# NUMERICAL SOLUTIONS OF COVID-19 SIRD MODEL IN NIGERIA

• Blessing O. Akogwu Sheda Science and Technology Complex
• J. O. Fatoba
Keywords: COVID-19, Nigeria, SIRD, Heunâ€™s method, Fourth-order Runge-Kutta method, Fifth-order Runge-Kutta method, Matlab,

### Abstract

A mathematical model of the Susceptible, Infectious, Recovery and Death (SIRD) for the spread of the COVID-19 disease in Nigeria was considered in this paper. The model values and parameters were obtained from Nigeria Centre for Disease Control Coronavirus COVID-19. The model was solved using Heun's method and Runge-Kutta's method of orders four and five to obtain an approximated solution for the model with the help of the Matlab Program.  The result obtained was illustrated in plots to show the progression of the disease in the various classes. The comparisons of the three numerical methods used correspond well with each other by showing the same behavior pattern

### References

Al-Raeei, M (2020). The forecasting of COVID-19 with mortality using SIRD epidemic model for the United States, Russia, China and the Syrian Arab Republic. AIP Advance, 10, 065325: https://doi.org/10.1063/5.0014275.

Calafiore, G. C., and Fracastoro, G. (2022). Age structure in SIRD models for the COVID-19 pandemic-A case study on Italy data and effects on mortality. PloS ONE, 17(2), e0264324. Doi:10.1371/journal.pone.0264324.

Ender, S., and David, M. (2003). An introduction to Numerical Analysis. Cambridge, University Press, ISBN 0-521-00794-1

Fernandez-Villaverde, J and Jones, C. I (2022). Estimating and Simulating a SIRD Model of COVID-19 for many Countries, States and Cities. Journal of Economic Dynamics and Control, 140, 104318. https://doi.org/10.1016/j.jedc.2022.104318

Ferrari, L., Gerardi, G., Manzi, G., Micheletti, A., Nicolussi, F., Biganzoli, E., and Salini S. (2021). Modeling Provincial Covid-19 Epidemic Data Using Adjusted Time-Dependent SIRD Model. Int. Environ.Res. Public Health, 8, 6563. https://doi.org/10.3390//ijerph.18126563.

Gopa, D. I., Murugesh, V., and Murugesan, K. (2006). Numerical solution of second-order robot arm control problem using Runge-Kutta butcher algorithm. International Journal of Computer Mathematics, 83(3), 345-356.

He, J. H. (2004). Comparison of homotopy perturbation method and homotopy analysis method. Applied Mathematics and Computation, 156, 527-539.

Islam, M. A. (2015). A comparative study on numerical solutions of initial value problems (IVP) for ordinary differential equations (ODE) with Euler and Runge Kutta Methods. Am J Computer Math 5, 393-404.

Kutta, W. (1901). Beitrag Zurn nÓ§herungsweisen Integration totaler Differential gleichungen. Z. Math. Phys., 46:435-453.

Martinez, V. A. (2021). Modified SIRD Model to Study the Evolution of the COVID-19 Pandemic in Spain. Symmery 2021, 13,723. https://dio.org/10.3390/sys13040723.

Mohamed, L. and Al-Raeei, M. (2021). Estimation of Epidemiological Indicators of COVID-19 in Algeria with SIRD Model. Eurasian Journal of Medicine and Oncology, 5(1), 54-58. DOI:10.14744/ejmo.2021.35428

Nigeria Centre for Disease Control (NCDC). (2020). First case of corona virus disease confirmed in Nigeria. Retrieved from https://ncdc.gov.ng/news/227/first-case-of-corona-virus-disease-confirmed-in-nigeria

Norah, I.A, Eman, Y. A. and Muazzam, A. S. (2020). An Agent-based Simulation of the SIRD model of COVID-19 Spread. International Journal of Biology and Biomedical Engineering, 14, 211-217. DOI:10.46300/91011.2020.14.28

Roslan, U. A. M., Salleh, Z., and KihÃ‡man, A. (2013). Solving zhou chaotic system using fourth-order Runge-Kutta method. World Applied Sciences Journal, 21(6), 939-944. DOI:10.5829/idosi.wasj.2013.21.6.2915

Runge, C. (1895). On the numerical solution of differential equation. Math ann, 46:167-178.

Sooppy Nisar K., Aman, S., Shah, K., Alrabaiah, H., and Arfan, M. (2020). Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data. Result in Physics, 103772. 2211-3797. https://doi.org/10.1016/j.rimp.2020.103772.