Authors : Kambale Kavuliwva Simon-Pierre; Mabela Makengo Matendo Rostin; Tawaba Musian Gérard; Ngoie Caleb Caleb

Volume/Issue : Volume 11 - 2026, Issue 5 - May

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DOI : https://doi.org/10.38124/ijisrt/26May1726

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Abstract : This document presents the detailed numerical solution of the SEIHFR (Susceptible, Exposed, Infectious, Hospitalized, Funeral, Recovered) model using the fourth-order Runge- Kutta (RK4) method. This model, dedicated to the transmission dynamics of the Ebola virus, is formulated as a system of six nonlinear ordinary differential equations. The study covers the mathematical formulation of the problem, the general principle of the RK4 method, its step-by-step application to the system, and a concrete numerical example of the first time step. The complete algorithm is presented in pseudocode, and the numerical properties of the solution, including the conservation of the total population and the convergence error, are analyzed.

Keywords : SEIHFR Model, Ebola, 4th Order Runge- Kutta, Numerical Solution, Ordinary Differential Equations, Mathematical Epidemiology, Numerical Simulation.

References :

1. Butcher, JC (2016). Numerical Methods for Ordinary Differential Equations (3rd ed.). John Wiley & Sons.
2. DEMAILLY, Jean-Pierre (2006). Numerical Analysis and Differential Equations. ISBN 2-86883-891-X.
3. Quarteroni , A., Sacco, R., & Saleri , F. (2007). Numerical Methods: Algorithms, Analysis and Applications. Springer.
4. Süli, E., & Mayers, D.F. (2003). An Introduction to Numerical Analysis. Cambridge University Press.
5. Anderson, R.M., & May, R.M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press.
6. Chowell , G., Hengartner , N.W., Castillo-Chavez, C., Fenimore, P.W., & Hyman, J.M. (2004). The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. Journal of Theoretical Biology, 229(1), 119–126.
7. Legrand, J., Grais , RF, Boelle , PY, Valleron, AJ, & Flahault , A. (2007). Understanding the dynamics of Ebola epidemics. Epidemiology and Infection, 135(4), 610–621.
8. WHO Ebola Response Team. (2014). Ebola Virus Disease in West Africa — The First 9 Months of the Epidemic and Forward Projections. New England Journal of Medicine, 371(16), 1481–1495.
9. Wodarz, D. (2014). Infectious Disease Dynamics: A Mathematical Modeling Approach. Princeton University Press.