Araştırma Makalesi
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Comparison of a random model of Hand-Foot-Mouth Disease model with Gaussian and Laplacian parameters

Yıl 2022, Cilt: 12 Sayı: 1, 200 - 210, 15.01.2022
https://doi.org/10.17714/gumusfenbil.973990

Öz

In this study, we investigate the transmission dynamics of Hand-Foot-Mouth disease (HFMD) using a differential equation system with random parameters. We transform the parameters of the existing deterministic model into random variables with Normal and Laplace distributions. Using the results from the simulations of the random model, we analyze the changes in the compartments of the total population. The random model, unlike the deterministic system, enables the analysis of the variations in the transmission dynamics of the disease. Finally, the randomness of the system is interpreted through the comparison of the results from the deterministic and random models.

Kaynakça

  • Chadsuthi, S. and Wichapeng, S. (2018). The modelling of hand, foot, and mouth disease in contaminated environments in Bangkok, Thailand. Computational and Mathematical Methods in Medicine, 2018, Article ID 5168931, https://doi.org/10.1155/2018/5168931.
  • Chen, S., Yang, D., Liu, R., Zhao, J., Yang, K. and Chen, T. (2019). Estimating the transmissibility of hand, foot, and mouth disease by a dynamic model. Public Health, 174, 42-48, https://doi.org/10.1016/j.puhe.2019.05.032.
  • Dai, C., Wang, Z., Wang, W., Li, Y. and Wang, K. (2019). Epidemics and underlying factors of multiple-peak pattern on hand, foot and mouth disease in Wenzhou, China. Mathematical Biosciences and Engineering, 16(4), 2168-2188, http://dx.doi.org/10.3934/mbe.2019106.
  • Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, John Wiley & Sons.
  • Huang, Z., Wang, M., Qiu, L., Wang, N., Zhao, Z., Rui, J. and Chen, T. (2019). Seasonality of the transmissibility of hand, foot and mouth disease: A modelling study in Xiamen City, China. Epidemiology and Infection, 147, E327, https://doi.org/10.1017/S0950268819002139.
  • Li, Y., Huang, M. and Peng, L. (2019). A multi-group model for estimating the transmission rate of hand, foot and mouth disease in mainland China. Mathematical Biosciences and Engineering, 16(4), 2305–2321, http://dx.doi.org/10.3934/mbe.2019115.
  • Liao, Y., He, Y., Lu, Y., Yang, H., Su, Y., Chiang, Y. and Chen, T. (2019). Relative transmissibility of hand, foot and mouth disease from male to female individuals. Epidemiology and Infection, 147, E284, https://doi.org/10.1017/S0950268819001729.
  • Luo, K., Rui, J., Hu, S., Hu, Q., Yang, D., Xiao, S., Zhao, Z., Wang, Y., Liu, X., Pan, L., An, R., Guo, D., Su, Y., Zhao, B., Gao, L. and Chen, T. (2020). Interaction analysis on transmissibility of main pathogens of hand, foot, and mouth disease: A modeling study (a STROBE-compliant article). Medicine, 99(11), e19286, https://dx.doi.org/10.1097/MD.0000000000019286.
  • Merdan, M., Bekiryazici, Z., Kesemen, T. and Khaniyev, T. (2017). Deterministic stability and random behavior of a Hepatitis C model. PloS one, 12(7), e0181571, https://doi.org/10.1371/journal.pone.0181571.
  • Merdan, M., Bekiryazici, Z., Kesemen, T. and Khaniyev, T. (2018). Analyzing the dynamics of Ebola transmission with random effects. Communications in Mathematical Biology and Neuroscience, 2018, Article ID 22, https://doi.org/10.28919/cmbn/3822.
  • Phonchan, P. and Naowarat, S. (2019). Sensitivity Analysis of Hand Foot Mouth Disease Model with Public Health Resources. Southeast Asian Journal of Sciences, 7(1), 59-70.
  • Pongsumpun, P. and Wongvanich, N. (2018). Age Structural Model of the Hand Foot Mouth Disease in Thailand. 2018 2nd European Conference on Electrical Engineering and Computer Science (EECS) (pp. 134-141). Bern, Switzerland, https://doi.org/10.1109/EECS.2018.00033.
  • Shi, R. and Lu, T. (2020). Dynamic analysis and optimal control of a fractional order model for hand-foot-mouth disease. Journal of Applied Mathematics and Computing, 64, 565–590, https://doi.org/10.1007/s12190-020-01369-w.
  • Tan, H. and Cao, H. (2018). The dynamics and optimal control of a hand-foot-mouth disease model. Computational and Mathematical Methods in Medicine, 2018, Article ID 9254794, https://doi.org/10.1155/2018/9254794.
  • World Health Organization (n.d.), Hand, Foot and Mouth Disease (2021, 24 March). https://www.who.int/westernpacific/emergencies/surveillance/archives/hand-foot-and-mouth-disease.

