# Interpolation of Point Prevalence Rate of the Highly Pathogenic Avian Influenza Subtype H5N8 Second Phase Epidemic in South Korea

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Inverse Distance Weighting (IDW)

_{i}is the distance between X

_{0}and X

_{i}, p stands for a parameter called ‘power’, and n denotes the number of sample points utilized in the prediction. The value of the power variable [37] is the most important element influencing IDW accuracy. Weights decrease as distance increases, specifically as the power variable value goes up; thus, close observations have a greater weight and have more influence on the prediction, and the resulting spatial interpolation is localized [37]. The power parameter and the neighboring zone are chosen at random [38]. The most common p value is 2, and the resulting approach is typically referred to as inverse distance squared ‘IDS’. The power variable can also be based primarily on inaccuracy measurements (for example, minimal mean absolute error), resulting in optimum IDW [39]. The smoothing of the predicted surface changes proportionally with the power variable, and it is determined that when p is 1 and 2, the estimated results are less good than when p is 4 [40]. IDW is referred to as a “moving average” when p is zero [41], “linear interpolation” in case p is 1, and “weighted moving average” in case p is not equal to 1 [42].

#### 2.2. Kriging

- A structural component with a fixed mean or pattern.
- A regionalized variable that is random yet geographically associated element.
- A noise or residual component that is random yet spatially uncorrelated.

^{2}[42].

