Mixture Distribution for Modeling Turkey Covid-19 Case

Hendri Fahrizal; Arisman Adnan; Rado Yendra

doi:https://doi.org/10.14445/22315373/IJMTT-V69I1P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 1 | Year 2023 | Article Id. IJMTT-V69I1P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I1P508

Mixture Distribution for Modeling Turkey Covid-19 Case

Hendri Fahrizal, Arisman Adnan, Rado Yendra

Received	Revised	Accepted	Published
26 Nov 2022	30 Dec 2022	09 Jan 2023	18 Jan 2023

Abstract

The COVID-19 pandemic hit the world in early 2020 and caused many deaths in various countries, one of which was Turkey. In March 2020, the first case of COVID-19 was confirmed by the Turkish Ministry of Health. In May 2021, the rise of cases continued to occur until it reached 5.2 million cases with a death toll of 47,271 people. In this research, a model for Turkey’s COVID-19 positive cases had built using a mixed distribution, namely log-normal, gamma and Weibull. Parameter estimation for each distribution was carried out using the maximum likelihood method. Then by using the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) tests, it was found that the 3-component gamma distribution is the best distribution to describe the pattern of spikes in positive cases of COVID-19 in Turkey.

Keywords

Covid-19, Gamma distribution, Log-normal distribution, Mixed distribution, Turkey, Weibull distribution.

References

[1] Henry de-Graft Acquah, “Comparison of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) in Selection of an Asymmetric Price Relationship,” Journal of Development and Agricultural Economics, vol. 2, no. 1, pp. 001-006, 2010.
[2] Kendall Atkinson, and Weimin Han, Elementary Numerical Analysis, 3rd Edition, John Wiley & Sons, New York, 2003.
[3] Lee Bain, and Max Engelhardt, Introduction to Probability and Mathematical Statistics, 2nd Edition, Duxbury Press, California, 1992.
[4] Sami Bourouis, Abdullah Alharbi, and Nizar Bouguila, “Bayesian Learning of Shifted-Scaled Dirichlet Mixture Models and its Application to Early COVID-19 Detection in Chest X-Ray Images,” Journal of Imaging, vol. 7, no. 1, pp. 1-14, 2021. Crossref, https://doi.org/10.3390/jimaging7010007
[5] G. Casella, and R. L. Berger, Statistical Inference, Second Edition, Pasific Grove, California, 2002.

[6] Charles Ebeling, An Introduction to Reliability and Maintainability Engineering, McGraw Hill Education, New York, 1997.
[7] M. A. T. Elshahat, and A. A. M. Mahmoud, “A Study on the Mixture of Exponentiated-Weibull Distribution, Part I (The Method of Maximum Like-Lihood Estimation),” International Journal of Mathematics and Statistics Studies, vol. 5, pp. 9-28, 2017.

[8] Niko A. Kaciroti et al., “A Bayesian Mixture Model for Predicting the COVID-19 Related Mortality in the United States,” The American Journal of Tropical Medicine and Hygiene, vol. 104, no. 4, pp. 1484-1492, 2021. Crossref, https://doi.org/10.4269/ajtmh.20-1147

[9] Robert V. Hogg, Joseph W. McKean, and Allen T. Craig, Introduction to Mathematical Statistics, 8th Edition, Macmillan Publishing Inc, Newyork, 2019.

[10] Cécile Kremer et al., “Quantifying Super Spreading for COVID-19 using Poisson Mixture Distributions,” Scientific Report, Nature Portofolio, 2021. Crossref, https://doi.org/10.1038/s41598-021-93578-x
[11] Athanase Polymenis, “An Application of a Mixture of Exponential Distributions for Assessing Hazard Rates from COVID-19,” Journal of Population Therapeutics & Clinical Pharmacology, vol. 27, no. SP1, pp. e58-e64, 2020. Crossref, https://doi.org/10.15586/jptcp.v27iSP1.721
[12] Q Qifang Bi et al., “Epidemiology and Transmission of COVID-19 in 391 Cases and 1286 of their Close Contacts in Shenzhen, China: A Retrospective Cohort Study,” Lancet Infectious Diseases, vol. 20, no. 8, pp. 911-919, 2020. Crossref, https://doi.org/10.1016/S1473-3099(20)30287-5
[13] Sheldon M. Ross, Introduction to Probability Models, 10th Edition, Elsevier, 2010.
[14] Tabassum Naz Sindhu et al., “Estimation Method of Mixture Distribution and Modeling of COVID-19 Pandemic,” AIMS Mathematics, vol. 7, pp. 9926-9956, 2022. Crossref, https://doi.org/10.3934/math.2022554
[15] World Health Organization, Coronavirus Disease COVID- Pandemic, Geneva, Switzerland: WHO, 2020. [Online]. Available: www.who.int/emergencies/diseases/novel-coronavirus-2019

[16] World Health Organization, WHO Coronavirus Disease, 2021. [Online]. Available: https://www.who.int/countries/tur

Citation :

Hendri Fahrizal, Arisman Adnan, Rado Yendra, "Mixture Distribution for Modeling Turkey Covid-19 Case," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 1, pp. 56-61, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I1P508