# A New Methodology to Comprehend the Effect of El Niño and La Niña Oscillation in Early Warning of Anthrax Epidemic Among Livestock

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*Zoonotic Diseases*2021–2022)

## Abstract

**:**

_{0}) for the districts that are significantly clustered were calculated. Early warning or risk prediction developed with a layer of R

_{0}superimposed on a risk map helps in the preparedness for the disease occurrence, and precautionary measures before the spread of the disease.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection

#### 2.1.1. Disease Incidence and ENSO Events Classification

^{2}area, 181 blocks spread across 30 districts, and 29,340 villages holding 27.7 million livestock animals. The current study included all 30 districts of the state over the period of 2004–2019. The village-level livestock anthrax outbreak data were retrieved from the Dept. of Animal husbandry, Bengaluru, Karnataka, India. The outbreak data were spatial and temporal referenced and cross-checked for coordinate data (X, Y), species, district codes, and month of occurrence and cleaned for all types of errors before storing the data in a database.

#### 2.1.2. Livestock Data

#### 2.1.3. Meteorological Data

^{2}), potential evaporation rate (w/m

^{2}), specific humidity (kg/kg), rainfall (kg/m

^{2}/s), air temperature (k), wind speed (m/s), and surface pressure (pa). These parameters were obtained from the Global Land Data Assimilation System https://ldas.gsfc.nasa.gov/gldas (new and reprocessed GLDAS version 2) (accessed on 10 February 2021), which uses advanced land surface modeling and data integration methods to capture satellite and ground-based observed data with a spatial resolution of 0.25° × 0.25° and a temporal resolution retrieved in network common data format (netCDF). This includes metadata as well as data that have a multidimensional array and data dimensions. The data were extracted using the ‘ncdf4’ package in the R tool.

#### 2.1.4. Remote Sensing Data

#### 2.1.5. Soil Profile

#### 2.2. Spatial Endemicity

#### 2.3. Getis-Ord Gi* Spatial Statistics to Identify Hotspots (Spatial Autocorrelation)

#### 2.4. Space-Time Cluster Analysis

#### 2.5. Identifying Risk Factors by Linear Discriminant Analysis

_{k}= scatter matrix

_{w}= within class scatter

_{b}= between class scatter

#### 2.6. Risk Modelling and Mapping

#### 2.7. Basic Reproduction Number (R_{0})

_{0}). The threshold of R

_{0}is where its significance lies. The number of affected people will increase if R

_{0}> 1. Additionally, the number will drop if R

_{0}< 1. The transmission rate of a disease is expressed by R

_{0}. The basic reproduction rate is a pandemic’s common phrase since it explicitly reflects the virus’s nature. There are numerous methods available for the estimation of the R

_{0}[43]. Maximum likelihood estimation (ML), exponential growth rate (EG), attack rate (AR), time-dependent method (TD), sequential Bayesian approach (SB), and various other methods can be implemented to calculate R

_{0}[44]. In the present work, R

_{0}was estimated using EG, ML, and AR approaches.

#### 2.7.1. Exponential Growth Rate (EG)

_{0}could be deduced from the exponential epidemic growth curve. In the initial stages of an epidemic, R

_{0}is associated with exponential growth as follows:

#### 2.7.2. Maximum Likelihood Estimate (ML)

#### 2.7.3. Attack Rate Estimate (AR)

_{0}on the anticipated risk maps, we gave a clear and in-depth insight into how a disease affects a specific area. Basic reproduction rate (R

_{0}) calculations were made using R statistical software (version 3.6.3). It is essential to evaluate a disease’s potential for transmission, predict the scale of epidemics, and spread awareness of preventative actions. Superimposing the R

_{0}on the risk map predicted using the density of livestock, soil parameters, meteorological, and remote sensing parameters provides a visualized and comprehensive view of the likelihood and impact of a disease in a given region.

#### 2.8. Statistical Software

_{0}, the R packages plyr, dplyr, rgdal, raster, data.table, openxlsx, tmap, sp, spdep, sf, BAMM tools, foreign, geosphere, MASS, biomod2, dismo, mgcv, randomforest, mda, gbm, earth data extraction, data alignment, annotation, analysis, modeling, and risk mapping were all performed using Getis ord’s Index. SaTScan v9.6 was implemented to obtain the spatial and temporal clusters in the respective study area.

