A Logistic Growth Epidemiological SEIR Model with Computational and Qualitative Results

This work presents a numerical method for solving fractional differential equations arising in mathematical biology. We specifically focus on two models: the fractional logistic growth model and the fractional SEIR model, which describe the population dynamics and the spread of epidemics, respectively. We use the fourth-order fractional Runge-Kutta (FRK4) method to approximate the solution of fractional differential equations (FDEs) associated with these models. The Caputo definition of the fractional derivative is used with our models, which is more appropriate for initial value problems involving real-life phenomena. The application of FRK4 provides a stable and accurate numerical solution for both models. The method is validated via numerical experiments, demonstrating efficiency and convergence in controlling fractional order dynamics. A comparative study with existing numerical techniques highlights the benefits of FRK4 in terms of accuracy and efficiency.