Prediction of Rabies Spread in Dogs and Humans in Muara Enim Regency Based on the SI–SEIR Model with Fourth-Order Runge–Kutta Numerical Solution

Rabies is a fatal zoonotic disease that is generally transmitted through the bite of an infected dog. This research aims to predict the spread of rabies in dog and human populations in Muara Enim Regency using a combined SI–SEIR mathematical model. The system of nonlinear differential equations was solved using the fourth-order Runge–Kutta (RK4) method. Rabies data on dogs and humans were obtained from the Lampung Veterinary Center for the period 2021–2024. The simulation results show that the number of infected dogs increased significantly at the beginning of the period, peaked in the third year, and then declined as the population of susceptible dogs decreased. In the human population, the increase in exposed and infected individuals occurred after the surge in the dog population, indicating cross-species transmission. This model provides a quantitative overview of rabies dynamics and can be used as a basis for rabies control strategies in Muara Enim Regency.