## 3. Results

#### 3.1. Temporal Distribution of Weather Parameters

#### 3.2. Spatial Endemicity of Anthrax

#### 3.3. Spatial Autocorrelation of Anthrax

#### 3.4. Space-Time Cluster Analysis of Anthrax

#### 3.5. Linear Discriminant Analysis of Anthrax

#### 3.6. Anthrax Risk Assessment and Estimation

#### 3.7. Anthrax Risk Prediction and Mapping

#### 3.8. Estimation of Basic Reproduction Number (R_{0}) of Anthrax

_{0}) and to model R

_{0}with risk already estimated using various risk factors. The result of this stage is more easy to interpret and projectable for the development of suitable preventive actions. The R

_{0}is defined as the exact number of projected secondary cases that one primary case in a susceptible population can generate. This value of R

_{0}has a significant impact on both the daily incidence and the extent of the outbreaks, indicating that more animals would become sick in the foreseeable. The management of diseases in the area can be aided by these insights.

_{0}was estimated for the districts falling in the significantly clustered zone generated by SaTScan and Getis Ord index in the study between 2004 and 2019 based on El Niño and La Niña years. The locations with an R

_{0}value exceeding 1.00 have an increasing trend in disease incidence, complexity, greater risk, and vice versa. The R

_{0}values for El Niño years ranged from 0.76 to 2.11, indicating that the southern and eastern regions are particularly vulnerable to anthrax (Figure 8A). Throughout the La Niña years, the R

_{0}value ranged between 0.98 and 1.99 with high symptom severity in the southern, northeastern, and central regions (Figure 8B). Furthermore, the mobility of infected animals from one location to the other could cause the regions with low R

_{0}values to change to high R

_{0}values in the coming years.

## 4. Discussion

## 5. Conclusions

_{0}superimposed on a risk map helps in the preparedness for the disease occurrence, precautionary measures before the spread of the disease, and finding an estimate of the population proportion that must be vaccinated to eliminate the infection from that population.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**A**) Diagrammatic representation of machine-learning powered early warning. (

**B**) Flowchart depicting the risk modeling and risk mapping.

**Figure 3.**District-wise cumulative incidence of anthrax in Karnataka (2004–2019), (

**A**) El Niño years & (

**B**) La Niña years, respectively.

**Figure 5.**Space-Time Analysis (2004–2014), (

**A**) El Niño years, and (

**B**) La Niña years, respectively. Where, red spots represent high risk disease incidence and pink spots represent incidence with negligible risk.

**Figure 6.**El Niño and La Niña years’ outbreaks are depicted on a map of Karnataka, respectively. (

**A**) Case data: red-colored circles denote locations where anthrax has been reported, (

**B**) control data: blue-colored dots denote locations where anthrax has not been reported, and (

**C**) case-control data: displays both the existence and absence of anthrax incidence.

**Figure 7.**Anthrax risk prediction map (2004–2019) El Niño years (

**A**) and La Niña years (

**B**), respectively. Where the red spots represent the disease incidence having high risk.

**Figure 8.**Anthrax R

_{0}values on risk prediction map district wise (2004–2019) (

**A**) El Niño years and (

**B**) La Niña years, respectively.

Parameters | El Niño | La Niña | ||||||
---|---|---|---|---|---|---|---|---|

Mean | SD | Max. | Min. | Mean | SD | Max. | Min. | |

Air temperature (k) | 23.91 | 1.69 | 27.43 | 13.21 | 23.16 | 1.69 | 27.13 | 13.21 |

Soil moisture (kg/m^{2}) | 23.37 | 2.31 | 28.87 | 13.21 | 23.94 | 2.42 | 30.15 | 13.21 |

Rainfall (kg/m^{2}/s) | 1.07 | 0.96 | 14.74 | 0.89 | 1.06 | 0.96 | 14.74 | 0.89 |

Vegetative index (−1 to +1) | 0.41 | 0.09 | 0.71 | -0.03 | 0.43 | 0.09 | 0.73 | −0.09 |

Parameters | Mean (Presence) | SD | F Value | p Value | 95% CI |
---|---|---|---|---|---|

