A computationally efficient RK4-FNN hybrid approach for high-precision tuberculosis dynamics modeling: SIR/SEIR model applications

In this study, we introduce a new approach for studying the dynamics of infectious diseases by integrating the advanced deep learning techniques with the typical numerical approaches. We address the challenges of accurately modeling the disease transmission by focusing on the susceptible-infectious-recovered (SIR) and susceptible-exposed-infectious-recovered (SEIR) models. The fourth-order Runge-Kutta (RK4) method is used to solve numerically complex epidemiological models with high accuracy. The method efficiently computes the temporal evolution of the models and serves as a reliable technique for further analysis. The datasets obtained from the models are used to train a feedforward neural network (FNN). The optimization of the FNN architecture is done using the Keras Tuner, which adjusts the parameters to increase the skill of the model in capturing complex patterns and temporal dynamics in the epidemiological data. To test the efficacy of this approach, a comparison is made between the FNN method and the RK4 method, analyzing their performance in solving epidemiological models. The tuned FNN achieved relative accuracy of 99.65% (validation) and 99.33% (training) for the SIR model and 99.91% (validation) and 99.92% (training) for the SEIR model.