## 3. Results

#### Descriptive Analysis

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Alexander, D.J. An overview of the epidemiology of avian influenza. Vaccine
**2007**, 25, 5637–5644. [Google Scholar] [CrossRef] [PubMed] - Moriguchi, S.; Onuma, M.; Goka, K. Potential risk map for avian influenza A virus invading Japan. Divers. Distrib.
**2012**, 1, 78–85. [Google Scholar] [CrossRef] - Lever, C. The Mandarin Duck; Bloomsbury Publishing: London, UK, 2013. [Google Scholar]
- Lee, D.-H.; Park, J.-K.; Youn, H.-N.; Lee, Y.-N.; Lim, T.-H.; Kim, M.-S.; Lee, J.-B.; Park, S.-Y.; Choi, I.-S.; Song, C.-S. Surveillance and Isolation of HPAI H5N1 from Wild Mandarin Ducks (Aix galericulata). J. Wildl. Dis.
**2011**, 47, 994–998. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kwon, J.-H.; Lee, D.-H.; Swayne, D.; Noh, J.-Y.; Yuk, S.-S.; Erdene-Ochir, T.-O.; Hong, W.-T.; Jeong, J.-H.; Jeong, S.; Gwon, G.-B.; et al. Highly Pathogenic Avian Influenza A(H5N8) Viruses Reintroduced into South Korea by Migratory Waterfowl, 2014–2015. Emerg. Infect. Dis.
**2016**, 22, 507–510. [Google Scholar] [CrossRef] [PubMed] - Kang, H.-M.; Lee, E.-K.; Song, B.-M.; Heo, G.-B.; Jung, J.; Jang, I.; Bae, Y.-C.; Jung, S.C.; Lee, Y.-J. Experimental infection of mandarin duck with highly pathogenic avian influenza A (H5N8 and H5N1) viruses. Veter. Microbiol.
**2017**, 198, 59–63. [Google Scholar] [CrossRef] [PubMed] - Kwon, J.-H.; Noh, Y.K.; Lee, D.-H.; Yuk, S.-S.; Erdene-Ochir, T.-O.; Noh, J.-Y.; Hong, W.-T.; Jeong, J.-H.; Jeong, S.; Gwon, G.-B.; et al. Experimental infection with highly pathogenic H5N8 avian influenza viruses in the Mandarin duck (Aix galericulata) and domestic pigeon (Columba livia domestica). Veter. Microbiol.
**2017**, 203, 95–102. [Google Scholar] [CrossRef] - Son, K.; Kim, Y.-K.; Oem, J.-K.; Jheong, W.-H.; Sleeman, J.M.; Jeong, J. Experimental infection of highly pathogenic avian influenza viruses, Clade 2.3.4.4 H5N6 and H5N8, in Mandarin ducks from South Korea. Transbound. Emerg. Dis.
**2018**, 65, 899–903. [Google Scholar] [CrossRef] [Green Version] - Jeong, S.; Lee, D.-H.; Kwon, J.-H.; Kim, Y.-J.; Lee, S.-H.; Cho, A.Y.; Kim, T.-H.; Park, J.-E.; Lee, S.-I.; Song, C.-S. Highly Pathogenic Avian Influenza Clade 2.3.4.4b Subtype H5N8 Virus Isolated from Mandarin Duck in South Korea. Viruses
**2020**, 12, 1389. [Google Scholar] [CrossRef] - Global Consortium for H5N8 and Related Influenza Viruses. Role for migratory wild birds in the global spread of avian influenza H5N8. Science
**2016**, 354, 213–217. [Google Scholar] [CrossRef] [Green Version] - Lee, M.S.; Chen, L.H.; Chen, Y.P.; Liu, Y.P.; Li, W.C.; Lin, Y.L.; Lee, F. Highly pathogenic avian influenza viruses H5N2, H5N3, and H5N8 in Taiwan in Vet. Microbiology
**2016**, 187, 50–57. [Google Scholar] - Baek, Y.-G.; Lee, Y.-N.; Lee, D.-H.; Shin, J.-I.; Lee, J.-H.; Chung, D.; Lee, E.-K.; Heo, G.-B.; Sagong, M.; Kye, S.-J.; et al. Multiple Reassortants of H5N8 Clade 2.3.4.4b Highly Pathogenic Avian Influenza Viruses Detected in South Korea during the Winter of 2020–2021. Viruses
**2021**, 13, 490. [Google Scholar] [CrossRef] - Short, K.; Richard, M.; Verhagen, J.H.; van Riel, D.; Schrauwen, E.J.; Brand, J.M.V.D.; Mänz, B.; Bodewes, R.; Herfst, S. One health, multiple challenges: The inter-species transmission of influenza A virus. One Health
**2015**, 1, 1–13. [Google Scholar] [CrossRef] [Green Version] - Song, B.-M.; Lee, E.-K.; Lee, Y.-N.; Heo, G.-B.; Lee, H.-S.; Lee, Y.-J. Phylogeographical characterization of H5N8 viruses isolated from poultry and wild birds during 2014–2016 in South Korea. J. Veter. Sci.
**2017**, 18, 89–94. [Google Scholar] [CrossRef] [Green Version] - Kwon, J.; Bahl, J.; Swayne, D.E.; Lee, Y.; Lee, Y.; Song, C.; Lee, D. Domestic ducks play a major role in the maintenance and spread of H5N8 highly pathogenic avian influenza viruses in South Korea. Transbound. Emerg. Dis.
