Araştırma Makalesi
BibTex RIS Kaynak Göster

Fitting the Itô Stochastic differential equation to the COVID-19 data in Turkey

Yıl 2021, , 192 - 197, 06.12.2021
https://doi.org/10.51354/mjen.929656

Öz

In this study, COVID-19 data in Turkey is investigated by Stochastic Differential Equation Modeling (SDEM). Firstly, parameters of SDE which occur in mentioned epidemic problem are estimated by using the maximum likelihood procedure. Then, we have obtained reasonable Stochastic Differential Equation (SDE) based on the given COVID-19 data. Moreover, by applying Euler-Maruyama Approximation Method trajectories of SDE are achieved. The performances of trajectories are established by Chi-Square criteria. The results are acquired by using statistical software R-Studio.These results are also corroborated by graphical representation.

Kaynakça

  • World Health Organization (WHO). Coronavirus. Available from: https://www.who.int/health-topics/coronavirus#tab=tab_1 (Accessed: April 15, 2021).
  • Iacus S.M., Simulation and Inference for Stochastic Differential Equations with R Examples. USA: Springer, 2008.
  • Oksendal B., Stochastic Differential Equations an Introduction with Applications, 5th ed., Corrected Printing. New York: Springer-Verlag Heidelberg, 2003.
  • Kostrista E., Çibuku D., “Introduction to Stochastic Differential Equations”, Journal of Natural Sciences and Mathematics of UT, 3, (2018), 5-6.
  • Ince N., Shamilov A., "An application of new method to obtain probability density function of solution of stochastic differential equations", Applied Mathematics and Nonlinear Sciences, 5.1 (2020), 337-348.
  • Mahrouf M. et al. "Modeling and forecasting of COVID-19 spreading by delayed stochastic differential equations", Axioms 10.1, (2021), 18.
  • Bak J., Nielsen A. and Madsen H., “Goodness of fit of stochastic differential equations”, 21th Symposium I Anvendt Statistik, Copenhagen Business School, Copenhagen, Denmark. 1999.
  • Rezaeyan R., Farnoosh R., “Stochastic Differential Equations and Application of the Kalman-Bucy Filter in the Modeling of RC Circuit”, Applied Mathematical Sciences, 4, (2010), 1119-1127.
  • Ang K. C., “A Simple Stochastic Model for an Epidemic-Numerical Experiments with MATLAB”, The Electronic Journal of Mathematics and Technology, 1, (2007), 117-128.
  • Simha A., Prasad R.V., and Narayana A.,. "A simple stochastic sir model for covid 19 infection dynamics for karnataka: Learning from europe." arXiv preprint arXiv:2003.11920, (2020).
  • Zhang Z., et al. "Dynamics of COVID-19 mathematical model with stochastic perturbation." Advances in Difference Equations, 2020.1, (2020), 1-12.
  • Allen E., Modeling with Itô Stochastic Differential Equations. USA: Springer, 2007.
  • Shamilov A., Measurement Theory, Probability and Lebesgue Integral, Eskişehir: Anadolu University Publications, 2007.
  • Shamilov A., Differential Equations with Theory and Solved Problems, Turkey: Nobel Publishing House, 2012.
  • Shamilov A., Probability Theory with Conceptional Interpretations and Applications. Turkey: Nobel Publishing House, 2014.
  • Andersson H., Britton T., Stochastic Epidemic Models and Their Statistical Analysis. New York: Springer, 2000.
  • Allen L.J.S., An Introduction to Stochastic Processes with Applications to Biology. Upper Saddle River, New Jersey: Pearson Education Inc., 2003.
  • Higham D.J., “An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations”, SIAM Review, 43, (2001), 525-546.
Yıl 2021, , 192 - 197, 06.12.2021
https://doi.org/10.51354/mjen.929656

