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

Year 2021, Volume: 9 Issue: 2, 192 - 197, 06.12.2021

Sevda Özdemir Çalıkuşu , Fevzi Erdoğan

https://doi.org/10.51354/mjen.929656

Abstract

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.

Keywords

Itô stochastic differential equation, Euler-Maruyama approximation method, Maximum likelihood estimation method, COVID-19 data

References

• 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.