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