**2019**, 67, 844–851. [Google Scholar] [CrossRef] - Hill, S.C.; Lee, Y.-J.; Song, B.-M.; Kang, H.-M.; Lee, E.-K.; Hanna, A.; Gilbert, M.; Brown, I.H.; Pybus, O.G. Wild waterfowl migration and domestic duck density shape the epidemiology of highly pathogenic H5N8 influenza in the Republic of Korea. Infect. Genet. Evol.
**2015**, 34, 267–277. [Google Scholar] [CrossRef] - Beerens, N.; Germeraad, E.A.; Venema, S.; Verheij, E.; Pritz-Verschuren, S.B.; Gonzales, J.L. Comparative pathogenicity and environmental transmission of recent highly pathogenic avian influenza H5 viruses. Emerg. Microbes Infect.
**2021**, 10, 97–108. [Google Scholar] [CrossRef] - Kim, W.-H.; An, J.-U.; Kim, J.; Moon, O.-K.; Bae, S.H.; Bender, J.; Cho, S. Risk factors associated with highly pathogenic avian influenza subtype H5N8 outbreaks on broiler duck farms in South Korea. Transbound. Emerg. Dis.
**2018**, 65, 1329–1338. [Google Scholar] [CrossRef] - Jeong, J.; Kang, H.-M.; Lee, E.-K.; Song, B.-M.; Kwon, Y.-K.; Kim, H.-R.; Choi, K.-S.; Kim, J.-Y.; Lee, H.-J.; Moon, O.-K.; et al. Highly pathogenic avian influenza virus (H5N8) in domestic poultry and its relationship with migratory birds in South Korea during 2014. Veter. Microbiol.
**2014**, 173, 249–257. [Google Scholar] [CrossRef] - Lee, Y.-J.; Kang, H.-M.; Lee, E.-K.; Song, B.-M.; Jeong, J.; Kwon, Y.-K.; Kim, H.-R.; Lee, K.-J.; Hong, M.-S.; Jang, I.; et al. Novel Reassortant Influenza A(H5N8) Viruses, South Korea. Emerg. Infect. Dis.
**2014**, 20, 1086–1089. [Google Scholar] [CrossRef] - Tian, H.; Zhou, S.; Dong, L.; Van Boeckel, T.P.; Cui, Y.; Newman, S.H.; Takekawa, J.Y.; Prosser, D.J.; Xiao, X.; Wu, Y.; et al. Avian influenza H5N1 viral and bird migration networks in Asia. Proc. Natl. Acad. Sci. USA
**2014**, 112, 172–177. [Google Scholar] [CrossRef] [Green Version] - Palm, E.C.; Newman, S.H.; Prosser, D.J.; Xiao, X.; Ze, L.; Batbayar, N.; Balachandran, S.; Takekawa, J.Y. Mapping migratory flyways in Asia using dynamic Brownian bridge movement models. Mov. Ecol.
**2015**, 3, 3. [Google Scholar] [CrossRef] [Green Version] - Newman, S.H.; Iverson, S.A.; Takekawa, J.Y.; Gilbert, M.; Prosser, D.J.; Batbayar, N.; Natsagdorj, T.; Douglas, D.C. Migration of Whooper Swans and Outbreaks of Highly Pathogenic Avian Influenza H5N1 Virus in Eastern Asia. PLoS ONE
**2009**, 4, e5729. [Google Scholar] [CrossRef] [Green Version] - Kwon, J.-H.; Jeong, S.; Lee, D.-H.; Swayne, D.E.; Kim, Y.; Lee, S.; Noh, J.-Y.; Erdene-Ochir, T.-O.; Jeong, J.-H.; Song, C.-S. New Reassortant Clade 2.3.4.4b Avian Influenza A(H5N6) Virus in Wild Birds, South Korea, 2017–18. Emerg. Infect. Dis.
**2018**, 24, 1953–1955. [Google Scholar] [CrossRef] [Green Version] - Yoo, D.-S.; Chun, B.; Min, K.-D.; Lim, J.-S.; Moon, O.-K.; Lee, K.-N. Elucidating the Local Transmission Dynamics of Highly Pathogenic Avian Influenza H5N6 in the Republic of Korea by Integrating Phylogenetic Information. Pathogens
**2021**, 10, 691. [Google Scholar] [CrossRef] - Yoo, D.-S.; Chun, B.C.; Kim, Y.; Lee, K.-N.; Moon, O.-K. Dynamics of inter-farm transmission of highly pathogenic avian influenza H5N6 integrating vehicle movements and phylogenetic information. Sci. Rep.
**2021**, 11, 24163. [Google Scholar] [CrossRef] - Burrough, P.A. Principles of geographical information systems for land resources assessment. Geocarto Int.
**1986**, 1, 54. [Google Scholar] [CrossRef] - Achilleos, G. The Inverse Distance Weighted interpolation method and error propagation mechanism—Creating a DEM from an analogue topographical map. J. Spat. Sci.
**2011**, 56, 283–304. [Google Scholar] [CrossRef] - Xu, T.; Liu, Y.; Tang, L.; Liu, C. Improvement of Kriging interpolation with learning kernel in environmental variables study. Int. J. Prod. Res.