Air_Temperature | 23.91 | 1.69 | 37.83 | <0.05 * | 23.13 to 24.68 |

EVI | 1.32 | 0.11 | 0.54 | 0.466 | 1.31 to 1.326 |

LAI | 2.01 | 2.44 | 0.78 | 0.379 | 1.84 to 2.17 |

LST | 27.9 | 3.26 | 1.04 | 0.309 | 27.65 to 28.14 |

NDVI | 1.44 | 0.12 | 0.00 | 0.947 | 1.43 to 1.441 |

PET | 943.96 | 259.63 | 2.49 | 0.116 | 913.31 to 974.60 |

Potential_evaporation_rate | 245.87 | 33.59 | 4.66 | 0.032 * | 240.45 to 251.28 |

Rain_precipitation_rate | 1.07 | 0.96 | 0.65 | 0.423 | 1.01 to 1.12 |

Soil_moisture | 23.37 | 2.31 | 0.58 | 0.449 | 23.23 to 23.50 |

Specific_humidity | 1.08 | 0.96 | 2.35 | 0.128 | 0.97 to 1.19 |

Surface_Pressure | 85,809.19 | 6584.11 | 1.83 | 0.178 | 85,143.10 to 86,475.27 |

Wind_speed | 4.19 | 0.99 | 22.32 | <0.05 * | 3.84 to 4.54 |

Parameter | Mean (Presence) | SD | F Value | p Value | 95% CI |
---|---|---|---|---|---|

Air_Temperature | 23.16 | 1.69 | 22.535 | <0.05 * | 22.59 to 23.73 |

EVI | 1.31 | 0.1 | 3.922 | 0.049 | 1.30 to 1.32 |

LAI | 2.03 | 2.44 | 2.576 | 0.111 | 1.75 to 2.31 |

LST | 26.96 | 3.32 | 0.622 | 0.431 | 26.77 to 27.15 |

NDVI | 1.45 | 0.12 | 7.959 | 0.005 * | 1.43 to 1.47 |

PET | 1015.63 | 249.43 | 0.383 | 0.537 | 1004.69 to 1026.57 |

Potential_evaporation_rate | 218.82 | 32.09 | 0.770 | 0.382 | 216.82 to 220.82 |

Rain_precipitation_rate | 1.06 | 0.96 | 2.732 | 0.100 | 0.95 to 1.17 |

Soil_moisture | 23.94 | 2.42 | 3.087 | 0.081 ** | 23.64 to 24.24 |

Specific_humidity | 1.07 | 0.96 | 9.857 | 0.002 * | 0.86 to 1.28 |

Surface_Pressure | 85,602.37 | 6581.58 | 3.074 | 0.082 | 84,784.33 to 86,420.41 |

Wind_speed | 3.72 | 0.95 | 22.909 | <0.05 * | 3.40 to 4.04 |

Sl.No | Model | Model Specification | KAPPA | ROC | TSS | AUC | ACCURACY | ERROR RATE | F1 SCORE | LOGLOSS |
---|---|---|---|---|---|---|---|---|---|---|

1 | GLM | $E(Y|X)=\mu ={g}^{-1}\left(X\beta \right)$ Y—Expected Value, X—Conditional, $X\beta $—Linear Predicator, g—Link Function | 0.698 | 0.943 | 0.769 | 0.9426 | 0.875 | 0.125 | 0.885 | 0.295 |

2 | GAM | $g\left(E\left(Y\right)\right)=\phantom{\rule{0ex}{0ex}}{\beta}_{0}+{f}_{1}\left({x}_{1}\right)\phantom{\rule{0ex}{0ex}}+{f}_{2}\left({x}_{2}\right)+........+{f}_{i}\left({x}_{i}\right)$ Y—Response Variable, g—Link Function, f _{i}—Specified Parametric Form, x_{i}—Predicator Variable | 0.698 | 0.943 | 0.769 | 0.9426 | 0.875 | 0.125 | 0.885 | 0.295 |

3 | RF | Y$={\displaystyle \sum}_{i=1}^{n}$ f(t_{n}) Y—Average of aggregated predictions of the multiple decision trees, t _{n}—multiple decision trees trained on different subset of the same training data | 0.849 | 0.999 | 0.972 | 0.9987 | 0.982 | 0.018 | 0.980 | 0.107 |

4 | GBM | $f\left(x\right)\phantom{\rule{0ex}{0ex}}=argmi{n}_{\theta}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}L\left({y}_{i},\theta \right)\phantom{\rule{0ex}{0ex}}+{\displaystyle {\displaystyle \sum}_{m=1}^{M}}\eta {\rho}_{m}{\varphi}_{m}\left(x\right)$ m—Iteration, $\eta $—Learning Rate, ${\rho}_{m}$—Step length | 0.634 | 0.966 | 0.863 | 0.9660 | 0.932 | 0.068 | 0.936 | 0.254 |

