Modeling and Numerical Analysis of Rabies Transmission between Dogs and Humans using Euler and RK4 Methods

A mathematical SEIR compartmental model is presented to study the transmission dynamics of rabies between dog and human populations. The model proposes dividing the two populations into susceptible, exposed, infected, and recovered compartments, to describe the spread and progression of the disease. The interaction between the epidemiological classes and transmission process of rabies is modelled by a system of nonlinear ordinary differential equations. In order to investigate the effectiveness of both numerical methods to solve the system accurately, the developed model is analyzed numerically with the Euler method and the Fourth-Order Runge–Kutta (RK4) method. Appropriate parameter values are taken and the time step is fixed to allow the numerical simulations to study the behavior of the disease dynamics. The accuracy, stability, convergence and numerical errors of both methods are checked and compared graphically and numerically. The simulation results demonstrate that the RK4 method has more stable and accurate approximations with much smaller numerical error than the Euler method, especially for larger step sizes and long-time simulation. The results show that RK4 is more stable and efficient for solving the nonlinear epidemiological models of rabies transmission. In this study, the dynamics of rabies is mathematically described and the significance of choosing appropriate numerical techniques for disease modelling, prediction and analysis of appropriate control strategies in epidemiological research is highlighted.