Numerical Study of Kermack-Mckendrik SIR Model to Predict the Outbreak of Ebola Virus Diseases Using Euler and Fourth Order Runge-Kutta Methods

Authors

  • Md. Tareque Hossain Department of Textile Engineering, City University, Birulia, Savar, Dhaka, Bangladesh
  • Md. Musa Miah Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh
  • Md. Babul Hossain Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh

Keywords:

Ebola, Outbreak, Evolution, Mathematical Modeling.

Abstract

Mathematical Modeling has emerged as a vital tool for understanding the dynamics of the spread of many infectious diseases, one amongst is Ebola virus. The main focus of this paper is to model mathematically the transmission dynamics of Ebola virus. For this purpose we tend to use basic SIR model of Ebola Virus to predict the outbreak of the diseases. As we cannot fully solve the 3 basic equations of SIR model with a certain formula solution, we introduce Euler and fourth-order Runge-Kutta methods (RK4). These two proposed strategies are quite efficient and practically well suited for solving initial value problem (IVP) for ordinary differential equations (ODE).We discuss the numerical comparisons between Euler method and Runge-Kutta methods and also discuss regarding their performances with the actual data. The population that we used for this model had roughly a similar number of individuals as the number was living in Republic of Liberia during 2014.

References

[1] "Ebola Virus Disease". World Health Organization. N.p., 2017. Web. 29 Mar. 2017.
<http://www.who.int/mediacentre/factsheets/fs103/en/>
[2] "2014-2016 Ebola Outbreak In West Africa| Ebola Hemorrhagic Fever | CDC". Cdc.gov. N.p., 2017. Web. 29 Mar. 2017.
<https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/ >
[3] "WHO Finds 70 Percent Ebola Mortality Rate". Aljazeera.com. N.p., 2017. Web. 29 Mar. 2017.
<http://www.aljazeera.com/news/africa/2014/10/ebola-outbreak-killing-70-percent-victims-20141014132345720164.html>
[4] "Previous Case Counts| Ebola Hemorrhagic Fever | CDC". Cdc.gov. N.p., 2017. Web. 29 Mar. 2017.
<https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/previous-case-counts.html >
[5] Dolgoarshinnykh, R. G., & Lalley, S. P. (2003). Epidemic Modelling: SIRS Models (Doctoral dissertation, University of Chicago, Department of Statistics).
[6] "Modelling Infectious Diseases." IB Maths Resources From British International School Phuket". ibmathsresources.com. N.p., 2017. Web. 29 Mar. 2017.
[7] "The Spread Of Infectious Diseases." The British Medical Journal 2.1281 (1885): 108. Web.
[8] Leone, S. Appendix: Additional Results and Technical Notes for the EbolaResponse Modeling Tool Additional Results. Population, 4, 3.
[9] "Previous Case Counts| Ebola Hemorrhagic Fever | CDC". Cdc.gov. N.p., 2017. Web. 29 Mar. 2017. Retrieve date: 03 August 2014
<https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/previous-case-counts.html >
[10] Clinaero, Inc. "Ebola Incubation Period". eMedTV: Health Information Brought To Life. N.p., 2017. Web. 29 Mar. 2017.
[11] "Kermack-Mckendrick Model – From Wolfram Mathworld". Mathworld.wolfram.com. N.p., 2017. Web. 29 Mar. 2017.
[12] "The SIR Model For Spread Of Disease - Euler's Method For Systems". Mathematical Association of America. N.p., 2017. Web. 29 Mar. 2017.
[13] Rahman, Prof. Dr. Md. Fazlur. Mathematical Modelling In Biology. 7th ed. ISBN-984-8759-19-0, 2015. Print.
[14] Tsai, Tony. “Tony Tsai.” RK4 Method for Solving SIR Model.N.p., n.d. Web. 16 Apr. 2017
<http://blog.tonytsai.name/blog/2014-11-24-rk4-method-for-solving-sir-model/>

Downloads

Published

2017-10-14

How to Cite

Hossain, M. T., Miah, M. M., & Hossain, M. B. (2017). Numerical Study of Kermack-Mckendrik SIR Model to Predict the Outbreak of Ebola Virus Diseases Using Euler and Fourth Order Runge-Kutta Methods. American Scientific Research Journal for Engineering, Technology, and Sciences, 37(1), 1–21. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/3424

Issue

Vol. 37 No. 1 (2017)

Section

Articles

License

Authors who submit papers with this journal agree to the following terms.