Bir rastgele El-Ayak-Ağız Hastalığı modelinin Normal ve Laplace dağılımına sahip parametrelerle karşılaştırılması

Yıl 2022, Cilt: 12 Sayı: 1, 200 - 210, 15.01.2022
https://doi.org/10.17714/gumusfenbil.973990

Öz

Bu çalışmada, El-Ayak-Ağız Hastalığının yayılım dinamikleri bir diferansiyel denklem sistemi ve rastgele parametreler kullanarak incelenmektedir. Var olan deterministik modelin parametreleri Normal dağılım ve Laplace dağılımına sahip rastgele değişkenler haline getirilmektedir. Rastgele modelin simülasyonlarından elde edilen sonuçlarla toplam nüfusun kompartmanlarındaki değişimler analiz edilmektedir. Rastgele model, deterministik sistemin aksine, hastalığın yayılım dinamiklerindeki varyasyonların analizine imkan sağlamaktadır. Son olarak, sistemin rastgele yapısı deterministik ve rastgele sonuçların karşılaştırılması ile yorumlanmaktadır.

Kaynakça

  • Chadsuthi, S. and Wichapeng, S. (2018). The modelling of hand, foot, and mouth disease in contaminated environments in Bangkok, Thailand. Computational and Mathematical Methods in Medicine, 2018, Article ID 5168931, https://doi.org/10.1155/2018/5168931.
  • Chen, S., Yang, D., Liu, R., Zhao, J., Yang, K. and Chen, T. (2019). Estimating the transmissibility of hand, foot, and mouth disease by a dynamic model. Public Health, 174, 42-48, https://doi.org/10.1016/j.puhe.2019.05.032.
  • Dai, C., Wang, Z., Wang, W., Li, Y. and Wang, K. (2019). Epidemics and underlying factors of multiple-peak pattern on hand, foot and mouth disease in Wenzhou, China. Mathematical Biosciences and Engineering, 16(4), 2168-2188, http://dx.doi.org/10.3934/mbe.2019106.
  • Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, John Wiley & Sons.
  • Huang, Z., Wang, M., Qiu, L., Wang, N., Zhao, Z., Rui, J. and Chen, T. (2019). Seasonality of the transmissibility of hand, foot and mouth disease: A modelling study in Xiamen City, China. Epidemiology and Infection, 147, E327, https://doi.org/10.1017/S0950268819002139.
  • Li, Y., Huang, M. and Peng, L. (2019). A multi-group model for estimating the transmission rate of hand, foot and mouth disease in mainland China. Mathematical Biosciences and Engineering, 16(4), 2305–2321, http://dx.doi.org/10.3934/mbe.2019115.
  • Liao, Y., He, Y., Lu, Y., Yang, H., Su, Y., Chiang, Y. and Chen, T. (2019). Relative transmissibility of hand, foot and mouth disease from male to female individuals. Epidemiology and Infection, 147, E284, https://doi.org/10.1017/S0950268819001729.
  • Luo, K., Rui, J., Hu, S., Hu, Q., Yang, D., Xiao, S., Zhao, Z., Wang, Y., Liu, X., Pan, L., An, R., Guo, D., Su, Y., Zhao, B., Gao, L. and Chen, T. (2020). Interaction analysis on transmissibility of main pathogens of hand, foot, and mouth disease: A modeling study (a STROBE-compliant article). Medicine, 99(11), e19286, https://dx.doi.org/10.1097/MD.0000000000019286.
  • Merdan, M., Bekiryazici, Z., Kesemen, T. and Khaniyev, T. (2017). Deterministic stability and random behavior of a Hepatitis C model. PloS one, 12(7), e0181571, https://doi.org/10.1371/journal.pone.0181571.
  • Merdan, M., Bekiryazici, Z., Kesemen, T. and Khaniyev, T. (2018). Analyzing the dynamics of Ebola transmission with random effects. Communications in Mathematical Biology and Neuroscience, 2018, Article ID 22, https://doi.org/10.28919/cmbn/3822.
  • Phonchan, P. and Naowarat, S. (2019). Sensitivity Analysis of Hand Foot Mouth Disease Model with Public Health Resources. Southeast Asian Journal of Sciences, 7(1), 59-70.
  • Pongsumpun, P. and Wongvanich, N. (2018). Age Structural Model of the Hand Foot Mouth Disease in Thailand. 2018 2nd European Conference on Electrical Engineering and Computer Science (EECS) (pp. 134-141). Bern, Switzerland, https://doi.org/10.1109/EECS.2018.00033.
  • Shi, R. and Lu, T. (2020). Dynamic analysis and optimal control of a fractional order model for hand-foot-mouth disease. Journal of Applied Mathematics and Computing, 64, 565–590, https://doi.org/10.1007/s12190-020-01369-w.
  • Tan, H. and Cao, H. (2018). The dynamics and optimal control of a hand-foot-mouth disease model. Computational and Mathematical Methods in Medicine, 2018, Article ID 9254794, https://doi.org/10.1155/2018/9254794.
  • World Health Organization (n.d.), Hand, Foot and Mouth Disease (2021, 24 March). https://www.who.int/westernpacific/emergencies/surveillance/archives/hand-foot-and-mouth-disease.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Zafer Bekiryazıcı 0000-0001-5671-9995

Saime Hasimoglu Bu kişi benim 0000-0003-3147-7816

Yayımlanma Tarihi 15 Ocak 2022
Gönderilme Tarihi 24 Temmuz 2021
Kabul Tarihi 24 Kasım 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 12 Sayı: 1

Kaynak Göster

APA Bekiryazıcı, Z., & Hasimoglu, S. (2022). Comparison of a random model of Hand-Foot-Mouth Disease model with Gaussian and Laplacian parameters. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 12(1), 200-210. https://doi.org/10.17714/gumusfenbil.973990