Numerical Solution of the SEITR Model with Standard Incidence for Hepatitis B Transmission Using the Fourth-Order Runge–Kutta Method
DOI:
https://doi.org/10.58987/zqzzpe91Keywords:
Hepatitis B transmission, SEITR model, Standard incidence rate, Fourth order Runge-Kutta methodAbstract
This study presents a numerical solution to a Susceptible–Exposed–Infected–Treated–Recovered (SEITR) epidemiological model with standard incidence for hepatitis B virus (HBV) transmission dynamics. The model is parameterized using real demographic and epidemiological data from Ambon, Indonesia (2020). The resulting system of five nonlinear ordinary differential equations is solved using the classical fourth order Runge Kutta (RK4) method with a time step of years. The numerical implementation is validated through three independent verification tests: (i) an empirical order of convergence test confirming that the global error decreases at the theoretically expected fourth order rate as the step size is refined; (ii) cross validation against MATLAB’s adaptive Runge Kutta Fehlberg solver (ode45), which reproduces the RK4 trajectories for all five subpopulations with absolute differences within 10-14–10-8; and (iii) a sensitivity analysis across a range of transmission rates β, showing that the infected subpopulation increases with transmission intensity, consistent with the expected epidemiological behavior of the model. The results confirm that RK4 provides an accurate and numerically stable solution for standard incidence SEITR models and supports its use for evaluating hepatitis B control strategies
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