相联。     

基于TM影像的荒漠绿洲交错带土壤有机质含量反演模型

选取Landsat TM影像的光谱反射率（R）、反射率之倒数（1/R）、反射率倒数之对数（lg（1/R））、反射率一阶导数（FDR）、波段深度（D）等5种光谱指标,分别建立了奇台县土壤有机质（SOM）含量的反演模型,并利用F检验来验证模型的显著性。结果表明：用各光谱指标建立的土壤各层和不同深度SOM含量的反演模型精度值由低到高的顺序均为lg（1/R）<R<1/R<FDR<D,以D反演SOM含量的模型效果最好,且对10～20 cm的SOM含量的反演精度最高,适用于对研究区SOM含量的反演,FDR的反演效果次之,1/R和R的模型精度一般,而lg（1/R）的模型精度最差;各层拟合模型的反演精准度由低到高的顺序为50～60 cm <40～50 cm <30～40 cm <20～30 cm <0～10 cm <10～20 cm,不同深度反演模型的优劣为0～60 cm <0～50 cm <0～40 cm <0～30 cm <0～10 cm <0～20 cm。     

A Test and Re-Estimation of Taylor’s Empirical Capacity–Reserve Relationship

In 1977, Taylor proposed a constant elasticity model relating capacity choice in mines to reserves. A test of this model using a very large (n = 1,195) dataset confirms its validity but obtains significantly different estimated values for the model coefficients. Capacity is somewhat inelastic with respect to reserves, with an elasticity of 0.65 estimated for open-pit plus block-cave underground mines and 0.56 for all other underground mines. These new estimates should be useful for capacity determinations as scoping studies and as a starting point for feasibility studies. The results are robust over a wide range of deposit types, deposit sizes, and time, consistent with physical constraints on mine capacity that are largely independent of technology.     

Assessing vegetation cover and biomass in restored erosion areas in Iceland using SPOT satellite data

Due to highly erodible volcanic soils and a harsh climate, livestock grazing in Iceland has led to serious soil erosion on about 40% of the country's surface. Over the last 100 years, various revegetation and restoration measures were taken on large areas distributed all over Iceland in an attempt to counteract this problem. The present research aimed to develop models for estimating percent vegetation cover (VC) and aboveground biomass (AGB) based on satellite data, as this would make it possible to assess and monitor the effectiveness of restoration measures over large areas at a fairly low cost. Models were developed based on 203 vegetation cover samples and 114 aboveground biomass samples distributed over five SPOT satellite datasets. All satellite datasets were atmospherically corrected, and digital numbers were converted into ground reflectance. Then a selection of vegetation indices (VIs) was calculated, followed by simple and multiple linear regression analysis of the relations between the field data and the calculated VIs.Best results were achieved using multiple linear regression models for both %VC and AGB. The model calibration and validation results showed that R² and RMSE values for most VIs do not vary very much. For percent VC, R² values range between 0.789 and 0.822, leading to RMSEs ranging between 15.89% and 16.72%. For AGB, R² values for low-biomass areas (AGB < 800 g/m²) range between 0.607 and 0.650, leading to RMSEs ranging between 126.08 g/m² and 136.38 g/m². The AGB model developed for all areas, including those with high biomass coverage (AGB > 800 g/m²), achieved R² values between 0.487 and 0.510, resulting in RMSEs ranging from 234 g/m² to 259.20 g/m². The models predicting percent VC generally overestimate observed low percent VC and slightly underestimate observed high percent VC. The estimation models for AGB behave in a similar way, but over- and underestimation are much more pronounced.These results show that it is possible to estimate percent VC with high accuracy based on various VIs derived from SPOT satellite data. AGB of restoration areas with low-biomass values of up to 800 g/m² can likewise be estimated with high accuracy based on various VIs derived from SPOT satellite data, whereas in the case of high biomass coverage, estimation accuracy decreases with increasing biomass values. Accordingly, percent VC can be estimated with high accuracy anywhere in Iceland, whereas AGB is much more difficult to estimate, particularly for areas with high-AGB variability.     

基于遥感和机器学习的内陆水体水深反演技术

文章主要根据机器学习算法（随机森林算法和极端梯度提升算法）和遥感水深反演的原理,利用Sentinel_2多光谱卫星数据和无人船实测水深数据,对内陆水体——梅州水库建立了随机森林（RF）、极端梯度提升（XGBoost）和支持向量机（SVM）水深反演模型,并对反演结果进行对比分析。结果表明：1）RF的训练精度为97%,测试精度为0.80;XGBoost模型的训练精度为97%,测试精度为0.79;SVM的训练精度为90%,测试精度为0.78。说明了在水深预测方面RF模型和XGBoost模型比SVM模型表现更好,对各个区段的水深值较为敏感。2）根据运行时间考察各个模型的效率,其中RF模型从读取数据至输出结果耗时3.92 s;XGBoost模型4.26 s;SVM模型6.66 s。因此,在反演精度和效率上RF模型优于XGBoost模型优于SVM模型,且RF模型的预测结果图细节更加丰富,轮廓更加分明;XGBoost模型次之,但总体效果也较好;SVM模型表现最差。由此可知,机器学习水深反演模型获得的水深结果精度明显提高,解决了传统水深反演模型精度不高的问题。     

A Spatial Variant of the Basic Reproduction Number for the New Orleans Yellow Fever Epidemic of 1878

A spatial variant of the basic reproduction number (R₀), here defined as the number of subsequent deaths attributed to an initial mortality, can be used to identify geographic variation within an epidemic. A spatial R₀ was calculated at the neighborhood level, here defined by a 50‐m buffer surrounding an index case, for mortality data from the 1878 yellow fever epidemic of New Orleans. The highest number of secondary mortalities linked to a neighborhood index case was twelve, with a further eighty‐seven extrapolated morbidity cases. Results also highlight the importance of multideath residences and cultural contacts in neighborhood‐level disease spread.