**2020**, 1–14. [Google Scholar] [CrossRef] - Lu, G.Y.; Wong, D.W. An adaptive inverse-distance weighting spatial interpolation technique. Comput. Geosci.
**2008**, 34, 1044–1055. [Google Scholar] [CrossRef] - Cressie, N. The origins of kriging. Math. Geol.
**1990**, 22, 239–252. [Google Scholar] [CrossRef] - Kim, W.-H.; Bae, S.; Cho, S. Spatiotemporal Dynamics of Highly Pathogenic Avian Influenza Subtype H5N8 in Poultry Farms, South Korea. Viruses
**2021**, 13, 274. [Google Scholar] [CrossRef] [PubMed] - Gardener, M. Beginning R: The Statistical Programming Language; John Wiley & Sons: Hobocken, NJ, USA, 2012. [Google Scholar]
- Ikechukwu, M.N.; Ebinne, E.; Idorenyin, U.; Raphael, N.I. Accuracy Assessment and Comparative Analysis of IDW, Spline and Kriging in Spatial Interpolation of Landform (Topography): An Experimental Study. J. Geogr. Inf. Syst.
**2017**, 9, 354–371. [Google Scholar] [CrossRef] [Green Version] - Watson, D.E. Contouring: A Guide to the Analysis and Display of Spatial Data; Elsevier Science, Inc.: Tarrytown, NY, USA; Pergamon Press: London, UK, 1992. [Google Scholar]
- Longley, P.A.; Goodchild, M.F.; Maguire, D.J.; Rhind, D.W. New Developments in Geographical Information Systems; Principles, Techniques, Management and Applications. In Geographical Information Systems: Principles, Techniques, Management and Applications, 2nd ed.; Longley, P., Goodchild, M., Maguire, D., Rhind, D., Eds.; John Wiley & Sons Inc.: Hobocken, NJ, USA, 2005; p. 404. [Google Scholar]
- Isaaks, E.; Srivastava, R. Applied Geostatistics; Oxford Univ. Press: New York, NY, USA, 1989. [Google Scholar]
- Webster, R.; Oliver, M. Geostatistics for Experimental Scientists; John Wiley and Sons ltd: Chichester, UK, 2001. [Google Scholar]
- Collins, J.; Bolstad, P.V. A comparison of spatial interpolation techniques in temperature estimation. Int. Conf. Workshop Integrat. GIS Environ. Model.
**1996**, 3, 38. [Google Scholar] - Ripley, B.D. Mapped Point Patterns. Clin. Trials
**1981**, 144–190. [Google Scholar] [CrossRef] - Brus, D.J.; De Gruijter, J.J.; Marsman, B.A.; Visschers, R.; Bregt, A.K.; Breeuwsma, A.; Bouma, J. The performance of spatial interpolation methods and choropleth maps to estimate properties at points: A soil survey case study. Environmetrics
**1996**, 7, 1–16. [Google Scholar] [CrossRef] - Burrough, P.A.; Mcdonnell, R.A. Data Models and Axioms. Princ. Geogr. Inf. Syst.
**1998**, 75, 17–34. [Google Scholar] [CrossRef] - R Core Development Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2017; Available online: http://cran.r-project.org (accessed on 1 August 2021).
- Baddeley, A.; Turner, R. Package ‘spatstat’. 2021. Available online: https://cran.r-project.org/web/packages/spatstat.data/spatstat.data.pdf (accessed on 25 January 2022).
- Hijmans, R.J.; Van Etten, J.; Cheng, J.; Mattiuzzi, M.; Sumner, M.; Greenberg, J.A.; Lamigueiro, O.P.; Bevan, A.; Racine, E.B.; Shortridge, A.; et al. Package ‘raster’. R package. 2015, 18, 734. Available online: https://mran.microsoft.com/snapshot/2015-03-02/web/packages/raster/raster.pdf (accessed on 25 January 2022).
- Pebesma, E.; Bivand, R.; Pebesma, M.E.; RColorBrewer, S.; Collate, A.A.A. Package ‘sp’. The Comprehensive R Archive Network. 2012. Available online: https://cran.r-project.org/ (accessed on 25 January 2022).
- Ribeiro, P.J., Jr.; Diggle, P.J.; Christensen, O.; Schlather, M.; Bivand, R.; Ripley, B. Package ‘geoR’. 2020. Available online: https://cran.r-project.org/web/packages/geoR/geoR.pdf (accessed on 25 January 2022).
- Warnes, G.R.; Bolker, B.; Lumley, T.; Warnes, M.G.R. Package ‘gtools’. R Package version, 3(1). 2015. Available online: https://cran.r-project.org/web/packages/gtools/index.html (accessed on 25 January 2022).
