Estimation of the epidemiological model with a system of differential equations (SIRD) using the Runge-Kutta method in Iraq

Document Type : Research Paper

Authors

Department of Statistics, College of Administration and Economics, Mustansiriyah University, Iraq

Abstract

In this paper, we will use the SIRD model to discuss the development of the Corona pandemic in Iraq; through a system of non-linear differential equations, we will use the (Runge-Kutta) method as a solution to the system of various non-linear equations such as the SIRD model, and the parameters used are based on This paper deals with confirmed cases of injury, recovery and deaths from the accurate data available for the period from (February 24, 2020) to (February 22, 2022), and we also present an estimate of the Basic Reproduction number $(R_0)$ for the (SIRD) model.

Keywords

[1] A. Abay, H. Weldegiorgis and H. Alemayehu, Results in physics mathematical modelling and analysis of COVID-19 epidemic and predicting its future situation in Ethiopia, Results Phys. 22 (2021), 103853.
[2] M. Al-Raeei, M.S. El-Daher and O. Solieva, Applying SEIR model without vaccination for COVID-19 in case of the United States, Russia, the United Kingdom, Brazil, France, and India, Epidem. Meth. 10 (2021), no. 1, 1–7.
[3] C. Anastassopoulou, L. Russo, A. Tsakris and C. Siettos, Data-based analysis, modelling and forecasting of the COVID-19 outbreak, PloS one 15 (2020), no. 3, 0230405.
[4] R. Breckon and A.J. Baczkowski, Epidemic Modelling, University of Leeds, 2015.
[5] A. Chakraborty, J. Chen, A. Desvars-larrive, P. Klimek, E.F. Tames, D. Garcia, L. Horstmeyer, M. Kaleta, J. Lasser, J. Reddish and B. Pinior, Analyzing Covid-19 data using SIRD models materials and methods, medRxiv, (2020).
[6] P.H.P. Cintra, M.F. Citeli and F.N. Fontinele, Mathematical models for describing and predicting the covid-19 pandemic crisis, arXiv preprint arXiv:2006.02507, (2020).
[7] J. Fern´andez-Villaverde and C.I. Jones, Estimating and simulating a SIRD model of COVID-19 for many countries, states, and cities, In Press in J. Econ. Dyn. Control (2022), 104318.
[8] L. Ferrari, G. Gerardi, G. Manzi, A. Micheletti, F. Nicolussi, E. Biganzoli and S. Salini, Modeling provincial COVID-19 epidemic data using an adjusted time-dependent SIRD model, Int. J. Environ. Res. Public Health 18(2021), no. 12, 6563.
[9] S. Gounane, Y. Barkouch, A. Atlas, M. Bendahmane, F. Karami and D. Meskine, An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting, Epidem. Meth. 10 (2021), no. 1, 1–14.
[10] R. Hasanli, A data-driven epidemic model to analyze and forecast the dynamics of COVID-19, Master’s thesis, Middle East Technical University, 2021.
[11] L. Pei and M. Zhang, Long-term predictions of COVID-19 in some countries by the SIRD model, Complexity 2021 (2021).
[12] R. Sameni, Mathematical modeling of epidemic diseases; a case study of the COVID-19 coronavirus, arXiv preprint arXiv:2003.11371, (2020).
[13] M.D. Samsuzzoha, A study on numerical solutions of epidemic models, Diss. PhD thesis, Swinburne University of Technology, Australia, 2012.
[14] A. Sedaghat, S. Band, A. Mosavi and L. Nadai, Predicting trends of Coronavirus disease (COVID-19) using SIRD and Gaussian-SIRD models, 2020, pp. 267–274.
[15] A. Sedaghat, S. Band, A. Mosavi and L. Nadai, Predicting COVID-19 (Coronavirus disease) outbreak dynamics using SIR-based models: comparative analysis of SIRD and Weibull-SIRD, IEEE 3rd Int. Conf. Workshop in Obuda on Electric. Power Engin., 2020, pp. 283–288. ´
[16] D. Sen and D. Sen, Use of a modified SIRD model to analyze COVID-19 data, Ind. Engin. Chem. Res. 60 (2021), no. 11, 4251–4260.
[17] K. Sooppy, S. Ahmad, A. Ullah, K. Shah, H. Alrabaiah and M. Arfan, Results in physics mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data, Results Phys. 21 (2021), 103772.
[18] E.G. Tsega, Fitting an epidemiological model to transmission dynamics of COVID-19, J. Math. Sci. Modell. 3 (2020), no. 3, 135–138.
Volume 13, Issue 2
July 2022
Pages 2807-2814
  • Receive Date: 08 February 2022
  • Revise Date: 18 March 2022
  • Accept Date: 29 April 2022