Infection Clearance Rate in Fractional-Order SEIR Model: Stability Analysis - Muhammad Iqbal; Mohammad Januar Ismail Burhan; Adam Adam (CAUCHY: Jurnal Matematika Murni dan Aplikasi, 2026)
Infectious disease has become a serious problem over the past few years. At the same time, research on disease dynamics keeps advancing, especially on diseases caused by viruses. One concept that has been used in epidemic models is fractional calculus, or more specifically, fractional differential equations. This paper discusses the analytical properties of a fractional-order SEIR model, which are then verified by numerical simulations. Fractional-order has the property of memory effect, which represents the past experience effect on the current behavior of people. Mathematically, the present state is affected by previous states. Analytical results have shown that fractional-order value does not change the stability condition for each equilibrium. It is shown that there exists a stronger sufficient condition for disease-free equilibrium to be globally asymptotically stable. For the endemic equilibrium, it is only proven to be locally asymptotically stable when the basic reproduction number is greater than 1. Simulation results from Explicit Fractional Order Runge--Kutta (EFORK) method are confirmed to be in agreement with the basic properties provided by the analysis. The results also illustrate the impact of fractional-order and infection clearance rate, indicating that smaller fractional-orders converge faster compared to larger orders.