- Bates, D.; Martin, M.; Ben, B.; Steven, W.; Rune, H.B.C.; Henrik, S.; Dai, B.; Scheipl, F.; Grothendieck, G. Package ‘lme4’. Linear Mixed-Effects Models Using S4 Classes. R Package Version 1, no. 6. 2011. Available online: https://cran.r-project.org/web/packages/lme4/lme4.pdf (accessed on 25 January 2022).
- Joe, C.; Karambelkar, B.; Xie, Y.; Wickham, H.; Russell, K.; Johnson, K. Create Interactive Web Maps with the JavaScript ‘leaflet’Library. R Package Version 2.0. 4.1. 2021. Available online: https://cran.r-project.org/web/packages/leaflet/index.html (accessed on 25 January 2022).
- Whitcher, B.; Volker, S.; Andrew, T.; Karsten, T.; Jon, C. Package ‘oro. nifti’. 2013. Available online: http://www2.uaem.mx/r-mirror/web/packages/oro.nifti/oro.nifti.pdf (accessed on 25 January 2022).
- Anderson, W. Wes Anderson; Faber & Faber: London, UK, 2020. [Google Scholar]
- Sekulić, A.; Kilibarda, M.; Heuvelink, G.B.; Nikolić, M.; Bajat, B. Random Forest Spatial Interpolation. Remote Sens.
**2020**, 12, 1687. [Google Scholar] [CrossRef] - Bivand, R.S.; Pebesma, E.; Gómez-Rubio, V. Applied Spatial Data Analysis with R. Vol. 747248717; Springer: Berlin, Germany, 2008. [Google Scholar]
- Yang, R.; Xing, B. A Comparison of the Performance of Different Interpolation Methods in Replicating Rainfall Magnitudes under Different Climatic Conditions in Chongqing Province (China). Atmosphere
**2021**, 12, 1318. [Google Scholar] [CrossRef] - Arétouyap, Z.; Nouck, N.P.; Nouayou, R.; Méli’i, J.L.; Kemgang Ghomsi, F.E.; Piepi Toko, A.D.; Asfahani, J. Influence of the Variogram Model on an Interpolative Survey Using Kriging Technique. J. Earth Sci. Clim. Change
**2015**, 6, 2. [Google Scholar] - Menezes, R.; Garcia-Soidän, P.; Febrero-Bande, M. A comparison of approaches for valid variogram achievement. Comput. Stat.
**2005**, 20, 623–642. [Google Scholar] [CrossRef] [Green Version] - Wild Waterfowl Migration and Domestic Duck Density Shape the Epidemiology of Highly Pathogenic H5N8 Influenza in the Republic of Korea—Scientific Figure on ResearchGate. Available online: https://www.researchgate.net/figure/Maps-showing-domestic-poultry-density-number-per-kilometer-colors-in-key-in-ROK_fig3_278412772 (accessed on 24 February 2022).
- Ajvazi, B.; Czimber, K. A Comparative analysis of different DEM interpolation methods in GIS: Case study of Rahovec, Kosovo. Geodesy Cartogr.
**2019**, 45, 43–48. [Google Scholar] [CrossRef] [Green Version] - Zarco-Perello, S.; Simões, N. Ordinary kriging vs inverse distance weighting: Spatial interpolation of the sessile community of Madagascar reef, Gulf of Mexico. PeerJ
**2017**, 5, e4078. [Google Scholar] [CrossRef] [Green Version] - Robinson, T.P.; Wint, G.R.W.; Conchedda, G.; Van Boeckel, T.P.; Ercoli, V.; Palamara, E.; Cinardi, G.; D’Aietti, L.; Hay, S.; Gilbert, M. Mapping the Global Distribution of Livestock. PLoS ONE
**2014**, 9, e96084. [Google Scholar] [CrossRef] [Green Version] - Sullivan, J.D.; Takekawa, J.Y.; Spragens, K.A.; Newman, S.H.; Xiao, X.; Leader, P.J.; Smith, B.; Prosser, D.J. Waterfowl Spring Migratory Behavior and Avian Influenza Transmission Risk in the Changing Landscape of the East Asian-Australasian Flyway. Front. Ecol. Evol.
**2018**, 6, 206. [Google Scholar] [CrossRef] [Green Version] - Dinh, P.N.; Long, H.T.; Tien, N.T.K.; Mai, L.T.Q.; Phong, L.H.; Van Tuan, L.; Van Tan, H.; Nguyen, N.B.; Van Tu, P.; Phuong, N.T.M. Risk Factors for Human Infection with Avian Influenza A H5N1, Vietnam. Emerg. Infect. Dis.
**2006**, 12, 1841–1847. [Google Scholar] [CrossRef] - Shimizu, Y.; Hayama, Y.; Yamamoto, T.; Murai, K.; Tsutsui, T. Matched case-control study of the influence of inland waters surrounding poultry farms on avian influenza outbreaks in Japan. Sci. Rep.
**2018**, 8, 3306. [Google Scholar] [CrossRef] [Green Version]

