The rapid spread of coronavirus disease (COVID-19) has increased the attention to the mathematical modeling of spreading the disease in the world. The behavior of spreading is not deterministic in the last year. The purpose of this paper is to present a stochastic differential equation for modeling the data sets of the COVID-19 involving infected, recovered, and dead cases. At first, the time series of the covid-19 is modeled with the Ornstein-Uhlenbeck process and then using the Ito lemma and Euler approximation the analytical and numerical simulations for the stochastic differential equations are achieved. Parameters estimation is done using the maximum likelihood estimator. Finally, numerical simulations are performed using reported data by the world health organization for case studies of Italy and Iran. The numerical simulations and root mean square error criteria confirm the accuracy and efficiency of the findings of the present study.
[1] A. Babaei, H. Jafari, S. Banihashemi, and M. Ahmadi, A stochastic mathematical model for COVID-19 according to different age groups, Applied and Computational Mathematics, 20 (2021), 140-159.
[2] M. A. Dokuyucu and E. C¸ elik, Analyzing a Novel Coronavirus Model (COVID-19) in the Sense of Caputo-Fabrizio Fractional Operator, Applied and Computational Mathematics, 20 (2021), 49-69.
[3] D. Fanelli and F. Piazza, Analysis and forecast of COVID-19 spreading in China, Italy and France, Chaos, Solitons and Fractals, 134 (2020). DOI: 10.1016/j.chaos.2020.109761
[4] B. Ivorra a, M. R. Ferr´andez b, M. Vela-P´erez a, and A. M. Ramos, Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China, Commun Nonlinear Sci Numer Simulat, 88 (2020). DOI: 10.1016/j.cnsns.2020.105303
[5] J. Jiao, Z. Liu, and Sh. Cai, Dynamics of an SEIR model with infectivity in incubation period and homestead- isolation on the susceptible, Applied Mathematics Letters, 107 (2020). DOI: 10.1016/j.aml.2020.106442
[6] S. Khajanchi, K. Sarkar, J. Mondal, and M. Perc, Dynamics of the COVID-19 pandemic in India, ArXiv preprint arXiv:2005.06286, (2020).
[7] S. H. A. Khoshnaw, R. H. Salih, and S. Sulaimany, Mathematical modelling for coronavirus disease in predicting future behaviors and sensitivity analysis, Mathematical Modelling of Natural Phenomena, 15 (2020). DOI: 10.1051/mmnp/2020020
[8] Q. Lina, S. Zhao, D. Gao, Y. Lou, S. Yang, and SS. Musa, A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan China with individual reaction and governmental action, Int J Inf Dis, 93 (2020), 211-216.
[9] M. Maleki, M. R. Mahmoudi, M. H. Heydari, and K. H. Pho, Modeling and forecasting the spread and death rate of coronavirus (COVID-19) in the world using time series models, Chaos, Solitons and Fractals, 140 (2020). DOI: 10.1016/j.chaos.2020.110151
[10] M. Mariani, M. Masum Bhuiyan, and T. Tweneboah, Estimation of stochastic volatility by using Orn- stein–Uhlenbeck type models, Physica A, 491 (2017), 167-176.
[11] S. Melliani, A. El Allaoui, L. S. Chadli, and S. P. Mondal, A Study on the Spread of Covid-19 in Brazil in Crisp and Fuzzy Environment via a Mathematical Model, Applied and Computational Mathematics, 20 (2021), 5-21.
[12] P. Nabati, The first order nonlinear autoregressive model with Ornstein-Uhlenbeck processes driven by white noise, Journal of Mathematics and Modeling in Finance, 1 (2021), 1-8.
[13] K. Sarkar, S. Khajanchi, and J. J. Nieto, Modeling and forecasting the COVID-19 pandemic in India, Chaos, Solitons and Fractals, 139 (2020). DOI: 10.1016/j.chaos.2020.110049
[14] G. T. Tilahun, S. Demie, and A. Eyob, Stochastic model of measles transmission dynamics with double dose vaccination, Infectious Disease Modelling, 5 (2020), 478-494.
[15] World Health Organization, Novel coronavirus (COVID-19) situation, Available from https://experience.arcgis.com/experience, (2020).
Nabati, P. (2022). A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes. Computational Methods for Differential Equations, 10(3), 738-745. doi: 10.22034/cmde.2021.43961.1864
MLA
Parisa Nabati. "A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes". Computational Methods for Differential Equations, 10, 3, 2022, 738-745. doi: 10.22034/cmde.2021.43961.1864
HARVARD
Nabati, P. (2022). 'A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes', Computational Methods for Differential Equations, 10(3), pp. 738-745. doi: 10.22034/cmde.2021.43961.1864
VANCOUVER
Nabati, P. A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes. Computational Methods for Differential Equations, 2022; 10(3): 738-745. doi: 10.22034/cmde.2021.43961.1864
)