Öz

Kaynakça

  • World Health Organization (WHO). Coronavirus. Available from: https://www.who.int/health-topics/coronavirus#tab=tab_1 (Accessed: April 15, 2021).
  • Iacus S.M., Simulation and Inference for Stochastic Differential Equations with R Examples. USA: Springer, 2008.
  • Oksendal B., Stochastic Differential Equations an Introduction with Applications, 5th ed., Corrected Printing. New York: Springer-Verlag Heidelberg, 2003.
  • Kostrista E., Çibuku D., “Introduction to Stochastic Differential Equations”, Journal of Natural Sciences and Mathematics of UT, 3, (2018), 5-6.
  • Ince N., Shamilov A., "An application of new method to obtain probability density function of solution of stochastic differential equations", Applied Mathematics and Nonlinear Sciences, 5.1 (2020), 337-348.
  • Mahrouf M. et al. "Modeling and forecasting of COVID-19 spreading by delayed stochastic differential equations", Axioms 10.1, (2021), 18.
  • Bak J., Nielsen A. and Madsen H., “Goodness of fit of stochastic differential equations”, 21th Symposium I Anvendt Statistik, Copenhagen Business School, Copenhagen, Denmark. 1999.
  • Rezaeyan R., Farnoosh R., “Stochastic Differential Equations and Application of the Kalman-Bucy Filter in the Modeling of RC Circuit”, Applied Mathematical Sciences, 4, (2010), 1119-1127.
  • Ang K. C., “A Simple Stochastic Model for an Epidemic-Numerical Experiments with MATLAB”, The Electronic Journal of Mathematics and Technology, 1, (2007), 117-128.
  • Simha A., Prasad R.V., and Narayana A.,. "A simple stochastic sir model for covid 19 infection dynamics for karnataka: Learning from europe." arXiv preprint arXiv:2003.11920, (2020).
  • Zhang Z., et al. "Dynamics of COVID-19 mathematical model with stochastic perturbation." Advances in Difference Equations, 2020.1, (2020), 1-12.
  • Allen E., Modeling with Itô Stochastic Differential Equations. USA: Springer, 2007.
  • Shamilov A., Measurement Theory, Probability and Lebesgue Integral, Eskişehir: Anadolu University Publications, 2007.
  • Shamilov A., Differential Equations with Theory and Solved Problems, Turkey: Nobel Publishing House, 2012.
  • Shamilov A., Probability Theory with Conceptional Interpretations and Applications. Turkey: Nobel Publishing House, 2014.
  • Andersson H., Britton T., Stochastic Epidemic Models and Their Statistical Analysis. New York: Springer, 2000.
  • Allen L.J.S., An Introduction to Stochastic Processes with Applications to Biology. Upper Saddle River, New Jersey: Pearson Education Inc., 2003.
  • Higham D.J., “An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations”, SIAM Review, 43, (2001), 525-546.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Sevda Özdemir Çalıkuşu 0000-0002-0238-2677

Fevzi Erdoğan 0000-0003-3745-0198

Yayımlanma Tarihi 6 Aralık 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Özdemir Çalıkuşu, S., & Erdoğan, F. (2021). Fitting the Itô Stochastic differential equation to the COVID-19 data in Turkey. MANAS Journal of Engineering, 9(2), 192-197. https://doi.org/10.51354/mjen.929656
AMA Özdemir Çalıkuşu S, Erdoğan F. Fitting the Itô Stochastic differential equation to the COVID-19 data in Turkey. MJEN. Aralık 2021;9(2):192-197. doi:10.51354/mjen.929656
Chicago Özdemir Çalıkuşu, Sevda, ve Fevzi Erdoğan. “Fitting the Itô Stochastic Differential Equation to the COVID-19 Data in Turkey”. MANAS Journal of Engineering 9, sy. 2 (Aralık 2021): 192-97. https://doi.org/10.51354/mjen.929656.
EndNote Özdemir Çalıkuşu S, Erdoğan F (01 Aralık 2021) Fitting the Itô Stochastic differential equation to the COVID-19 data in Turkey. MANAS Journal of Engineering 9 2 192–197.
IEEE S. Özdemir Çalıkuşu ve F. Erdoğan, “Fitting the Itô Stochastic differential equation to the COVID-19 data in Turkey”, MJEN, c. 9, sy. 2, ss. 192–197, 2021, doi: 10.51354/mjen.929656.
ISNAD Özdemir Çalıkuşu, Sevda - Erdoğan, Fevzi. “Fitting the Itô Stochastic Differential Equation to the COVID-19 Data in Turkey”. MANAS Journal of Engineering 9/2 (Aralık 2021), 192-197. https://doi.org/10.51354/mjen.929656.
JAMA Özdemir Çalıkuşu S, Erdoğan F. Fitting the Itô Stochastic differential equation to the COVID-19 data in Turkey. MJEN. 2021;9:192–197.
MLA Özdemir Çalıkuşu, Sevda ve Fevzi Erdoğan. “Fitting the Itô Stochastic Differential Equation to the COVID-19 Data in Turkey”. MANAS Journal of Engineering, c. 9, sy. 2, 2021, ss. 192-7, doi:10.51354/mjen.929656.
Vancouver Özdemir Çalıkuşu S, Erdoğan F. Fitting the Itô Stochastic differential equation to the COVID-19 data in Turkey. MJEN. 2021;9(2):192-7.

Manas Journal of Engineering 

16155