Routh–Hurwitz Stability and Quasiperiodic Attractors in a Fractional-Order Model for Awareness Programs: Applications to COVID-19 Pandemic

Abstract

This work explores Routh–Hurwitz stability and complex dynamics in models for awareness programs to mitigate the spread of epidemics. Here, the investigated models are the integer-order model for awareness programs and their corresponding fractional form. A non-negative solution is shown to exist inside the globally attracting set (GAS) of the fractional model. It is also shown that the diseasefree steady state is locally asymptotically stable (LAS) given that $R_0$ is less than one, where $R_0$ is the basic reproduction number. However, as $R_0>1$ , an endemic steady state is created whose stability analysis is studied according to the extended fractional Routh–Hurwitz scheme, as the order lies in the interval (0,2]. Furthermore, the proposed awareness program models are numerically simulated based on the predictor-corrector algorithm and some clinical data of the COVID-19 pandemic in KSA. Besides, the model’s basic reproduction number in KSA is calculated using the selected data $\left(R_0=1.977828168\right)$ . In conclusion, the findings indicate the effectiveness of fractional-order calculus to simulate, predict, and control the spread of epidemiological diseases.