5 | NNET | $Y=f\left({\displaystyle {\displaystyle \sum}_{i=1}^{n}}{x}_{i}{w}_{i}\right)+b$ Y—Output, ${x}_{i}$—Inputs, ${w}_{i}$—Weights, $b$—Bias | 0.004 | 0.527 | 0 | 0.5269 | 0.629 | 0.371 | 0.500 | NA |

6 | MARS | $\widehat{f}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{k}}{c}_{i}{B}_{i}\left(x\right)$ ${c}_{i}$—Constant Coefficient, ${B}_{i}\left(x\right)$—Basis Function | 0.595 | 0.942 | 0.773 | 0.9416 | 0.885 | 0.115 | 0.902 | 0.301 |

7 | FDA | ${\eta}_{l}\left(x\right)={X}^{T}{\beta}_{l}$ | 0.625 | 0.805 | 0.609 | 0.8047 | 0.832 | 0.168 | 0.873 | 5.818 |

8 | CT | $f\left(x\right)={\displaystyle {\displaystyle \sum}_{j=1}^{T}}{w}_{j}I\left(x\in {R}_{j}\right)$ | 0.764 | 0.95 | 0.787 | 0.9504 | 0.889 | 0.111 | 0.921 | 0.255 |

9 | SVM | $\left\{x:f\left(x\right)={x}^{T}\beta +{\beta}_{0}=0\right\}$ | 0.645 | 0.931 | 0.759 | 0.9307 | 0.871 | 0.129 | 0.878 | 0.439 |

10 | NB | $P(c|x)=\frac{P(x|c)P\left(c\right)}{P\left(x\right)}$ $P(c|x)$—Posterior Probability, $P(x|c)$—Likelihood, $P\left(c\right)$—Class Prior Probability, $P\left(c\right)$—Predictor Prior Probability | −0.46 | 0.819 | −0.309 | 0.8189 | 0.319 | 0.681 | 0.143 | 9.099 |

11 | ADA | ${F}_{T}\left(x\right)={\displaystyle {\displaystyle \sum}_{t=1}^{T}}{f}_{t}\left(x\right)$ ${f}_{t}$—Weak Learner, $x$—Input,$T\u2014T$th Positive or Negative Classifier | 0.838 | 0.924 | 0.847 | 0.9237 | 0.925 | 0.075 | 0.941 | 2.600 |

Sl.No | Model | Model Specification | KAPPA | ROC | TSS | AUC | ACCURACY | ERROR RATE | F1SCORE | LOGLOSS |

1 | GLM | $E(Y|X)=\mu ={g}^{-1}\left(X\beta \right)$ Y—Expected Value, X—Conditional, $X\beta $—Linear Predicator, g—Link Function | 0.472 | 0.867 | 0.624 | 0.8670 | 0.803 | 0.197 | 0.886 | 0.419 |

2 | GAM | $g\left(E\left(Y\right)\right)\phantom{\rule{0ex}{0ex}}={\beta}_{0}+{f}_{1}\left({x}_{1}\right)\phantom{\rule{0ex}{0ex}}+{f}_{2}\left({x}_{2}\right)+........+{f}_{i}\left({x}_{i}\right)$ Y—Response Variable, g—Link Function, f _{i}—Specified Parametric Form, x_{i}—Predicator Variable | 0.472 | 0.867 | 0.624 | 0.8670 | 0.803 | 0.197 | 0.886 | 0.419 |

3 | RF | Y$={\displaystyle \sum}_{i=1}^{n}$ f(t_{n}) Y—Average of aggregated predictions of the multiple decision trees, t _{n}—multiple decision trees trained on different subset of the same training data | 0.765 | 1 | 0.99 | 0.9998 | 0.997 | 0.003 | 0.995 | 0.093 |

4 | GBM | $f\left(x\right)\phantom{\rule{0ex}{0ex}}=argmi{n}_{\theta}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}L\left({y}_{i},\theta \right)\phantom{\rule{0ex}{0ex}}+{\displaystyle {\displaystyle \sum}_{m=1}^{M}}\eta {\rho}_{m}{\varphi}_{m}\left(x\right)$ m—Iteration, $\eta $—Learning Rate, ${\rho}_{m}$—Step length | 0.629 | 0.973 | 0.85 | 0.9725 | 0.926 | 0.074 | 0.939 | 0.238 |