**Figure 2.**The known point prevalence rate of HPAI H5N8 epidemic phase 2. Brown dots denote high prevalence while white circles denote low prevalence.

**Figure 4.**Depicts the comparison of observed prevalence rate with cross validated predicted prevalence rate. (

**A**) Mean squared error against different powers. (

**B**) “Predicted prevalence” vs. “observed prevalence”. (

**C**) “Cross-validated predicted prevalence” vs. “observed prevalence”.

**Figure 5.**Showing a measure of variability between pairs of points at various distances. (

**A**) A variogram displayed as a “vario cloud”. (

**B**) Bin points by distance using 2nd order trend, depicting relationship between semi-variance and distance class. (

**C**) Simplified variogram depicting relationship between semi-variance and bin points at distances using decimal degrees. (

**D**) Variogram binning at 0.2 decimal degrees. (

**E**) The blue line indicates spherical model fit, while red line indicates exponential model fit.

**Figure 6.**Showing the intensity of the point prevalence rate on xy coordinate plane. (

**A**) Kriged predictions of HPAI H5N8 epidemic second phase in the coordinate plane indicating longitude on X-axis and latitude on Y-axis. (

**B**) Prediction raster with colored scale from gray to yellow and green on the right panel indicating the intensity of the point prevalence rate. The green color shows the highest predicted point prevalence rate followed by yellow, gray, and then white for the lowest point prevalence rate.

**Figure 7.**Showing the point prevalence rate of HPAI H5N8 during 2nd phase, also depicting risk predictions based on kriging and IDW methods. (

**A**) Known point prevalence rate during second phase of HPAI H5N8 epidemic. (

**B**) Kriged prediction from the points where data were collected. (

**C**) IDW predictions from the points of collected data. (

**D**) Kriged prediction for the whole prediction grid window. (

**E**) IDW prediction for the whole prediction grid window. (

**F**) Comparison of known prevalence and kriged predicted prevalence with scale bar on the upper right corner. (

**G**) The difference between using IDW versus kriging to interpolate our point prevalence data. Regions of greatest difference are indicated in green.

**Figure 8.**Maps showing domestic poultry density (number per square kilometer, colors in key) in ROK according to Gridded Livestock of the World 2.0 (Robinson et al., 2014). (

**a**) Domestic chicken density. (

**b**) Domestic duck density. (

**c**) Map of provinces. Colors correspond to the branch color scheme used in Figure 3. Province abbreviations are as follows; CB: Chungbuk, CN: Chungnam, DG: Daegu, GB: Gyeongbuk, GG: Gyeonggi, GN: Gyeongnam, GW: Gangwon, IC: Incheon, JB: Jeonbuk, JJ: Jeju, JN: Jeonnam, US: Ulsan. (For interpretation of the references to colors in this figure legend, the reader is referred to the web version of this article.).

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**MDPI and ACS Style**

Ahmad, S.; Koh, K.-Y.; Lee, J.-i.; Suh, G.-H.; Lee, C.-M.
Interpolation of Point Prevalence Rate of the Highly Pathogenic Avian Influenza Subtype H5N8 Second Phase Epidemic in South Korea. *Vet. Sci.* **2022**, *9*, 139.
https://doi.org/10.3390/vetsci9030139

**AMA Style**

Ahmad S, Koh K-Y, Lee J-i, Suh G-H, Lee C-M.
Interpolation of Point Prevalence Rate of the Highly Pathogenic Avian Influenza Subtype H5N8 Second Phase Epidemic in South Korea. *Veterinary Sciences*. 2022; 9(3):139.
https://doi.org/10.3390/vetsci9030139

**Chicago/Turabian Style**

Ahmad, Saleem, Kye-Young Koh, Jae-il Lee, Guk-Hyun Suh, and Chang-Min Lee.
2022. "Interpolation of Point Prevalence Rate of the Highly Pathogenic Avian Influenza Subtype H5N8 Second Phase Epidemic in South Korea" *Veterinary Sciences* 9, no. 3: 139.
https://doi.org/10.3390/vetsci9030139