5 | NNET | $Y=f\left({\displaystyle {\displaystyle \sum}_{i=1}^{n}}{x}_{i}{w}_{i}\right)+b$ Y—Output, ${x}_{i}$—Inputs, ${w}_{i}$—Weights, $b$—Bias | 0.018 | 0.512 | 0.025 | 0.5125 | 0.671 | 0.329 | 0.500 | NA |

6 | MARS | $\widehat{f}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{k}}{c}_{i}{B}_{i}\left(x\right)$ ${c}_{i}$—Constant Coefficient, ${B}_{i}\left(x\right)$—Basis Function | 0.595 | 0.952 | 0.779 | 0.9524 | 0.893 | 0.107 | 0.912 | 0.274 |

7 | FDA | ${\eta}_{l}\left(x\right)={X}^{T}{\beta}_{l}$ | 0.543 | 0.75 | 0.5 | 0.7498 | 0.813 | 0.187 | 0.870 | 6.469 |

8 | CT | $f\left(x\right)={\displaystyle {\displaystyle \sum}_{j=1}^{T}}{w}_{j}I\left(x\in {R}_{j}\right)$ | 0.69 | 0.937 | 0.784 | 0.9367 | 0.893 | 0.107 | 0.918 | 0.270 |

9 | SVM | $\left\{x:f\left(x\right)={x}^{T}\beta +{\beta}_{0}=0\right\}$ | 0.689 | 0.938 | 0.749 | 0.9379 | 0.876 | 0.124 | 0.914 | 0.388 |

10 | NB | $P(c|x)=\frac{P(x|c)P\left(c\right)}{P\left(x\right)}$ $P(c|x)$—Posterior Probability, $P(x|c)$—Likelihood, $P\left(c\right)$—Class Prior Probability, $P\left(c\right)$—Predictor Prior Probability | −0.302 | 0.714 | −0.199 | 0.7136 | 0.301 | 0.699 | 0.076 | 9.829 |

11 | ADA | ${F}_{T}\left(x\right)={\displaystyle {\displaystyle \sum}_{t=1}^{T}}{f}_{t}\left(x\right)$ ${f}_{t}\u2014$Weak Learner, $x$—Input,$T\u2014T$ ^{th} Positive or Negative Classifier | 0.886 | 0.94 | 0.88 | 0.9399 | 0.950 | 0.050 | 0.963 | 1.733 |

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## Share and Cite

**MDPI and ACS Style**

Suresh, K.P.; Bylaiah, S.; Patil, S.; Kumar, M.; Indrabalan, U.B.; Panduranga, B.A.; Srinivas, P.T.; Shivamallu, C.; Kollur, S.P.; Cull, C.A.;
et al. A New Methodology to Comprehend the Effect of El Niño and La Niña Oscillation in Early Warning of Anthrax Epidemic Among Livestock. *Zoonotic Dis.* **2022**, *2*, 267-290.
https://doi.org/10.3390/zoonoticdis2040022

**AMA Style**

Suresh KP, Bylaiah S, Patil S, Kumar M, Indrabalan UB, Panduranga BA, Srinivas PT, Shivamallu C, Kollur SP, Cull CA,
et al. A New Methodology to Comprehend the Effect of El Niño and La Niña Oscillation in Early Warning of Anthrax Epidemic Among Livestock. *Zoonotic Diseases*. 2022; 2(4):267-290.
https://doi.org/10.3390/zoonoticdis2040022

**Chicago/Turabian Style**

Suresh, Kuralayanapalya Puttahonnappa, Sushma Bylaiah, Sharanagouda Patil, Mohan Kumar, Uma Bharathi Indrabalan, Bhavya Anenahalli Panduranga, Palya Thimmaiah Srinivas, Chandan Shivamallu, Shiva Prasad Kollur, Charley A. Cull,
and et al. 2022. "A New Methodology to Comprehend the Effect of El Niño and La Niña Oscillation in Early Warning of Anthrax Epidemic Among Livestock" *Zoonotic Diseases* 2, no. 4: 267-290.
https://doi.org/10.3390/zoonoticdis2040022